2cos (problem 3.3.5)

Time bar (total: 10.2s)

start0.0ms (0%)

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

analyze45.0ms (0.4%)

Memory
23.9MiB live, 68.4MiB allocated; 13ms collecting garbage
Algorithm
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)

sample8.0s (78%)

Memory
-63.3MiB live, 7 671.7MiB allocated; 2.2s collecting garbage
Samples
3.1s26 307×0invalid
2.7s5 836×2valid
482.0ms2 359×1valid
8.0ms61×0valid
Precisions
Click to see histograms. Total time spent on operations: 5.0s
ival-cos: 2.3s (47.3% of total)
ival-sub: 630.0ms (12.7% of total)
adjust: 497.0ms (10% of total)
const: 493.0ms (10% of total)
ival-add: 296.0ms (6% of total)
ival-fabs: 240.0ms (4.8% of total)
ival-mult: 221.0ms (4.5% of total)
ival-<: 141.0ms (2.8% of total)
ival-and: 79.0ms (1.6% of total)
ival-assert: 13.0ms (0.3% of total)
Bogosity

explain305.0ms (3%)

Memory
-30.8MiB live, 433.1MiB allocated; 90ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1331(5.0831603809725566e-160 1.3082134105429102e-164)0-(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
20-0-(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))cancellation1340
cos.f64(cos.f64 (+.f64 x eps))sensitivity20
Confusion
Predicted +Predicted -
+1340
-1121
Precision
0.9925925925925926
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+13400
-10121
Precision?
0.9925925925925926
Recall?
1.0
Freqs
test
numberfreq
0121
1134
21
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
219.0ms366×2valid
25.0ms144×1valid
0.0ms0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 206.0ms
ival-cos: 155.0ms (75.2% of total)
adjust: 36.0ms (17.5% of total)
ival-sub: 9.0ms (4.4% of total)
ival-add: 5.0ms (2.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess262.0ms (2.6%)

Memory
-0.2MiB live, 138.8MiB allocated; 42ms 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
iter limit
node limit
iter limit
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 (sin.f64 (fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)) (+.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)

prune0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.5%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

series5.0ms (0%)

Memory
8.6MiB live, 8.6MiB 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
1.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms
eps
@inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms
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))

rewrite155.0ms (1.5%)

Memory
-2.1MiB live, 233.1MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0148544
0153528
1883525
08275504
Stop Event
iter limit
node limit
iter limit
Counts
42 → 113
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)
#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 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)) (*.f64 #s(literal -1 binary64) x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)) (*.f64 #s(literal -1 binary64) x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)) x) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (*.f64 #s(literal -1 binary64) x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (*.f64 #s(literal -1 binary64) 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 (fma.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) #s(literal 2 binary64) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps))) (PI.f64))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (/.f64 (fma.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) #s(literal 2 binary64) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps))) (PI.f64))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))) (-.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x)))) (neg.f64 (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))) (*.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))))) (-.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x)))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))) (*.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))))))
(/.f64 (*.f64 (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))) (-.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x))) (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))))
(/.f64 (*.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))) (*.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))))) (-.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))) (*.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))))))
(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 (*.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))) (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))))))
(-.f64 (/.f64 (pow.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))) (*.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))) (*.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)))))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) 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))) (+.f64 (*.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))) (+.f64 (*.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 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) 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 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (/.f64 (fma.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) #s(literal 2 binary64) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps))) (PI.f64))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps))) #s(literal 2 binary64))))
(-.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 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))))
(cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) 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 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) 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 (fma.f64 #s(literal -1 binary64) eps x) (+.f64 eps x))) (neg.f64 (fma.f64 #s(literal -1 binary64) eps x)))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1 binary64) x eps) (+.f64 eps x))) (neg.f64 (fma.f64 #s(literal -1 binary64) x eps)))
(/.f64 (neg.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 (*.f64 eps eps) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 x x)))))
(/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) eps x) (+.f64 eps x)) (fma.f64 #s(literal -1 binary64) eps x))
(/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) x eps) (+.f64 eps x)) (fma.f64 #s(literal -1 binary64) x eps))
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps))))
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 eps eps) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 x x))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps)))) (/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps)))))
(-.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 x x)))) (/.f64 (*.f64 (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 x x)))))
(-.f64 (/.f64 (*.f64 x x) (fma.f64 #s(literal -1 binary64) eps x)) (/.f64 (*.f64 eps eps) (fma.f64 #s(literal -1 binary64) eps x)))
(-.f64 (/.f64 (*.f64 eps eps) (fma.f64 #s(literal -1 binary64) x eps)) (/.f64 (*.f64 x x) (fma.f64 #s(literal -1 binary64) x eps)))
(-.f64 eps (*.f64 #s(literal -1 binary64) x))
(-.f64 x (*.f64 #s(literal -1 binary64) eps))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 x x) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 eps eps)))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 x x)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 (*.f64 eps eps) #s(literal 1 binary64) (fma.f64 (*.f64 eps x) #s(literal -1 binary64) (*.f64 x x)))))
(+.f64 eps (*.f64 (*.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(+.f64 eps x)
(+.f64 x (*.f64 (*.f64 #s(literal -1 binary64) 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 (*.f64 #s(literal -1 binary64) 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)) (fma.f64 #s(literal 1 binary64) (cos.f64 eps) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64) #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 (fma.f64 #s(literal 1 binary64) (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 (fma.f64 #s(literal 1 binary64) (cos.f64 eps) #s(literal -1 binary64))))
#s(approx (cos (+ x eps)) (cos.f64 eps))
#s(approx (cos (+ x eps)) (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1 binary64) (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 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 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 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))))
#s(approx (+ x eps) x)
#s(approx (+ x eps) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1 binary64) #s(literal 1 binary64)) x))
#s(approx (cos x) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))))
#s(approx (+ x eps) (*.f64 (*.f64 (fma.f64 (*.f64 (/.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64) #s(literal -1 binary64)) x) #s(literal -1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1 binary64)))
#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 (*.f64 (sin.f64 x) eps) #s(literal -1 binary64) (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) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 1 binary64) #s(literal 1 binary64)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))))
#s(approx (+ x eps) (*.f64 (*.f64 (fma.f64 (*.f64 (/.f64 x eps) #s(literal -1 binary64)) #s(literal 1 binary64) #s(literal -1 binary64)) eps) #s(literal -1 binary64)))

