2sin (example 3.3)

Time bar (total: 8.6s)

start0.0ms (0%)

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

analyze56.0ms (0.6%)

Memory
-12.8MiB live, 40.1MiB allocated; 24ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample5.5s (64.2%)

Memory
152.5MiB live, 5 196.2MiB allocated; 2.3s collecting garbage
Samples
2.3s26 556×0invalid
1.4s5 152×1valid
331.0ms3 104×0valid
Precisions
Click to see histograms. Total time spent on operations: 2.5s
ival-sin: 665.0ms (27% of total)
const: 435.0ms (17.6% of total)
ival-add: 310.0ms (12.6% of total)
ival-fabs: 214.0ms (8.7% of total)
ival-mult: 209.0ms (8.5% of total)
ival-<: 187.0ms (7.6% of total)
adjust: 183.0ms (7.4% of total)
ival-sub: 181.0ms (7.3% of total)
ival-and: 71.0ms (2.9% of total)
ival-assert: 13.0ms (0.5% of total)
Bogosity

explain106.0ms (1.2%)

Memory
41.9MiB live, 131.7MiB allocated; 18ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2342(1.426545282838167e-173 1.282384061444727e-175)2(2.6186011180871923e-289 5.503058705349603e-291)(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10-0-(sin.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(sin.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))cancellation2343
sin.f64(sin.f64 (+.f64 x eps))sensitivity10
Confusion
Predicted +Predicted -
+2322
-220
Precision
0.9914529914529915
Recall
0.9914529914529915
Confusion?
Predicted +Predicted MaybePredicted -
+23220
-2119
Precision?
0.9873417721518988
Recall?
1.0
Freqs
test
numberfreq
022
1233
21
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
44.0ms338×1valid
8.0ms170×0valid
4.0ms4×3valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 39.0ms
ival-sin: 20.0ms (50.9% of total)
adjust: 10.0ms (25.4% of total)
ival-add: 4.0ms (10.2% of total)
ival-sub: 4.0ms (10.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess122.0ms (1.4%)

Memory
-33.6MiB live, 66.2MiB allocated; 67ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02150
12550
23250
34050
45350
58150
614050
738550
8145150
9523050
067
0107
1117
0117
Stop Event
1×iter limit
1×saturated
1×iter limit
1×node limit
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Outputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶60.0%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

series5.0ms (0.1%)

Memory
8.3MiB live, 8.3MiB allocated; 0ms collecting garbage
Counts
6 → 36
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos 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 (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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

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

rewrite151.0ms (1.8%)

Memory
28.0MiB live, 162.0MiB allocated; 33ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0150538
0155526
1931520
08567489
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
42 → 105
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos 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 (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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- 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)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(*.f64 (*.f64 (cos.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 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(fma.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(fma.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (*.f64 (cos.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 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (sin.f64 x))))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin.f64 (+.f64 eps x))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 eps)) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps)))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (sin.f64 x)))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (*.f64 (-.f64 eps x) (+.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (*.f64 (-.f64 eps x) (+.f64 eps x)) (-.f64 eps x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (*.f64 x (-.f64 x eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(-.f64 eps (neg.f64 x))
(-.f64 x (neg.f64 eps))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(+.f64 eps (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(+.f64 eps x)
(+.f64 x (*.f64 (neg.f64 eps) #s(literal -1 binary64)))
(+.f64 x eps)
x
eps
(sin.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (sin.f64 eps))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx x x)
#s(approx (sin x) x)
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x))
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x))
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) x)
#s(approx (+ x eps) (fma.f64 (/.f64 eps x) x x))
#s(approx (sin x) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 eps x) #s(literal -1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (sin (+ x eps)) (sin.f64 x))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x)))
#s(approx eps eps)
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64))))

eval23.0ms (0.3%)

Memory
-32.1MiB live, 27.2MiB allocated; 9ms collecting garbage
Compiler

Compiled 1 964 to 373 computations (81% saved)

prune7.0ms (0.1%)

