2cos (problem 3.3.5)

Time bar (total: 20.0s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze195.0ms (1%)

Memory
-1.7MiB live, 49.5MiB allocated; 139ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample14.5s (72.7%)

Memory
-38.0MiB live, 6 989.9MiB allocated; 4.5s collecting garbage
Samples
5.7s5 721×2valid
4.9s26 260×0invalid
859.0ms2 470×1valid
13.0ms65×0valid
Precisions
Click to see histograms. Total time spent on operations: 8.5s
ival-cos: 4.6s (54.6% of total)
adjust: 936.0ms (11% of total)
const: 776.0ms (9.1% of total)
ival-add: 523.0ms (6.1% of total)
ival-sub: 512.0ms (6% of total)
ival-fabs: 440.0ms (5.2% of total)
ival-mult: 322.0ms (3.8% of total)
ival-<: 220.0ms (2.6% of total)
ival-and: 116.0ms (1.4% of total)
ival-assert: 23.0ms (0.3% of total)
Bogosity

explain454.0ms (2.3%)

Memory
25.3MiB live, 243.3MiB allocated; 91ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1231(5.965021874600728e-157 2.160405577665521e-167)0-(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
30-0-(cos.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(cos.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))cancellation1240
cos.f64(cos.f64 (+.f64 x eps))sensitivity30
Confusion
Predicted +Predicted -
+1230
-1132
Precision
0.9919354838709677
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+12300
-10132
Precision?
0.9919354838709677
Recall?
1.0
Freqs
test
numberfreq
0132
1121
23
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
278.0ms368×2valid
40.0ms142×1valid
0.0ms2×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 263.0ms
ival-cos: 173.0ms (65.7% of total)
adjust: 71.0ms (26.9% of total)
ival-sub: 11.0ms (4.2% of total)
ival-add: 7.0ms (2.7% of total)
ival-assert: 1.0ms (0.4% of total)
ival-true: 1.0ms (0.4% of total)

preprocess559.0ms (2.8%)

Memory
4.2MiB live, 57.2MiB allocated; 66ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02148
15348
29348
312448
413248
515448
623848
780048
8517548
067
0107
1227
2407
3657
4787
51007
61847
77427
850737
085057
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Outputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶57.6%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

series10.0ms (0%)

Memory
2.8MiB live, 2.8MiB allocated; 0ms collecting garbage
Counts
6 → 36
Calls
Call 1
Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(cos.f64 x)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
2.0ms
eps
@inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
2.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
2.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
2.0ms
x
@-inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms
eps
@0
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))

rewrite283.0ms (1.4%)

Memory
10.0MiB live, 57.3MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0144528
1874525
08259504
Stop Event
1×iter limit
1×node limit
Counts
42 → 113
Calls
Call 1
Inputs
(- (cos (+ x eps)) (cos x))
(cos (+ x eps))
(+ x eps)
x
eps
(cos x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x)))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x)))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))))))
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(sin.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 eps))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (sin.f64 x))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))
(cos.f64 (neg.f64 (neg.f64 (+.f64 eps x))))
(cos.f64 (neg.f64 (+.f64 eps x)))
(cos.f64 (+.f64 eps x))
(+.f64 (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(/.f64 (neg.f64 (*.f64 (-.f64 eps x) (+.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (-.f64 eps x) (+.f64 eps x)) (-.f64 eps x))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps eps (*.f64 x (-.f64 x eps))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(-.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(-.f64 eps (neg.f64 x))
(-.f64 x (neg.f64 eps))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(+.f64 eps (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(+.f64 eps x)
(+.f64 x (*.f64 (neg.f64 eps) #s(literal -1 binary64)))
(+.f64 x eps)
x
eps
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (cos (+ x eps)) (cos.f64 eps))
#s(approx (cos (+ x eps)) (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)))
#s(approx (cos (+ x eps)) (fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) x (cos.f64 eps)))
#s(approx (cos (+ x eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) x (cos.f64 eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx x x)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) x)
#s(approx (+ x eps) (fma.f64 (/.f64 eps x) x x))
#s(approx (cos x) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (fma.f64 (/.f64 eps x) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (cos (+ x eps)) (cos.f64 x))
#s(approx (cos (+ x eps)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))
#s(approx (cos (+ x eps)) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps (cos.f64 x)))
#s(approx (cos (+ x eps)) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x)))
#s(approx eps eps)
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 eps)))

eval20.0ms (0.1%)

Memory
9.4MiB live, 9.4MiB allocated; 0ms collecting garbage
Compiler

Compiled 2 017 to 430 computations (78.7% saved)

prune16.0ms (0.1%)

Memory
8.5MiB live, 8.5MiB allocated; 0ms collecting garbage
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1029111
Fresh000
Picked011
Done000
Total10210112
Accuracy
99.8%
Counts
112 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶57.6%
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
57.6%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓57.6%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
56.1%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
55.9%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶55.8%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶99.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
99.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
▶99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
▶81.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
Compiler

Compiled 309 to 232 computations (24.9% saved)

series60.0ms (0.3%)

Memory
-29.3MiB live, 17.3MiB allocated; 5ms collecting garbage
Counts
34 → 177
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(sin.f64 x)
x
#s(literal 1/6 binary64)
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
eps
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(+.f64 eps x)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 eps)))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* -1/2 (cos x)) #s(hole binary64 -1/2))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (* 1/2 (PI)))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (* 1/2 (PI)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (+ x (* 1/2 (PI))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (+ x (* 1/2 (PI)))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 x))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ eps (* 1/2 (PI))) (* -1 x)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/6 (sin x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ x (* 1/2 (PI)))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ x (* 1/2 (PI))) (* -1 eps)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
13.0ms
x
@inf
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* -1/2 (cos x)) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (/ (PI) 2) (PI) 2 (+ eps x))
12.0ms
eps
@0
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* -1/2 (cos x)) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (/ (PI) 2) (PI) 2 (+ eps x))
8.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* -1/2 (cos x)) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (/ (PI) 2) (PI) 2 (+ eps x))
7.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* -1/2 (cos x)) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (/ (PI) 2) (PI) 2 (+ eps x))
7.0ms
x
@-inf
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* -1/2 (cos x)) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (/ (PI) 2) (PI) 2 (+ eps x))

rewrite385.0ms (1.9%)