eval12.0ms (0.1%)

Memory
23.7MiB live, 23.7MiB allocated; 0ms collecting garbage
Compiler

Compiled 2 428 to 441 computations (81.8% saved)

prune22.0ms (0.2%)

Memory
-10.8MiB live, 35.8MiB allocated; 2ms collecting garbage
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1092111
Fresh000
Picked101
Done000
Total1102112
Accuracy
99.8%
Counts
112 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.5%
(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
99.6%
#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))
Compiler

Compiled 45 to 30 computations (33.3% saved)

series41.0ms (0.4%)

Memory
-17.2MiB live, 44.2MiB allocated; 25ms collecting garbage
Counts
22 → 142
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)
(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(neg.f64 (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 eps) (cos.f64 x))
(cos.f64 eps)
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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ 1/2 (* -1/2 (cos eps))))))) 1)))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))))))) 1)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (cos eps)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1/2 (* x (cos eps))))))))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))))
#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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (- (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))) (cos x))))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (* (cos eps) (cos x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #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) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (cos x)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos x) (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))))
#s(approx (neg (sin eps)) #s(hole binary64 (* -1 eps)))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* 1/6 (pow eps 2)) 1))))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2)))) 1))))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120)))) 1))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))))
#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 (* (- (* (+ (* (+ (* (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 (neg (sin eps)) #s(hole binary64 (* -1 (sin eps))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (cos eps) #s(hole binary64 (cos 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)))))))
Calls

6 calls:

TimeVariablePointExpression
16.0ms
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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (neg (sin eps)) (sin eps) (* (cos eps) (cos x)) (cos eps))
6.0ms
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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (neg (sin eps)) (sin eps) (* (cos eps) (cos x)) (cos eps))
5.0ms
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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (neg (sin eps)) (sin eps) (* (cos eps) (cos x)) (cos eps))
4.0ms
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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (neg (sin eps)) (sin eps) (* (cos eps) (cos x)) (cos eps))
4.0ms
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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (neg (sin eps)) (sin eps) (* (cos eps) (cos x)) (cos eps))

rewrite175.0ms (1.7%)