Memory
10.8MiB live, 10.8MiB allocated; 0ms collecting garbage
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New958103
Fresh000
Picked011
Done000
Total959104
Accuracy
100.0%
Counts
104 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶33.4%
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
60.0%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓60.0%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
60.0%
(*.f64 (*.f64 (cos.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))
▶97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
▶99.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
▶99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶96.8%
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Compiler

Compiled 281 to 192 computations (31.7% saved)

series49.0ms (0.6%)

Memory
0.1MiB live, 44.5MiB allocated; 12ms collecting garbage
Counts
33 → 194
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
(sin.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(*.f64 (sin.f64 eps) x)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
#s(literal 2 binary64)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#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 x #s(hole binary64 x))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))))
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (sin eps)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
#s(approx (* (sin eps) x) #s(hole binary64 (* x (sin eps))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (sin eps)))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (+ (sin eps) (* x (- (* 2 (cos eps)) (+ 1 (cos eps)))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (sin eps)))))) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (pow (sin eps) 2)))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (+ (* 2 (* x (* (cos eps) (sin eps)))) (pow (sin eps) 2))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (- (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) 1)))) (pow (sin eps) 2))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (- (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (pow (cos eps) 2))) 1)))) (pow (sin eps) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (pow (sin eps) 2)))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* 2 (* x (* (cos eps) (sin eps)))) (pow (sin eps) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))))) (pow (sin eps) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (pow (cos eps) 2)))))) (pow (sin eps) 2))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (pow (sin x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (sin eps)))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (cos eps))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* 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 (sin x)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* -1/2 (* (pow x 2) (sin eps)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* x (sin eps)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (- (pow (sin (+ eps x)) 2) (pow (sin x) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (pow (sin (+ eps x)) 2)))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (pow (sin x) 2) #s(hole binary64 (pow (sin x) 2)))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (+ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (pow (sin (- eps (* -1 x))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- eps (* -1 x)))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (- (pow (sin (- eps (* -1 x))) 2) (pow (sin x) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (pow (sin (- eps (* -1 x))) 2)))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (- eps (* -1 x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx eps #s(hole binary64 eps))
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps x)))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* -1/6 (* (pow eps 2) x))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (cos x))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (+ (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))) (sin x))) (+ (* -1/4 (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (+ (* -1/12 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x)))))) (sin x)))))))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (* 2 (* eps (* (cos x) (sin x))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2))))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* -1/3 (* (cos x) (sin x))) (* eps (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))))) (pow (cos x) 2))))))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (pow (sin x) 2)))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* 2 (* eps (* (cos x) (sin x)))) (pow (sin x) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2)))))) (pow (sin x) 2))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin x)))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (* 2 (sin x))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (cos x)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- x (* -1 eps)))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (pow (sin (- x (* -1 eps))) 2)))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (- x (* -1 eps))))))
Calls

6 calls:

TimeVariablePointExpression
17.0ms
x
@-inf
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) x eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (- (cos eps) 1) (cos eps) 1 (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow (sin (+ eps x)) 2) (sin (+ eps x)) (+ eps x) 2 (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))
7.0ms
x
@0
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) x eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (- (cos eps) 1) (cos eps) 1 (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow (sin (+ eps x)) 2) (sin (+ eps x)) (+ eps x) 2 (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))
6.0ms
eps
@0
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) x eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (- (cos eps) 1) (cos eps) 1 (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow (sin (+ eps x)) 2) (sin (+ eps x)) (+ eps x) 2 (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))
5.0ms
eps
@-inf
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) x eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (- (cos eps) 1) (cos eps) 1 (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow (sin (+ eps x)) 2) (sin (+ eps x)) (+ eps x) 2 (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))
5.0ms
eps
@inf
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) x eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (- (cos eps) 1) (cos eps) 1 (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow (sin (+ eps x)) 2) (sin (+ eps x)) (+ eps x) 2 (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))

rewrite241.0ms (2.8%)