Memory
28.0MiB live, 71.2MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06834807
142644807
084744450
Stop Event
1×iter limit
1×node limit
Counts
211 → 314
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps)))
(* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps)
(- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x))
(* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps)
(+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x)))
(+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24))
(sin x)
x
1/6
(* (* (cos x) eps) 1/24)
(* (cos x) eps)
(cos x)
eps
1/24
(* -1/2 (cos x))
-1/2
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
(- (cos eps) 1)
(cos eps)
1
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* (neg eps) (sin x))))
(* (neg eps) (sin x))
(neg eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps)))
(* (- (* (* -1/2 (cos x)) eps) (sin x)) eps)
(- (* (* -1/2 (cos x)) eps) (sin x))
(* (* -1/2 (cos x)) eps)
(- (sin (+ (/ (PI) 2) (+ eps x))) (cos x))
(sin (+ (/ (PI) 2) (+ eps x)))
(+ (/ (PI) 2) (+ eps x))
(/ (PI) 2)
(PI)
2
(+ eps x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 eps)))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* -1/2 (cos x)) #s(hole binary64 -1/2))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (* 1/2 (PI)))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (* 1/2 (PI)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (+ x (* 1/2 (PI))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (+ x (* 1/2 (PI)))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 x))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ eps (* 1/2 (PI))) (* -1 x)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/6 (sin x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ x (* 1/2 (PI)))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ x (* 1/2 (PI))) (* -1 eps)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(*.f64 eps (-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))))
(-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(*.f64 eps (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) eps))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (*.f64 eps (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) eps))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 eps (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) eps))
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#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (-.f64 (*.f64 (+.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (*.f64 eps x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/36 binary64) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 #s(literal 1/6 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) #s(literal 1/4 binary64)) x (*.f64 #s(literal 1/6 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (*.f64 #s(literal 1/24 binary64) eps))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/48 binary64) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/24 binary64) eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/24 binary64) eps)))
#s(approx (sin x) x)
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx x x)
#s(approx (* (* (cos x) eps) 1/24) (*.f64 #s(literal 1/24 binary64) eps))
#s(approx (* (* (cos x) eps) 1/24) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/48 binary64) (*.f64 #s(literal 1/24 binary64) eps)))
#s(approx (* (* (cos x) eps) 1/24) (fma.f64 (fma.f64 #s(literal 1/576 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/48 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/24 binary64) eps)))
#s(approx (* (* (cos x) eps) 1/24) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/17280 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/576 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/48 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/24 binary64) eps)))
#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64))
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
#s(approx (* (* -1/2 (cos x)) eps) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (* (* -1/2 (cos x)) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) eps)))
#s(approx (* (* -1/2 (cos x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/48 binary64) (*.f64 #s(literal 1/4 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)))
#s(approx (* (* -1/2 (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/1440 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/48 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/4 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) x (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) x (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) x) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)))) x (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) x (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) #s(literal 1 binary64)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) x (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) x (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) x (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (* (cos x) eps) 1/24) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (cos x) (cos.f64 x))
#s(approx (* -1/2 (cos x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))
#s(approx (* (* -1/2 (cos x)) eps) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (sin.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps)) (cos.f64 x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps)))
#s(approx (+ (/ (PI) 2) (+ eps x)) x)
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) x) #s(literal 1 binary64)) x))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (cos.f64 (-.f64 eps (neg.f64 x))) (cos.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) (neg.f64 x))) (cos.f64 x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) (neg.f64 x))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (neg.f64 x) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) x)) #s(literal 1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
#s(approx eps eps)
#s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/40320 binary64) (*.f64 eps eps)) #s(literal 1/720 binary64)) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (neg eps) (neg.f64 eps))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (cos.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) (cos.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) (cos.f64 x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64))) eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) (cos.f64 x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64))) eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) (cos.f64 x)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (*.f64 (fma.f64 (/.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))) (*.f64 eps eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) eps))
#s(approx (- (cos eps) 1) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) eps)
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps) #s(literal 1 binary64)) eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (*.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) eps)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (*.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps))) (*.f64 eps eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (*.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (neg.f64 eps))) (cos.f64 x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (neg.f64 eps))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps)) #s(literal 1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval158.0ms (0.8%)

Memory
-14.7MiB live, 37.8MiB allocated; 84ms collecting garbage
Compiler

Compiled 12 469 to 1 876 computations (85% saved)

prune79.0ms (0.4%)

Memory
-15.8MiB live, 35.0MiB allocated; 9ms collecting garbage
Pruning

35 alts after pruning (31 fresh and 4 done)

PrunedKeptTotal
New37529404
Fresh224
Picked235
Done011
Total37935414
Accuracy
100.0%
Counts
414 → 35
Alt Table
Click to see full alt table
StatusAccuracyProgram
57.6%
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
57.6%
(-.f64 (sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))) (cos.f64 x))
57.6%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓57.6%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
55.9%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶99.7%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
55.8%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
▶55.7%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
35.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))))) eps))
✓99.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
✓99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
▶98.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
98.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
98.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
✓81.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
80.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
80.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
79.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
97.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
96.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
31.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) eps))))) eps))
97.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
▶96.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
96.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
56.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
23.4%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 4 binary64)))))
24.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64)))))
97.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
96.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
96.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
▶80.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
80.4%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
80.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
Compiler

Compiled 2 192 to 1 400 computations (36.1% saved)

series86.0ms (0.4%)

Memory
25.1MiB live, 25.1MiB allocated; 0ms collecting garbage
Counts
52 → 213
Calls
Call 1
Inputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos eps) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 eps x) #s(literal 1/4 binary64))
(*.f64 eps x)
#s(literal 1/4 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps))
(fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps))
(fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps))
#s(literal 1/5040 binary64)
(*.f64 (*.f64 x x) eps)
(*.f64 x x)
(*.f64 #s(literal -1/120 binary64) eps)
#s(literal -1/120 binary64)
(*.f64 #s(literal 1/6 binary64) eps)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x))
(*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps)
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)))
(-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x))
(fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64))
(-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64))
(*.f64 #s(literal 1/1440 binary64) (*.f64 x x))
#s(literal 1/1440 binary64)
#s(literal 1/48 binary64)
#s(literal 1/2 binary64)
Outputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (* 1/2 (PI)))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 -1/2))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/6 (* eps x)) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* -1/2 (cos x)) #s(hole binary64 -1/2))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 -1))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (- (* 1/4 (* eps x)) 1)))
#s(approx (* (* eps x) 1/4) #s(hole binary64 (* 1/4 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (- (* 1/6 (* eps (pow x 2))) eps)))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (- (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))) eps)))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (- (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))) eps)))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* 1/6 eps)))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (* -1/120 eps)))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* 1/4 (pow x 2))))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 1/4))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* -1/48 (pow x 2)))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))))
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 -1/48))
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 (- (* 1/1440 (pow x 2)) 1/48)))
#s(approx (* 1/1440 (* x x)) #s(hole binary64 (* 1/1440 (pow x 2))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* 1/4 (* eps (pow x 2)))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (* 1/4 (* eps x))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (* x (- (* 1/4 eps) (/ 1 x)))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* 1/5040 (* eps (pow x 7)))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1 (/ eps (pow x 6))) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4)))))))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 6)))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1 (/ eps (pow x 6))) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4)))))))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 4)))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 2)))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* 1/1440 (pow x 6))))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* 1/1440 (pow x 6))))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* 1/1440 (pow x 4))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 (* 1/1440 (pow x 2))))
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (* -1 (* x (+ (* -1/4 eps) (/ 1 x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2)))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/5040 eps) (+ (* 1/120 (/ eps (pow x 2))) (/ eps (pow x 6)))))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ x (* 1/2 (PI)))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 x)))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* eps (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1)))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* eps (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* eps (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120))))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (* eps (- (* 1/5040 (pow x 2)) 1/120))))
#s(approx (* -1/120 eps) #s(hole binary64 (* -1/120 eps)))
#s(approx (* 1/6 eps) #s(hole binary64 (* 1/6 eps)))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/6 (* (pow eps 3) (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* 1/6 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/4 (pow x 2)) 1/2))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (* eps (- (* 1/4 x) (/ 1 eps)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (* -1 (* eps (+ (* -1/4 x) (/ 1 eps))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (* -1 (* eps (+ 1/120 (* -1/5040 (pow x 2)))))))
Calls