Memory
-14.6MiB live, 222.4MiB allocated; 16ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05744008
06093816
135483816
082743663
Stop Event
iter limit
node limit
iter limit
Counts
164 → 290
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)
(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(neg.f64 (sin.f64 eps))
(sin.f64 eps)
(*.f64 (cos.f64 eps) (cos.f64 x))
(cos.f64 eps)
#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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ 1/2 (* -1/2 (cos eps))))))) 1)))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))))))) 1)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (cos eps)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1/2 (* x (cos eps))))))))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))))
#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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (- (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))) (cos x))))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (* (cos eps) (cos x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) #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) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (cos x)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos x) (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) #s(hole binary64 (+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))))))
#s(approx (neg (sin eps)) #s(hole binary64 (* -1 eps)))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* 1/6 (pow eps 2)) 1))))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2)))) 1))))
#s(approx (neg (sin eps)) #s(hole binary64 (* eps (- (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120)))) 1))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))))
#s(approx (* (cos eps) (cos x)) #s(hole binary64 (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))))
#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 (* (- (* (+ (* (+ (* (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 (neg (sin eps)) #s(hole binary64 (* -1 (sin eps))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (cos eps) #s(hole binary64 (cos 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)))))))
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))
(*.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 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 (neg.f64 (-.f64 (pow.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) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) (neg.f64 (fma.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 (neg.f64 (-.f64 (pow.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) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.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) (*.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 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.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 (-.f64 (pow.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) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) (fma.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 (-.f64 (pow.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) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.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) (*.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 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.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 (*.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)
(*.f64 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 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps) eps))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)))
(+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps) eps))
(+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps))))
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(fma.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal -1 binary64) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 x) (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 #s(literal -1 binary64) (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x)))
(sin.f64 (+.f64 (neg.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))) x))
(sin.f64 (+.f64 x (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))
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(-.f64 (*.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 eps)) (cos.f64 x)))
(cos.f64 (neg.f64 (neg.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps)))))
(cos.f64 (-.f64 (*.f64 #s(literal -1 binary64) eps) x))
(cos.f64 (neg.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))))
(cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps)))
(+.f64 (*.f64 (sin.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x)))
(+.f64 (*.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(*.f64 (sin.f64 eps) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (sin.f64 eps))
(neg.f64 (sin.f64 eps))
(fma.f64 (sin.f64 eps) (cos.f64 (PI.f64)) (*.f64 (cos.f64 eps) (sin.f64 (PI.f64))))
(sin.f64 (+.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (*.f64 #s(literal -1 binary64) eps))
(sin.f64 (+.f64 eps (PI.f64)))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (sin.f64 eps) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 (PI.f64))) (*.f64 (cos.f64 eps) (sin.f64 (PI.f64))))
(sin.f64 eps)
(*.f64 (cos.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 eps x)) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps))))) #s(literal -2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1 binary64) x))) (sin.f64 (+.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1 binary64) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1 binary64) eps))) (sin.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) eps)) (sin.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) eps))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 (-.f64 (*.f64 #s(literal -1 binary64) eps) (*.f64 #s(literal -1 binary64) x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) eps x)) (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 eps (*.f64 #s(literal -1 binary64) x))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 eps) (*.f64 (sin.f64 x) #s(literal -1 binary64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1 binary64) eps))) (cos.f64 (-.f64 (*.f64 #s(literal -1 binary64) x) (*.f64 #s(literal -1 binary64) eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -1 binary64) x eps)) (cos.f64 (-.f64 (*.f64 #s(literal -1 binary64) x) eps))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (*.f64 #s(literal -1 binary64) eps))) (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 x eps))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 eps x)) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))) #s(literal 2 binary64))
(fma.f64 (sin.f64 eps) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 eps) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (fma.f64 #s(literal -1 binary64) eps (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (*.f64 #s(literal -1 binary64) eps)))
(cos.f64 (*.f64 #s(literal -1 binary64) eps))
(cos.f64 eps)
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#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 (*.f64 (sin.f64 eps) x) #s(literal -1 binary64) (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 (* (- (* (+ (* (+ (* (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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (-.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (-.f64 (fma.f64 (fma.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 (*.f64 (sin.f64 eps) #s(literal -1 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos.f64 eps))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1 binary64) (cos.f64 eps)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64) (*.f64 (sin.f64 eps) #s(literal -1 binary64))) x (cos.f64 eps)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) x (*.f64 (sin.f64 eps) #s(literal -1 binary64))) x (cos.f64 eps)))
#s(approx (* (cos eps) (cos x)) (cos.f64 eps))
#s(approx (* (cos eps) (cos x)) (fma.f64 (*.f64 (*.f64 x x) (cos.f64 eps)) #s(literal -1/2 binary64) (cos.f64 eps)))
#s(approx (* (cos eps) (cos x)) (fma.f64 (fma.f64 (*.f64 (*.f64 x x) (cos.f64 eps)) #s(literal 1/24 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) (*.f64 x x) (cos.f64 eps)))
#s(approx (* (cos eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) (cos.f64 eps)) #s(literal -1/720 binary64) (*.f64 (cos.f64 eps) #s(literal 1/24 binary64))) (*.f64 x x) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) (*.f64 x x) (cos.f64 eps)))
#s(approx (- (cos (+ x eps)) (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 (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 x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.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)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.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))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (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))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (* (cos x) eps) 1/24) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
#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 (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (-.f64 (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))))
#s(approx (* (cos eps) (cos x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 eps) (*.f64 (sin.f64 x) #s(literal -1 binary64)))) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1 binary64)))
#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 (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 (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (*.f64 (sin.f64 x) 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 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1 binary64))) 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 (*.f64 (sin.f64 x) #s(literal -1 binary64))) 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 (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 (*.f64 (sin.f64 x) #s(literal -1 binary64))) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (sin.f64 x) #s(literal -1 binary64)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (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 (cos.f64 x) eps) #s(literal -1/2 binary64)))
#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 (sin.f64 x) #s(literal 1/6 binary64)))
#s(approx eps eps)
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1 binary64)))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1 binary64))) eps))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (*.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 (*.f64 (sin.f64 x) #s(literal -1 binary64))) eps))
#s(approx (- (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos x)) (*.f64 (fma.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 (*.f64 (sin.f64 x) #s(literal -1 binary64))) eps))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (cos.f64 x))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1 binary64) (cos.f64 x)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1 binary64))) eps (cos.f64 x)))
#s(approx (+ (* (sin x) (neg (sin eps))) (* (cos eps) (cos x))) (fma.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 (*.f64 (sin.f64 x) #s(literal -1 binary64))) eps (cos.f64 x)))
#s(approx (neg (sin eps)) (*.f64 #s(literal -1 binary64) eps))
#s(approx (neg (sin eps)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
#s(approx (neg (sin eps)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) (*.f64 eps eps)) #s(literal 1 binary64)) eps))
#s(approx (neg (sin eps)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/5040 binary64) (*.f64 eps eps)) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal 1/6 binary64)) (*.f64 eps eps)) #s(literal 1 binary64)) eps))
#s(approx (sin eps) eps)
#s(approx (sin eps) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (*.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* (cos eps) (cos x)) (cos.f64 x))
#s(approx (* (cos eps) (cos x)) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x) (cos.f64 x)))
#s(approx (* (cos eps) (cos x)) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps) (cos.f64 x)))
#s(approx (* (cos eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) (*.f64 eps eps)) (cos.f64 x) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps eps) (cos.f64 x)))
#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 (* (- (* (+ (* (+ (* (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 (*.f64 eps eps) #s(literal 2 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 (*.f64 eps eps) #s(literal 2 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 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps)) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64)) (*.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 (*.f64 eps eps) #s(literal 2 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) (*.f64 (*.f64 eps eps) eps)) (cos.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (*.f64 (*.f64 eps eps) eps) (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 (*.f64 (*.f64 eps eps) eps) (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)) (fma.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) (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) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 eps eps) eps)) (cos.f64 x)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) (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 (*.f64 (*.f64 eps eps) eps) (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 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
#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 (neg (sin eps)) (*.f64 (sin.f64 eps) #s(literal -1 binary64)))
#s(approx (sin eps) (sin.f64 eps))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 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 (fma.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(literal -1 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 (*.f64 eps eps) #s(literal 2 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 (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal -1 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps) #s(literal -1 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#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) eps) #s(literal -1 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 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) #s(literal -1 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 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps) #s(literal -1 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) #s(literal -1 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 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 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 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.f64 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) #s(literal -1 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 (fma.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(literal -1 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 (*.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (*.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64))) eps) #s(literal -1 binary64)))