6 calls:

TimeVariablePointExpression
22.0ms
eps
@0
((- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (- (* (* eps x) 1/4) 1) (* (* eps x) 1/4) (* eps x) 1/4 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) 1/5040 (* (* x x) eps) (* x x) (* -1/120 eps) -1/120 (* 1/6 eps) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (- (* 1/1440 (* x x)) 1/48) (* 1/1440 (* x x)) 1/1440 1/48 1/2)
14.0ms
eps
@-inf
((- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (- (* (* eps x) 1/4) 1) (* (* eps x) 1/4) (* eps x) 1/4 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) 1/5040 (* (* x x) eps) (* x x) (* -1/120 eps) -1/120 (* 1/6 eps) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (- (* 1/1440 (* x x)) 1/48) (* 1/1440 (* x x)) 1/1440 1/48 1/2)
13.0ms
eps
@inf
((- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (- (* (* eps x) 1/4) 1) (* (* eps x) 1/4) (* eps x) 1/4 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) 1/5040 (* (* x x) eps) (* x x) (* -1/120 eps) -1/120 (* 1/6 eps) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (- (* 1/1440 (* x x)) 1/48) (* 1/1440 (* x x)) 1/1440 1/48 1/2)
11.0ms
x
@-inf
((- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (- (* (* eps x) 1/4) 1) (* (* eps x) 1/4) (* eps x) 1/4 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) 1/5040 (* (* x x) eps) (* x x) (* -1/120 eps) -1/120 (* 1/6 eps) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (- (* 1/1440 (* x x)) 1/48) (* 1/1440 (* x x)) 1/1440 1/48 1/2)
10.0ms
x
@inf
((- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (- (* (* eps x) 1/4) 1) (* (* eps x) 1/4) (* eps x) 1/4 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) 1/5040 (* (* x x) eps) (* x x) (* -1/120 eps) -1/120 (* 1/6 eps) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (- (* 1/1440 (* x x)) 1/48) (* 1/1440 (* x x)) 1/1440 1/48 1/2)

rewrite386.0ms (1.9%)

Memory
-14.4MiB live, 76.2MiB allocated; 13ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07575995
143955991
081755600
Stop Event
1×iter limit
1×node limit
Counts
265 → 411
Calls
Call 1
Inputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps)))
(* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps)
(- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x))
(* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps)
(+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x)))
(* (sin x) eps)
(sin x)
x
eps
1/6
(* -1/2 (cos x))
-1/2
(cos x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- #s(approx (cos eps) #s(hole binary64 1)) 1)))
(- #s(approx (cos eps) #s(hole binary64 1)) 1)
#s(approx (cos eps) #s(hole binary64 1))
1
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)))) eps)))
(* #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)))) eps)
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps))))
(+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps))
(- (* (* eps x) 1/4) 1)
(* (* eps x) 1/4)
(* eps x)
1/4
(* -1/2 eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 #s(approx (* (neg eps) (sin x)) #s(hole binary64 (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x)))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x)))
(* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x)
(+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps))
(+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps))
(+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps))
1/5040
(* (* x x) eps)
(* x x)
(* -1/120 eps)
-1/120
(* 1/6 eps)
(neg eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* (- (* #s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2))) eps) (sin x)) eps)))
(* (- (* #s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2))) eps) (sin x)) eps)
(- (* #s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2))) eps) (sin x))
(* #s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2))) eps)
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2)))
(- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2)
(* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x))
(+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4)
(- (* 1/1440 (* x x)) 1/48)
(* 1/1440 (* x x))
1/1440
1/48
1/2
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (* 1/2 (PI)))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 -1/2))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/6 (* eps x)) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* -1/2 (cos x)) #s(hole binary64 -1/2))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 -1))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (- (* 1/4 (* eps x)) 1)))
#s(approx (* (* eps x) 1/4) #s(hole binary64 (* 1/4 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (- (* 1/6 (* eps (pow x 2))) eps)))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (- (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))) eps)))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (- (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))) eps)))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* 1/6 eps)))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (* -1/120 eps)))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2)))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* 1/4 (pow x 2))))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 1/4))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* -1/48 (pow x 2)))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))))
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 -1/48))
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 (- (* 1/1440 (pow x 2)) 1/48)))
#s(approx (* 1/1440 (* x x)) #s(hole binary64 (* 1/1440 (pow x 2))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* 1/4 (* eps (pow x 2)))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (* 1/4 eps) (/ 1 x)))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (* 1/4 (* eps x))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (* x (- (* 1/4 eps) (/ 1 x)))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* 1/5040 (* eps (pow x 7)))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1 (/ eps (pow x 6))) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4)))))))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 6)))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1 (/ eps (pow x 6))) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4)))))))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 4)))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 2)))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* 1/1440 (pow x 6))))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* 1/1440 (pow x 6))))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* 1/1440 (pow x 4))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 (* 1/1440 (pow x 2))))
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2)))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (* -1 (* x (+ (* -1/4 eps) (/ 1 x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2)))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/5040 eps) (+ (* 1/120 (/ eps (pow x 2))) (/ eps (pow x 6)))))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ x (* 1/2 (PI)))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 x)))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2)))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* eps (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1)))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* eps (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* eps (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120))))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (* eps (- (* 1/5040 (pow x 2)) 1/120))))
#s(approx (* -1/120 eps) #s(hole binary64 (* -1/120 eps)))
#s(approx (* 1/6 eps) #s(hole binary64 (* 1/6 eps)))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/6 (* (pow eps 3) (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* 1/6 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/4 (pow x 2)) 1/2))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (* eps (- (* 1/4 x) (/ 1 eps)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ x eps)))))))
#s(approx (- (* (* eps x) 1/4) 1) #s(hole binary64 (* -1 (* eps (+ (* -1/4 x) (/ 1 eps))))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) #s(hole binary64 (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) #s(hole binary64 (* -1 (* eps (+ 1/120 (* -1/5040 (pow x 2)))))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(*.f64 eps (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))))
(-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(*.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))))
(/.f64 (fma.f64 (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (sin.f64 x) (*.f64 #s(literal 1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal -1/6 binary64) (*.f64 (sin.f64 x) eps)))
(+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(*.f64 (sin.f64 x) eps)
(*.f64 eps (sin.f64 x))
(sin.f64 x)
x
eps
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
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#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/1440 binary64)))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (*.f64 (-.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/1440 binary64)) (/.f64 #s(literal 1/48 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))))
#s(approx (- (* 1/1440 (* x x)) 1/48) (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)))
#s(approx (- (* 1/1440 (* x x)) 1/48) (*.f64 (-.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 x x))) (*.f64 x x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) (neg.f64 x))) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (neg.f64 x))) (cos.f64 x)))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (neg.f64 (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (*.f64 x x)))
#s(approx (- (* (* eps x) 1/4) 1) (neg.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) eps) x #s(literal 1 binary64))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) (neg.f64 (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) eps)) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) (neg.f64 (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/6 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) eps))) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) (neg.f64 (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/6 binary64) (fma.f64 #s(literal -1/5040 binary64) eps (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/120 binary64) (/.f64 eps (pow.f64 x #s(literal 6 binary64)))))) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))) eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) (cos.f64 x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx eps eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/40320 binary64) (*.f64 eps eps)) #s(literal 1/720 binary64)) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (neg.f64 x))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))
#s(approx (* -1/2 eps) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) (*.f64 (*.f64 x eps) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x)) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps))
#s(approx (* -1/120 eps) (*.f64 #s(literal -1/120 binary64) eps))
#s(approx (* 1/6 eps) (*.f64 #s(literal 1/6 binary64) eps))
#s(approx (neg eps) (neg.f64 eps))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 3 binary64))) (sin.f64 x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) (sin.f64 x)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (*.f64 eps eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps))
#s(approx (- (cos eps) 1) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (*.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (/.f64 (neg.f64 x) eps)) #s(literal 1/2 binary64)) eps))
#s(approx (- (* (* eps x) 1/4) 1) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) (pow.f64 eps #s(literal -1 binary64))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (neg.f64 eps))) (cos.f64 x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (/.f64 x eps)) #s(literal 1/2 binary64))))
#s(approx (- (* (* eps x) 1/4) 1) (neg.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) x) eps #s(literal 1 binary64))))
#s(approx (* (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) x) (*.f64 (neg.f64 eps) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (+ (* (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (* x x)) (neg eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (* x x)) (* 1/6 eps)) (*.f64 (neg.f64 eps) (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64))))
#s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))))

eval134.0ms (0.7%)

Memory
2.0MiB live, 51.1MiB allocated; 13ms collecting garbage
Compiler

Compiled 22 227 to 2 963 computations (86.7% saved)

prune88.0ms (0.4%)

Memory
-6.1MiB live, 41.5MiB allocated; 2ms collecting garbage
Pruning

40 alts after pruning (33 fresh and 7 done)

PrunedKeptTotal
New53516551
Fresh91726
Picked235
Done044
Total54640586
Accuracy
100.0%
Counts
586 → 40
Alt Table
Click to see full alt table
StatusAccuracyProgram
57.6%
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
▶57.6%
(-.f64 (sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))) (cos.f64 x))
57.6%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓57.6%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
55.9%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶99.7%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) eps) (sin.f64 x)) eps))
✓99.7%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
97.2%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
96.8%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
46.1%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (*.f64 eps eps))) eps))
56.9%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
81.7%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))))))
55.8%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
✓55.7%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓99.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
✓99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
✓98.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
97.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
97.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
96.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
98.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
98.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
✓81.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
80.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
80.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
▶79.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
▶97.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
96.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
96.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
96.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
23.4%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 4 binary64)))))
24.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64)))))
97.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
96.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
80.4%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
80.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
▶80.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
80.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
Compiler

Compiled 2 537 to 1 684 computations (33.6% saved)

series71.0ms (0.4%)