eval48.0ms (0.5%)

Memory
2.3MiB live, 95.5MiB allocated; 5ms collecting garbage
Compiler

Compiled 12 437 to 1 791 computations (85.6% saved)

prune164.0ms (1.6%)

Memory
43.9MiB live, 226.5MiB allocated; 36ms collecting garbage
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New3572359
Fresh000
Picked022
Done000
Total3574361
Accuracy
100.0%
Counts
361 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.5%
(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
99.6%
#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))
31.6%
#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 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) (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))))))) eps))
99.0%
#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) (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)))))
Compiler

Compiled 197 to 112 computations (43.1% saved)

series92.0ms (0.9%)

Memory
-31.7MiB live, 64.9MiB allocated; 30ms collecting garbage
Counts
42 → 214
Calls
Call 1
Inputs
#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) (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)) 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))))
(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)))
(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))
(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)))
(*.f64 eps x)
eps
x
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))
#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))
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64))
#s(literal -1/48 binary64)
#s(literal 1/4 binary64)
(*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.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))
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal 1/2 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)) (fma.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) (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))))))) eps))
(*.f64 #s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) (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))))))) eps)
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) (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)))))))
(fma.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) (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 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps))
(*.f64 (sin.f64 x) #s(literal -1 binary64))
(sin.f64 x)
#s(literal -1 binary64)
(*.f64 (*.f64 eps eps) eps)
(*.f64 (*.f64 (*.f64 eps eps) eps) (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)))))
(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 (cos.f64 x) (*.f64 eps eps))
(cos.f64 x)
#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 (sin.f64 x) eps)
(*.f64 #s(literal 1/24 binary64) (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 (* (- (* (+ (* (+ (* (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 (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps 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 (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps 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 (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* eps (- (* 1/6 (pow eps 2)) 1))))
#s(approx (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
#s(approx (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (+ (* 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)))))))))
#s(approx (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) #s(hole binary64 (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2))))))
#s(approx (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) #s(hole binary64 (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (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)))))
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#s(approx (+ (* (/ (* (sin x) -1) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos 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 (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos 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 (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) #s(hole binary64 (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x)))))
Calls

6 calls:

TimeVariablePointExpression
28.0ms
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) (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) (* eps x) eps x (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps)) (+ (* -1/48 (* eps eps)) 1/4) -1/48 1/4 (* (- (* (* eps eps) 1/6) 1) eps) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) 1 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 1/2 (- (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) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (/ (* (sin x) -1) (* (* eps eps) eps)) (* (sin x) -1) (sin x) -1 (* (* eps eps) eps) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) (/ (cos x) (* eps eps)) (cos x) -1/2 (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))) (/ (sin x) eps) (* 1/24 (cos x)))
26.0ms
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) (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) (* eps x) eps x (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps)) (+ (* -1/48 (* eps eps)) 1/4) -1/48 1/4 (* (- (* (* eps eps) 1/6) 1) eps) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) 1 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 1/2 (- (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) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (/ (* (sin x) -1) (* (* eps eps) eps)) (* (sin x) -1) (sin x) -1 (* (* eps eps) eps) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) (/ (cos x) (* eps eps)) (cos x) -1/2 (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))) (/ (sin x) eps) (* 1/24 (cos x)))
12.0ms
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) (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) (* eps x) eps x (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps)) (+ (* -1/48 (* eps eps)) 1/4) -1/48 1/4 (* (- (* (* eps eps) 1/6) 1) eps) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) 1 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 1/2 (- (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) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (/ (* (sin x) -1) (* (* eps eps) eps)) (* (sin x) -1) (sin x) -1 (* (* eps eps) eps) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) (/ (cos x) (* eps eps)) (cos x) -1/2 (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))) (/ (sin x) eps) (* 1/24 (cos 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) (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) (* eps x) eps x (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps)) (+ (* -1/48 (* eps eps)) 1/4) -1/48 1/4 (* (- (* (* eps eps) 1/6) 1) eps) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) 1 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 1/2 (- (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) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (/ (* (sin x) -1) (* (* eps eps) eps)) (* (sin x) -1) (sin x) -1 (* (* eps eps) eps) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) (/ (cos x) (* eps eps)) (cos x) -1/2 (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))) (/ (sin x) eps) (* 1/24 (cos 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) (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) (* eps x) eps x (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps)) (+ (* -1/48 (* eps eps)) 1/4) -1/48 1/4 (* (- (* (* eps eps) 1/6) 1) eps) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) 1 (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 1/2 (- (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) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (/ (* (sin x) -1) (* (* eps eps) eps)) (* (sin x) -1) (sin x) -1 (* (* eps eps) eps) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) (/ (cos x) (* eps eps)) (cos x) -1/2 (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))) (/ (sin x) eps) (* 1/24 (cos x)))

rewrite212.0ms (2.1%)