Memory
25.6MiB live, 25.6MiB allocated; 0ms collecting garbage
Counts
52 → 255
Calls
Call 1
Inputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) eps) (sin.f64 x))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(literal -1/2 binary64)
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
(*.f64 (neg.f64 eps) #s(approx (sin x) x))
(neg.f64 eps)
#s(approx (sin x) x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64))
(*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x)
(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
#s(literal 1/4 binary64)
(*.f64 #s(literal 1/6 binary64) x)
#s(literal 1 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x))
(*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)
(fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps))
(*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x)
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps))
(*.f64 x x)
(fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps))
(*.f64 (*.f64 x x) #s(literal 1/5040 binary64))
#s(literal 1/5040 binary64)
(*.f64 #s(literal -1/120 binary64) eps)
#s(literal -1/120 binary64)
(*.f64 #s(literal 1/6 binary64) eps)
(-.f64 (sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))) (cos.f64 x))
(sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps)))
#s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps)
(fma.f64 #s(literal 1/2 binary64) (PI.f64) x)
#s(literal 1/2 binary64)
(cos.f64 x)
Outputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (* 1/2 (PI)))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin (* 1/2 (PI)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) (sin (* 1/2 (PI))))) (* eps (* x (- (* eps (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps))) 1))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) (sin (* 1/2 (PI))))) (* x (+ (* 1/4 (* (pow eps 2) (* x (sin (* 1/2 (PI)))))) (* eps (- (* eps (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps))) 1)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) (sin (* 1/2 (PI))))) (* x (+ (* eps (- (* eps (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps))) 1)) (* x (+ (* 1/4 (* (pow eps 2) (sin (* 1/2 (PI))))) (* eps (* x (+ 1/6 (* eps (+ (* -1/36 eps) (* 1/12 (cos (* 1/2 (PI))))))))))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* -1/2 (* eps (sin (* 1/2 (PI)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* x (- (* eps (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps))) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* x (- (+ (* 1/4 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps)))) 1)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* x (- (+ (* eps (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps))) (* x (+ (* 1/4 (* eps (sin (* 1/2 (PI))))) (* x (+ 1/6 (* eps (+ (* -1/36 eps) (* 1/12 (cos (* 1/2 (PI))))))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* -1/2 (* eps (sin (* 1/2 (PI)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* eps (* x (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* x (+ (* 1/4 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps))))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* x (+ (* eps (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps))) (* x (+ (* 1/4 (* eps (sin (* 1/2 (PI))))) (* eps (* x (+ (* -1/36 eps) (* 1/12 (cos (* 1/2 (PI))))))))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (* -1/2 (sin (* 1/2 (PI))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (cos (* 1/2 (PI)))) (+ (* 1/6 eps) (* 1/4 (* x (sin (* 1/2 (PI)))))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (cos (* 1/2 (PI)))) (+ (* 1/6 eps) (* x (+ (* 1/4 (sin (* 1/2 (PI)))) (* x (+ (* -1/36 eps) (* 1/12 (cos (* 1/2 (PI))))))))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* -1/2 (sin (* 1/2 (PI))))))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/2 (* x (cos (* 1/2 (PI))))))))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/4 (* x (sin (* 1/2 (PI))))))))))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (cos (* 1/2 (PI)))) (* x (+ (* 1/12 (* x (cos (* 1/2 (PI))))) (* 1/4 (sin (* 1/2 (PI)))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 -1))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (- (* 1/4 (* eps x)) 1)))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* 1/4 (* eps x))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* x (+ (* 1/6 x) (* 1/4 eps)))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* 1/4 eps)))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (+ (* 1/6 x) (* 1/4 eps))))
#s(approx (* 1/6 x) #s(hole binary64 (* 1/6 x)))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (- (* 1/6 (* eps (pow x 2))) eps)))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (- (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))) eps)))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (- (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))) eps)))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* 1/6 (* eps x))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* 1/6 eps)))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (* -1/120 eps)))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))
#s(approx (* (* x x) 1/5040) #s(hole binary64 (* 1/5040 (pow x 2))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (* 1/2 (PI)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (+ x (* 1/2 (PI))))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (+ eps (* 1/2 (PI)))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (+ eps (+ x (* 1/2 (PI))))))
#s(approx (+ (* 1/2 (PI)) x) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ (* 1/2 (PI)) x) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* 1/6 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* -1/2 (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 x))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* 1/6 (pow x 3))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* (pow x 2) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* 1/6 x)))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* x (+ 1/6 (* 1/4 (/ eps x))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* 1/5040 (* eps (pow x 7)))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1 (/ eps (pow x 6))) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4)))))))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 6)))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1 (/ eps (pow x 6))) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4)))))))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* 1/5040 (* eps (pow x 5)))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* (pow x 5) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* (pow x 5) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 4)))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 2)))))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (+ x (* 1/2 (PI)))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 x))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 x))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))))
#s(approx (+ (* 1/2 (PI)) x) #s(hole binary64 x))
#s(approx (+ (* 1/2 (PI)) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (sin (- (* 1/2 (PI)) (* -1 x)))) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (sin (- (* 1/2 (PI)) (* -1 x)))) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* eps (+ (* -1/2 (sin (- (* 1/2 (PI)) (* -1 x)))) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1/2 (sin (- (* 1/2 (PI)) (* -1 x)))) (* 1/6 (* eps (sin x))))))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* -1/2 (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* (pow x 2) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x))))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2))))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2)))))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/5040 eps) (+ (* 1/120 (/ eps (pow x 2))) (/ eps (pow x 6)))))))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* -1 (* (pow x 5) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2))))))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2)))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ eps (* 1/2 (PI))) (* -1 x)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))))
#s(approx (+ (* 1/2 (PI)) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ x (* 1/2 (PI)))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* 1/6 (* eps (sin x)))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (* -1/2 (sin (+ x (* 1/2 (PI)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (- (* 1/6 (pow x 2)) 1)))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x)))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* eps (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1)))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* eps (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* eps (* x (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* eps (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120))))))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (* eps (- (* 1/5040 (pow x 2)) 1/120))))
#s(approx (* -1/120 eps) #s(hole binary64 (* -1/120 eps)))
#s(approx (* 1/6 eps) #s(hole binary64 (* 1/6 eps)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* 1/6 (* (pow eps 3) (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (* 1/6 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/4 (pow x 2)) 1/2))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* 1/4 (* eps x))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* eps (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* eps (+ 1/4 (* 1/6 (/ x eps))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 eps))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (sin (+ x (* 1/2 (PI)))))) eps)) (* -1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (sin (+ x (* 1/2 (PI))))) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* -1 (* eps (+ (* -1/4 x) (* -1/6 (/ (pow x 2) eps)))))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* -1 (* eps (* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (* -1 (* eps (+ 1/120 (* -1/5040 (pow x 2)))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ x (* 1/2 (PI))) (* -1 eps)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
12.0ms
eps
@-inf
((- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (sin (+ x (/ (PI) 2)))) -1/2 (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) 2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) (* (+ (* 1/4 eps) (* 1/6 x)) x) (+ (* 1/4 eps) (* 1/6 x)) 1/4 (* 1/6 x) 1 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) (* (* x x) 1/5040) 1/5040 (* -1/120 eps) -1/120 (* 1/6 eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (+ (+ (* 1/2 (PI)) x) eps) (+ (* 1/2 (PI)) x) 1/2 (cos x))
11.0ms
eps
@inf
((- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (sin (+ x (/ (PI) 2)))) -1/2 (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) 2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) (* (+ (* 1/4 eps) (* 1/6 x)) x) (+ (* 1/4 eps) (* 1/6 x)) 1/4 (* 1/6 x) 1 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) (* (* x x) 1/5040) 1/5040 (* -1/120 eps) -1/120 (* 1/6 eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (+ (+ (* 1/2 (PI)) x) eps) (+ (* 1/2 (PI)) x) 1/2 (cos x))
11.0ms
x
@-inf
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10.0ms
x
@inf
((- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (sin (+ x (/ (PI) 2)))) -1/2 (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) 2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) (* (+ (* 1/4 eps) (* 1/6 x)) x) (+ (* 1/4 eps) (* 1/6 x)) 1/4 (* 1/6 x) 1 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) (* (* x x) 1/5040) 1/5040 (* -1/120 eps) -1/120 (* 1/6 eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (+ (+ (* 1/2 (PI)) x) eps) (+ (* 1/2 (PI)) x) 1/2 (cos x))
10.0ms
eps
@0
((- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (* (sin x) eps) (sin x) x eps 1/6 (* -1/2 (sin (+ x (/ (PI) 2)))) -1/2 (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) 2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) (* (+ (* 1/4 eps) (* 1/6 x)) x) (+ (* 1/4 eps) (* 1/6 x)) 1/4 (* 1/6 x) 1 (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) (* (* x x) 1/5040) 1/5040 (* -1/120 eps) -1/120 (* 1/6 eps) (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (sin (+ (/ (PI) 2) (+ eps x))) (+ (/ (PI) 2) (+ eps x)) (+ (+ (* 1/2 (PI)) x) eps) (+ (* 1/2 (PI)) x) 1/2 (cos x))

rewrite408.0ms (2%)