Memory
1.7MiB live, 238.9MiB allocated; 38ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08968936
09648425
155448425
082468158
Stop Event
iter limit
node limit
iter limit
Counts
256 → 404
Calls
Call 1
Inputs
#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) (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)) 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))))
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(*.f64 eps x)
eps
x
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))
#s(literal -1/36 binary64)
(*.f64 eps eps)
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#s(literal 1 binary64)
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#s(literal 1/2 binary64)
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#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)))
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#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)))
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#s(approx (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) #s(hole binary64 (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx x #s(hole binary64 x))
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#s(approx (/ (* (sin x) -1) (* (* eps eps) eps)) #s(hole binary64 (* -1 (/ x (pow eps 3)))))
#s(approx (/ (* (sin x) -1) (* (* eps eps) eps)) #s(hole binary64 (* x (- (* 1/6 (/ (pow x 2) (pow eps 3))) (/ 1 (pow eps 3))))))
#s(approx (/ (* (sin x) -1) (* (* eps eps) eps)) #s(hole binary64 (* x (- (* (pow x 2) (+ (* -1/120 (/ (pow x 2) (pow eps 3))) (* 1/6 (/ 1 (pow eps 3))))) (/ 1 (pow eps 3))))))
#s(approx (/ (* (sin x) -1) (* (* eps eps) eps)) #s(hole binary64 (* x (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/5040 (/ (pow x 2) (pow eps 3))) (* 1/120 (/ 1 (pow eps 3))))) (* 1/6 (/ 1 (pow eps 3))))) (/ 1 (pow eps 3))))))
#s(approx (* (sin x) -1) #s(hole binary64 (* -1 x)))
#s(approx (* (sin x) -1) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (* (sin x) -1) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (* (sin x) -1) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#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 (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) #s(hole binary64 (* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2))))))))
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#s(approx (/ (cos x) (* eps eps)) #s(hole binary64 (/ 1 (pow eps 2))))
#s(approx (/ (cos x) (* eps eps)) #s(hole binary64 (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (/ 1 (pow eps 2)))))
#s(approx (/ (cos x) (* eps eps)) #s(hole binary64 (+ (* (pow x 2) (- (* 1/24 (/ (pow x 2) (pow eps 2))) (* 1/2 (/ 1 (pow eps 2))))) (/ 1 (pow eps 2)))))
#s(approx (/ (cos x) (* eps eps)) #s(hole binary64 (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/720 (/ (pow x 2) (pow eps 2))) (* 1/24 (/ 1 (pow eps 2))))) (* 1/2 (/ 1 (pow eps 2))))) (/ 1 (pow eps 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)))))
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#s(approx (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))) #s(hole binary64 1/24))
#s(approx (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))) #s(hole binary64 (+ 1/24 (* 1/6 (/ x eps)))))
#s(approx (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))) #s(hole binary64 (+ 1/24 (* x (+ (* -1/48 x) (* 1/6 (/ 1 eps)))))))
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#s(approx (/ (sin x) eps) #s(hole binary64 (/ x eps)))
#s(approx (/ (sin x) eps) #s(hole binary64 (* x (+ (* -1/6 (/ (pow x 2) eps)) (/ 1 eps)))))
#s(approx (/ (sin x) eps) #s(hole binary64 (* x (+ (* (pow x 2) (- (* 1/120 (/ (pow x 2) eps)) (* 1/6 (/ 1 eps)))) (/ 1 eps)))))
#s(approx (/ (sin x) eps) #s(hole binary64 (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/5040 (/ (pow x 2) eps)) (* 1/120 (/ 1 eps)))) (* 1/6 (/ 1 eps)))) (/ 1 eps)))))
#s(approx (* 1/24 (cos x)) #s(hole binary64 1/24))
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#s(approx (* 1/24 (cos x)) #s(hole binary64 (+ 1/24 (* (pow x 2) (- (* (pow x 2) (+ 1/576 (* -1/17280 (pow x 2)))) 1/48)))))
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#s(approx (/ (* (sin x) -1) (* (* eps eps) eps)) #s(hole binary64 (* -1 (/ (sin x) (pow eps 3)))))
#s(approx (* (sin x) -1) #s(hole binary64 (* -1 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
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#s(approx (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) #s(hole binary64 (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (/ (cos x) (* eps eps)) #s(hole binary64 (/ (cos x) (pow eps 2))))
#s(approx (cos x) #s(hole binary64 (cos x)))
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#s(approx (/ (sin x) eps) #s(hole binary64 (/ (sin x) eps)))
#s(approx (* 1/24 (cos x)) #s(hole binary64 (* 1/24 (cos x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
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#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 (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (* x (- (* 1/36 (pow x 2)) 1/6)) eps)) (* -1/48 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6))) eps)) (* -1/48 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6))) eps)) (* -1/48 (pow x 2)))))))
#s(approx (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* 1/36 (pow x 2)) 1/6) eps)) (* -1/48 x)))))
#s(approx (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6) eps)) (* -1/48 x)))))
#s(approx (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6) eps)) (* -1/48 x)))))
#s(approx (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (* -1 (/ (- (* 1/36 x) (* 1/4 (/ 1 eps))) eps)) 1/48))))
#s(approx (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (* -1 (/ (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x)) eps)) 1/48))))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)))))
#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) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (/ (* (sin x) -1) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos 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) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos 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 (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos 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 (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) #s(hole binary64 (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x)))))
Outputs
#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) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) x (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) 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 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) x (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) x)) (*.f64 (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) x) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)))
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(fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) x))
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) x))
(fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) x (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
(fma.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) x))
(fma.f64 x (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
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(+.f64 (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)) x))
(/.f64 (-.f64 (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x))) (-.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/4 binary64)) (*.f64 (*.f64 eps x) (fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64)))) x)))
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#s(approx (* eps x) (*.f64 eps x))
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#s(approx (+ (* -1/48 (* eps eps)) 1/4) (*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 eps eps) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 1/2304 binary64)) (fma.f64 (pow.f64 (*.f64 eps eps) #s(literal -1 binary64)) #s(literal 1/4 binary64) #s(literal 1/48 binary64))) (*.f64 eps eps)))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal 1/6 binary64)))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) (*.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (*.f64 eps eps) #s(literal -1 binary64))) (*.f64 (*.f64 eps eps) eps)))
#s(approx (- (* (* eps eps) 1/6) 1) (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)))
#s(approx (- (* (* eps eps) 1/6) 1) (*.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (*.f64 eps eps) #s(literal -1 binary64))) (*.f64 eps eps)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (*.f64 (pow.f64 (*.f64 eps eps) #s(literal 2 binary64)) #s(literal 1/24 binary64)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (*.f64 (pow.f64 (*.f64 eps eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 (*.f64 eps eps) #s(literal -1 binary64)) #s(literal 1/2 binary64)))))
#s(approx (- (* (* eps eps) 1/24) 1/2) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)))
#s(approx (- (* (* eps eps) 1/24) 1/2) (*.f64 (-.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 (*.f64 eps eps) #s(literal -1 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 #s(literal 1/24 binary64) (*.f64 (*.f64 eps eps) eps)) (cos.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (*.f64 (*.f64 eps eps) eps) (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 (*.f64 (*.f64 eps eps) eps) (fma.f64 (/.f64 (/.f64 (cos.f64 x) 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 (sin.f64 x) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) eps)) (fma.f64 (/.f64 (/.f64 (cos.f64 x) 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 (*.f64 eps eps) eps)))
#s(approx (+ (* (/ (* (sin x) -1) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 eps eps) eps)) (cos.f64 x)))
#s(approx (+ (* (/ (* (sin x) -1) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (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) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 (/.f64 (/.f64 (cos.f64 x) 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) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (*.f64 (fma.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) eps)) (fma.f64 (/.f64 (/.f64 (cos.f64 x) 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 (*.f64 eps eps) eps)))
#s(approx (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 eps eps) eps)) (cos.f64 x)))
#s(approx (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))
#s(approx (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) (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) eps) 1/6) (* 1/24 (cos x))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 x) (neg.f64 (sin.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 (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps) #s(literal -1 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 (*.f64 eps eps) #s(literal 2 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 (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal -1 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps) #s(literal -1 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x) eps) #s(literal -1 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64))) #s(literal 1/24 binary64)) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (+.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps) #s(literal -1 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x)) eps) #s(literal -1 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64))) #s(literal 1/24 binary64)) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (+ (* (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (+.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x) eps) #s(literal -1 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) #s(literal -1 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x)) eps) #s(literal -1 binary64) (*.f64 (*.f64 x x) #s(literal -1/48 binary64))) #s(literal 1/24 binary64)) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) #s(literal -1 binary64) (*.f64 #s(literal -1/48 binary64) x)) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 x eps) (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64))) eps) #s(literal -1 binary64) (*.f64 #s(literal -1/48 binary64) x)) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (+ (* (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) eps) #s(literal -1 binary64) (*.f64 #s(literal 1/4 binary64) x)) eps) #s(literal -1 binary64) (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64))) eps) #s(literal -1 binary64) (*.f64 #s(literal -1/48 binary64) x)) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) (*.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/36 binary64) x) eps) (/.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/4 binary64)) eps)) #s(literal -1 binary64)) #s(literal 1/48 binary64)) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (+ (* (* eps x) (+ (* -1/36 (* eps eps)) 1/6)) (* (+ (* -1/48 (* eps eps)) 1/4) (* eps eps))) (*.f64 (-.f64 (*.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) eps) #s(literal -1 binary64) (*.f64 #s(literal 1/36 binary64) x)) eps) #s(literal -1 binary64)) #s(literal 1/48 binary64)) (pow.f64 (*.f64 eps eps) #s(literal 2 binary64))))
#s(approx (* (- (* (* eps eps) 1/6) 1) eps) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (-.f64 (pow.f64 (*.f64 eps eps) #s(literal -1 binary64)) #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 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (*.f64 #s(literal -1/6 binary64) (/.f64 (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 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.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(literal -1 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 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps) #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) #s(literal -1 binary64) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))
#s(approx (+ (* (/ (* (sin x) -1) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (+ (* (/ (* (sin x) -1) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.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(literal -1 binary64) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))
#s(approx (+ (* (/ (* (sin x) -1) (* (* eps eps) eps)) (* (* eps eps) eps)) (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))))) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps) #s(literal -1 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) #s(literal -1 binary64) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))
#s(approx (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (* (* (* eps eps) eps) (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x))))) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) eps) #s(literal -1 binary64)) (fma.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(literal -1 binary64) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))
#s(approx (+ (* (/ (cos x) (* eps eps)) -1/2) (+ (* (/ (sin x) eps) 1/6) (* 1/24 (cos x)))) (fma.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(literal -1 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))