Memory
-17.0MiB live, 74.4MiB allocated; 11ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09027163
151347163
081446585
Stop Event
1×iter limit
1×node limit
Counts
307 → 456
Calls
Call 1
Inputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps)))
(* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps)
(- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x))
(* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps)
(+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2)))))
(* (sin x) eps)
(sin x)
x
eps
1/6
(* -1/2 (sin (+ x (/ (PI) 2))))
-1/2
(sin (+ x (/ (PI) 2)))
(+ x (/ (PI) 2))
(/ (PI) 2)
(PI)
2
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* (neg eps) #s(approx (sin x) #s(hole binary64 x)))))
(* (neg eps) #s(approx (sin x) #s(hole binary64 x)))
(neg eps)
#s(approx (sin x) #s(hole binary64 x))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)))) eps)))
(* #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)))) eps)
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps))))
(+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps))
(- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1)
(* (+ (* 1/4 eps) (* 1/6 x)) x)
(+ (* 1/4 eps) (* 1/6 x))
1/4
(* 1/6 x)
1
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#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x)))
(* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x)
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(* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x)
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(* x x)
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(* (* x x) 1/5040)
1/5040
(* -1/120 eps)
-1/120
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#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ (+ (* 1/2 (PI)) x) eps)))
(+ (+ (* 1/2 (PI)) x) eps)
(+ (* 1/2 (PI)) x)
1/2
(cos x)
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (* 1/2 (PI)))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin (* 1/2 (PI)))))))
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#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* -1/2 (* eps (sin (* 1/2 (PI)))))))
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#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* x (- (+ (* eps (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps))) (* x (+ (* 1/4 (* eps (sin (* 1/2 (PI))))) (* x (+ 1/6 (* eps (+ (* -1/36 eps) (* 1/12 (cos (* 1/2 (PI))))))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* -1/2 (* eps (sin (* 1/2 (PI)))))))
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#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (* -1/2 (sin (* 1/2 (PI))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/6 eps))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (cos (* 1/2 (PI)))) (+ (* 1/6 eps) (* 1/4 (* x (sin (* 1/2 (PI)))))))))))
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#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
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#s(approx (sin x) #s(hole binary64 x))
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#s(approx x #s(hole binary64 x))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* -1/2 (sin (* 1/2 (PI))))))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/2 (* x (cos (* 1/2 (PI))))))))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (cos (* 1/2 (PI)))) (* 1/4 (* x (sin (* 1/2 (PI))))))))))
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#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
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#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
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#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
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#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 -1))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (- (* 1/4 (* eps x)) 1)))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* 1/4 (* eps x))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* x (+ (* 1/6 x) (* 1/4 eps)))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* 1/4 eps)))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (+ (* 1/6 x) (* 1/4 eps))))
#s(approx (* 1/6 x) #s(hole binary64 (* 1/6 x)))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (- (* 1/6 (* eps (pow x 2))) eps)))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (- (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))) eps)))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (- (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))) eps)))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* 1/6 (* eps x))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* x (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* x (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* 1/6 eps)))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (* -1/120 eps)))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))
#s(approx (* (* x x) 1/5040) #s(hole binary64 (* 1/5040 (pow x 2))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (* 1/2 (PI)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ eps (+ x (* 1/2 (PI))))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (+ eps (* 1/2 (PI)))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (+ eps (+ x (* 1/2 (PI))))))
#s(approx (+ (* 1/2 (PI)) x) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ (* 1/2 (PI)) x) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* 1/6 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* -1/2 (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 x))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* 1/6 (pow x 3))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* (pow x 2) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* 1/6 x)))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* x (+ 1/6 (* 1/4 (/ eps x))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* 1/5040 (* eps (pow x 7)))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* (pow x 7) (+ (* -1 (/ eps (pow x 6))) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4)))))))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 6)))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* (pow x 6) (+ (* -1 (/ eps (pow x 6))) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4)))))))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* 1/5040 (* eps (pow x 5)))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* (pow x 5) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* (pow x 5) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 4)))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/120 (/ eps (pow x 2))) (+ (* 1/5040 eps) (* 1/6 (/ eps (pow x 4))))))))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (* 1/5040 (* eps (pow x 2)))))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1/120 (/ eps (pow x 2))) (* 1/5040 eps)))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ eps (+ x (* 1/2 (PI)))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 x))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 x))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))))
#s(approx (+ (* 1/2 (PI)) x) #s(hole binary64 x))
#s(approx (+ (* 1/2 (PI)) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (sin (- (* 1/2 (PI)) (* -1 x)))) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (sin (- (* 1/2 (PI)) (* -1 x)))) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* eps (+ (* -1/2 (sin (- (* 1/2 (PI)) (* -1 x)))) (* 1/6 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1/2 (sin (- (* 1/2 (PI)) (* -1 x)))) (* 1/6 (* eps (sin x))))))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* -1/2 (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* (pow x 2) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x))))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2))))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2)))))))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* -1 (* (pow x 7) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/5040 eps) (+ (* 1/120 (/ eps (pow x 2))) (/ eps (pow x 6)))))))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* -1 (* (pow x 5) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2))))))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 4))) (+ (* -1/5040 eps) (* 1/120 (/ eps (pow x 2)))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ eps (* 1/2 (PI))) (* -1 x)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))))
#s(approx (+ (* 1/2 (PI)) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (+ x (* 1/2 (PI)))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* 1/6 (* eps (sin x)))))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (* -1/2 (sin (+ x (* 1/2 (PI)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (- (* 1/6 (pow x 2)) 1)))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x)))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* eps (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1)))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* eps (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* eps (* x (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* eps (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120))))))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (* eps (- (* 1/5040 (pow x 2)) 1/120))))
#s(approx (* -1/120 eps) #s(hole binary64 (* -1/120 eps)))
#s(approx (* 1/6 eps) #s(hole binary64 (* 1/6 eps)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* 1/6 (* (pow eps 3) (sin x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x)))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* 1/6 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (* 1/6 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/6 (sin x))))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/4 (pow x 2)) 1/2))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* 1/4 (* eps x))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* eps (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* eps (+ 1/4 (* 1/6 (/ x eps))))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 eps))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(hole binary64 (- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (sin (+ x (* 1/2 (PI)))))) eps)) (* -1/6 (sin x)))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (sin (+ x (* 1/2 (PI))))) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (sin (+ x (* 1/2 (PI)))) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) #s(hole binary64 (* -1 (* eps (+ (* -1/4 x) (* -1/6 (/ (pow x 2) eps)))))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) #s(hole binary64 (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) #s(hole binary64 (* -1 (* eps (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) #s(hole binary64 (* -1 (* eps (* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) #s(hole binary64 (* -1 (* eps (+ 1/120 (* -1/5040 (pow x 2)))))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) #s(hole binary64 (sin (- (+ x (* 1/2 (PI))) (* -1 eps)))))
#s(approx (+ (/ (PI) 2) (+ eps x)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(*.f64 eps (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))))
(-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(+.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) eps))
(+.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (*.f64 eps (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))))
(/.f64 (fma.f64 (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (sin.f64 x) (*.f64 #s(literal 1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal -1/6 binary64) (*.f64 (sin.f64 x) eps)))
(+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
(*.f64 (sin.f64 x) eps)
(*.f64 eps (sin.f64 x))
(sin.f64 x)
x
eps
#s(literal 1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))
(+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)
(/.f64 (neg.f64 (PI.f64)) #s(literal -2 binary64))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (sin x) x) (neg.f64 eps)))
(*.f64 #s(approx (sin x) x) (neg.f64 eps))
(*.f64 (neg.f64 eps) #s(approx (sin x) x))
(neg.f64 (*.f64 eps #s(approx (sin x) x)))
(*.f64 #s(literal -1 binary64) eps)
(*.f64 eps #s(literal -1 binary64))
(neg.f64 eps)
#s(approx (sin x) x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
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(-.f64 (sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 x eps)))) (cos.f64 x))
(sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 x eps))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 x eps)))
(/.f64 (-.f64 (*.f64 eps eps) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) #s(literal 2 binary64))) (-.f64 eps (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))
(/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) #s(literal 2 binary64)) (*.f64 eps eps)) (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) #s(literal 2 binary64)) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) #s(literal 2 binary64)) (-.f64 (*.f64 eps eps) (*.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 x eps))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 x eps))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps)
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (+.f64 x eps))
(+.f64 (+.f64 x eps) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(+.f64 eps (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 2 binary64)) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 2 binary64))) (-.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))))
(/.f64 (fma.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 2 binary64)) (-.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 2 binary64)) (*.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) x)
(fma.f64 (PI.f64) #s(literal 1/2 binary64) x)
(-.f64 x (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)
(+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64)))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) x (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) x (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) x) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)))) x (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) x (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps))) #s(literal 1 binary64)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (fma.f64 (*.f64 x eps) (-.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) eps)) eps) #s(literal 1 binary64)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (fma.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) eps)) eps) #s(literal 1 binary64)) eps (*.f64 (*.f64 (*.f64 (*.f64 eps eps) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal 1/4 binary64))) x (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (fma.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) eps)) eps) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 x eps) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/36 binary64) eps)) eps #s(literal 1/6 binary64)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))) x)) x (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) eps)) eps) #s(literal 1 binary64)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) x) (-.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) eps)) eps) #s(literal 1 binary64))) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/36 binary64) eps)) eps #s(literal 1/6 binary64)) x (*.f64 (*.f64 #s(literal 1/4 binary64) eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))) x (*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) eps)) eps)) #s(literal 1 binary64)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (fma.f64 (*.f64 x eps) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal 1/4 binary64) (*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) eps)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 x eps) (fma.f64 #s(literal 1/12 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/36 binary64) eps)) (*.f64 (*.f64 #s(literal 1/4 binary64) eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))) x (*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) eps)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (fma.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) eps)) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (fma.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal 1/6 binary64) eps))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (fma.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/36 binary64) eps)) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/4 binary64))) x (*.f64 #s(literal 1/6 binary64) eps))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))))
#s(approx (* (sin x) eps) (*.f64 x eps))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (sin x) x)
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx x x)
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) (*.f64 #s(literal -1/2 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) (fma.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/4 binary64))) x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))))
#s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (+ x (/ (PI) 2)) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
#s(approx (+ x (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (-.f64 (*.f64 (+.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/5040 binary64) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
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#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (*.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (*.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (*.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))))
#s(approx (* -1/2 (sin (+ x (/ (PI) 2)))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (*.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)))
#s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (*.f64 #s(literal 1 binary64) x))))
#s(approx (+ x (/ (PI) 2)) (*.f64 (neg.f64 x) (-.f64 (*.f64 (/.f64 (PI.f64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (neg.f64 x))) (cos.f64 x)))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 eps x)) #s(literal 1/6 binary64))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (neg.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) eps) (pow.f64 x #s(literal -1 binary64))) x)) #s(literal 1/6 binary64))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) eps (neg.f64 (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) x)) #s(literal 1/6 binary64))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) eps (pow.f64 x #s(literal -1 binary64))) x) #s(literal -1 binary64) #s(literal 1/6 binary64)) (*.f64 x x)))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 (neg.f64 x) (-.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 eps x)) #s(literal 1/6 binary64))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) (neg.f64 (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) eps)) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) (neg.f64 (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/6 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) eps))) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) (neg.f64 (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/6 binary64) (fma.f64 #s(literal -1/5040 binary64) eps (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/120 binary64) (/.f64 eps (pow.f64 x #s(literal 6 binary64)))))) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) (neg.f64 (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) eps)) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) (neg.f64 (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/6 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) eps))) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) (neg.f64 x))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (neg.f64 x) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) x)) #s(literal 1 binary64))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) (*.f64 (neg.f64 x) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) x)) #s(literal 1 binary64))))
#s(approx (+ (* 1/2 (PI)) x) (*.f64 (neg.f64 x) (-.f64 (*.f64 (/.f64 (PI.f64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))) eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) (cos.f64 x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (neg.f64 (sin.f64 x))) eps))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (*.f64 (fma.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps))) eps (neg.f64 (sin.f64 x))) eps))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64)))
#s(approx eps eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (neg eps) (neg.f64 eps))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (neg.f64 (sin.f64 x)))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (-.f64 (*.f64 (*.f64 x eps) #s(literal 1/4 binary64)) #s(literal 1 binary64))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (*.f64 (*.f64 x eps) #s(literal 1/4 binary64))))
#s(approx (* -1/2 eps) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) (*.f64 (*.f64 x eps) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x)) #s(literal 1 binary64))))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) x) eps))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) eps))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps))
#s(approx (* -1/120 eps) (*.f64 #s(literal -1/120 binary64) eps))
#s(approx (* 1/6 eps) (*.f64 #s(literal 1/6 binary64) eps))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (fma.f64 (fma.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))) eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) eps (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (*.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 3 binary64))) (sin.f64 x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1 binary64) (fma.f64 (/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) (sin.f64 x)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (*.f64 (fma.f64 (/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1 binary64) (fma.f64 (/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (*.f64 eps eps)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (*.f64 (fma.f64 (/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x)))
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (*.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)) #s(literal 1/2 binary64)) eps))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) (*.f64 (*.f64 x eps) #s(literal 1/4 binary64)))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) (*.f64 (-.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) x)) (pow.f64 eps #s(literal -1 binary64))) eps))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) (*.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) x)) eps))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) eps))
#s(approx (+ (/ (PI) 2) (+ eps x)) eps)
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps) #s(literal 1 binary64)) eps))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) eps)
#s(approx (+ (+ (* 1/2 (PI)) x) eps) (*.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps) #s(literal 1 binary64)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (neg.f64 eps))) (cos.f64 x)))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps) #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)))))
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) eps) (sin x)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)) eps))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/6) (* -1/2 (sin (+ x (/ (PI) 2))))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) eps) #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x)))
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) x) (* -1/2 eps)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))) #s(literal 1/2 binary64))))
#s(approx (- (* (+ (* 1/4 eps) (* 1/6 x)) x) 1) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/4 binary64) x (neg.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)))))
#s(approx (* (+ (* 1/4 eps) (* 1/6 x)) x) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/4 binary64) x))))
#s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 (neg.f64 eps) (-.f64 (*.f64 (/.f64 x eps) #s(literal -1/6 binary64)) #s(literal 1/4 binary64))))
#s(approx (* (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) x) (*.f64 (neg.f64 eps) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (+ (* (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) x) (neg eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (* (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) x) (*.f64 (neg.f64 eps) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) x)))
#s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 (neg.f64 eps) (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64))))
#s(approx (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))))
#s(approx (sin (+ (/ (PI) 2) (+ eps x))) (sin.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (neg.f64 eps))))
#s(approx (+ (/ (PI) 2) (+ eps x)) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps)) #s(literal 1 binary64))))
#s(approx (+ (+ (* 1/2 (PI)) x) eps) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps)) #s(literal 1 binary64))))