eval127.0ms (1.2%)

Memory
-1.1MiB live, 190.9MiB allocated; 24ms collecting garbage
Compiler

Compiled 51 716 to 3 589 computations (93.1% saved)

prune415.0ms (4.1%)

Memory
42.7MiB live, 464.4MiB allocated; 38ms collecting garbage
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New6220622
Fresh000
Picked022
Done022
Total6224626
Accuracy
100.0%
Counts
626 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.5%
(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
99.6%
#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))
31.6%
#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 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) (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))))))) eps))
99.0%
#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) (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)))))
Compiler

Compiled 401 to 190 computations (52.6% saved)

regimes21.0ms (0.2%)

Memory
-50.0MiB live, 8.5MiB allocated; 29ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
#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) (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 (- (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 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) (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))))))) 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))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
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:

16.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
99.6%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory
5.1MiB live, 5.1MiB allocated; 0ms collecting garbage
Accuracy

Total -43.6b remaining (-7114.8%)

Threshold costs -43.6b (-7114.8%)

Counts
2 → 1
Calls
Call 1
Inputs
#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) (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 (- (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 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 eps eps) eps) (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))))))) eps))
Outputs
#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) (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)))))
Calls

3 calls:

1.0ms
eps
1.0ms
x
1.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.0%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.0%1x
99.0%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify48.0ms (0.5%)

Memory
3.1MiB live, 48.4MiB allocated; 8ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
052109
189109
2175109
3466108
41138108
52858108
Stop Event
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 (- (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) (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)))))
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 (- (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) (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)))))

derivations60.0ms (0.6%)

Memory
-2.1MiB live, 44.7MiB allocated; 4ms collecting garbage
Stop Event
done
Compiler

Compiled 109 to 55 computations (49.5% saved)

preprocess30.0ms (0.3%)

Memory
-2.8MiB live, 44.7MiB allocated; 1ms collecting garbage
Compiler

Compiled 232 to 122 computations (47.4% saved)

end0.0ms (0%)

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

Profiling

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