eval140.0ms (0.7%)

Memory
-1.9MiB live, 48.3MiB allocated; 13ms collecting garbage
Compiler

Compiled 20 440 to 2 746 computations (86.6% saved)

prune90.0ms (0.5%)

Memory
-2.0MiB live, 45.7MiB allocated; 2ms collecting garbage
Pruning

40 alts after pruning (30 fresh and 10 done)

PrunedKeptTotal
New5145519
Fresh32528
Picked235
Done077
Total51940559
Accuracy
100.0%
Counts
559 → 40
Alt Table
Click to see full alt table
StatusAccuracyProgram
57.6%
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
✓57.6%
(-.f64 (sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))) (cos.f64 x))
57.6%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓57.6%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
55.9%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
99.7%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))) eps) (sin.f64 x)) eps))
✓99.7%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
97.2%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
96.8%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
46.1%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (*.f64 eps eps))) eps))
56.9%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
81.7%
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))))))
55.8%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
✓55.7%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓99.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
✓99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
✓98.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
97.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
97.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
96.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
98.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
98.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
✓81.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
80.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
80.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
✓79.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
✓97.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
97.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
97.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
96.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
96.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
96.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
23.4%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 4 binary64)))))
24.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64)))))
96.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
80.4%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
80.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
80.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
Compiler

Compiled 3 458 to 1 357 computations (60.8% saved)

regimes91.0ms (0.5%)

Memory
24.1MiB live, 24.1MiB allocated; 0ms collecting garbage
Counts
60 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (*.f64 eps eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) eps))))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) (pow.f64 eps #s(literal 4 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
Calls

3 calls:

32.0ms
x
32.0ms
eps
19.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.8%1x
99.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes59.0ms (0.3%)

Memory
-24.6MiB live, 22.2MiB allocated; 3ms collecting garbage
Counts
54 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal -1 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (*.f64 eps eps))) eps))
Outputs
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))) eps) (sin.f64 x)) eps))
Calls

3 calls:

23.0ms
eps
18.0ms
x
13.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes61.0ms (0.3%)

Memory
22.0MiB live, 22.0MiB allocated; 0ms collecting garbage
Counts
51 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
Calls

3 calls:

22.0ms
x
18.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
17.0ms
eps
Results
AccuracySegmentsBranch
99.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes64.0ms (0.3%)

Memory
-26.2MiB live, 20.6MiB allocated; 3ms collecting garbage
Counts
49 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))))
(-.f64 (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
Calls

3 calls:

23.0ms
eps
22.0ms
x
15.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.4%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.4%1x
99.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes49.0ms (0.2%)

Memory
19.1MiB live, 19.1MiB allocated; 0ms collecting garbage
Counts
44 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (sin.f64 #s(approx (+ (/ (PI) 2) (+ eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) eps))) (cos.f64 x))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
Calls

3 calls:

16.0ms
x
16.0ms
eps
13.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.6%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.6%1x
98.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes46.0ms (0.2%)

Memory
17.8MiB live, 17.8MiB allocated; 0ms collecting garbage
Counts
40 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
Calls

3 calls:

15.0ms
eps
15.0ms
x
12.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.6%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.6%1x
98.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes47.0ms (0.2%)

Memory
-34.0MiB live, 16.8MiB allocated; 4ms collecting garbage
Counts
38 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
Calls

3 calls:

15.0ms
eps
14.0ms
x
11.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.5%1x
98.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes42.0ms (0.2%)

Memory
17.2MiB live, 17.2MiB allocated; 0ms collecting garbage
Counts
37 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
Calls

3 calls:

14.0ms
eps
14.0ms
x
11.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.9%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.9%1x
97.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes39.0ms (0.2%)

Memory
-32.0MiB live, 15.5MiB allocated; 2ms collecting garbage
Counts
33 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
Calls

3 calls:

13.0ms
eps
13.0ms
x
10.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.7%1x
97.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.2%)

Memory
14.3MiB live, 14.3MiB allocated; 0ms collecting garbage
Counts
31 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))))) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (+ (* 1/5040 (* (* x x) eps)) (* -1/120 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) #s(literal 1/120 binary64)) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/5040 binary64)) eps (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Calls

3 calls:

12.0ms
eps
12.0ms
x
9.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.3%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.3%1x
97.3%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.1%)

Memory
10.8MiB live, 10.8MiB allocated; 0ms collecting garbage
Counts
20 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/120 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x eps))) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Calls

3 calls:

8.0ms
eps
8.0ms
x
6.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.2%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.2%1x
97.2%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.1%)

Memory
8.8MiB live, 8.8MiB allocated; 0ms collecting garbage
Counts
15 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
Calls

3 calls:

7.0ms
x
6.0ms
eps
5.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.2%1eps
97.2%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.2%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.1%)

Memory
8.5MiB live, 8.5MiB allocated; 0ms collecting garbage
Counts
14 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Calls

3 calls:

6.0ms
x
6.0ms
eps
5.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.2%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.2%1x
97.2%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.1%)

Memory
-39.9MiB live, 7.5MiB allocated; 1ms collecting garbage
Counts
11 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (+ (* (* x x) (+ (* (* (* x x) 1/5040) eps) (* -1/120 eps))) (* 1/6 eps)) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(approx (+ (* (- (* (* eps x) 1/4) 1) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x eps)) #s(literal 1 binary64)) x))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Calls

3 calls:

6.0ms
x
5.0ms
eps
4.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
96.9%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
96.9%1x
96.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes11.0ms (0.1%)

Memory
5.9MiB live, 5.9MiB allocated; 0ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
Calls

3 calls:

4.0ms
eps
3.0ms
x
3.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
96.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
96.8%1x
96.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0%)

Memory
5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* -1/2 (cos x))) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
Calls

3 calls:

3.0ms
eps
3.0ms
x
2.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
79.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
79.8%1x
79.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory
4.0MiB live, 4.0MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
Calls

3 calls:

2.0ms
eps
2.0ms
x
1.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
55.7%1x
55.7%1eps
55.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify77.0ms (0.4%)

Memory
11.8MiB live, 11.8MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0155534
1218534
2289534
3367534
4580534
52700534
Stop Event
1×node limit
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 eps #s(literal -1/2 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(approx (+ (* 1/4 eps) (* 1/6 x)) (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (sin (+ (/ (PI) 2) (+ eps x))) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

derivations958.0ms (4.8%)

Memory
16.3MiB live, 63.3MiB allocated; 4ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 602 to 155 computations (74.3% saved)

preprocess157.0ms (0.8%)

Memory
-35.8MiB live, 57.5MiB allocated; 40ms collecting garbage
Compiler

Compiled 1 252 to 352 computations (71.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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