Memory
1.5MiB live, 186.7MiB allocated; 41ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08275022
08834649
152484621
082234441
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
227 → 362
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
(sin.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(*.f64 (sin.f64 eps) x)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
#s(literal 2 binary64)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#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 x #s(hole binary64 x))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))))
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (sin eps)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
#s(approx (* (sin eps) x) #s(hole binary64 (* x (sin eps))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (sin eps)))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (+ (sin eps) (* x (- (* 2 (cos eps)) (+ 1 (cos eps)))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (sin eps)))))) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (+ (/ 1 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))))) (+ 1 (cos eps)))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (pow (sin eps) 2)))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (+ (* 2 (* x (* (cos eps) (sin eps)))) (pow (sin eps) 2))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (- (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) 1)))) (pow (sin eps) 2))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (- (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (pow (cos eps) 2))) 1)))) (pow (sin eps) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (pow (sin eps) 2)))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* 2 (* x (* (cos eps) (sin eps)))) (pow (sin eps) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))))) (pow (sin eps) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* x (+ (* 2 (* (cos eps) (sin eps))) (* x (+ (* -1 (pow (sin eps) 2)) (+ (* x (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (pow (cos eps) 2)))))) (pow (sin eps) 2))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (pow (sin x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (sin eps)))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (cos eps))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* 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 (sin x)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* -1/2 (* (pow x 2) (sin eps)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* x (sin eps)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (- (pow (sin (+ eps x)) 2) (pow (sin x) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (pow (sin (+ eps x)) 2)))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (pow (sin x) 2) #s(hole binary64 (pow (sin x) 2)))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (+ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (pow (sin (- eps (* -1 x))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- eps (* -1 x)))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (- (pow (sin (- eps (* -1 x))) 2) (pow (sin x) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (pow (sin (- eps (* -1 x))) 2)))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (- eps (* -1 x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx eps #s(hole binary64 eps))
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps x)))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* -1/6 (* (pow eps 2) x))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))))
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (cos x))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (+ (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))) (sin x))) (+ (* -1/4 (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (+ (* -1/12 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x)))))) (sin x)))))))) (+ (* -1/4 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* 1/2 (/ (pow (cos x) 2) (sin x))))) (sin x))))))) (* 1/2 (/ (pow (cos x) 2) (sin x)))))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (* 2 (* eps (* (cos x) (sin x))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2))))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (+ (* -1/3 (* (cos x) (sin x))) (* eps (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))))) (pow (cos x) 2))))))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (pow (sin x) 2)))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* 2 (* eps (* (cos x) (sin x)))) (pow (sin x) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (+ (* eps (+ (* 2 (* (cos x) (sin x))) (* eps (+ (* -1 (pow (sin x) 2)) (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))) (pow (cos x) 2)))))) (pow (sin x) 2))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin x)))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (* 2 (sin x))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (cos x)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2)) (+ (sin x) (sin (- x (* -1 eps)))))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) #s(hole binary64 (- (pow (sin (- x (* -1 eps))) 2) (pow (sin x) 2))))
#s(approx (pow (sin (+ eps x)) 2) #s(hole binary64 (pow (sin (- x (* -1 eps))) 2)))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (- x (* -1 eps))))))
Outputs
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(*.f64 eps (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(fma.f64 (cos.f64 x) eps (*.f64 eps (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(fma.f64 eps (cos.f64 x) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(fma.f64 eps (cos.f64 x) (*.f64 eps (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 eps (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
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(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (sin.f64 x) #s(literal 6 binary64))) (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (+.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 2 binary64)))))
(-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 (sin.f64 (+.f64 eps x)))) (exp.f64 (log.f64 (sin.f64 (+.f64 eps x)))))
(*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))
(pow.f64 (exp.f64 (log.f64 (sin.f64 (+.f64 eps x)))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 eps x) (+.f64 eps x))) (cos.f64 (+.f64 (+.f64 eps x) (+.f64 eps x)))) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (sin.f64 (+.f64 eps x))) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (sin.f64 (+.f64 eps x))) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)))
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal -1 binary64)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin.f64 (+.f64 eps x))
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
(exp.f64 (*.f64 (log.f64 (sin.f64 (+.f64 eps x))) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 eps eps) (*.f64 eps x))))
(+.f64 eps x)
(+.f64 x eps)
#s(literal 2 binary64)
(*.f64 (exp.f64 (log.f64 (sin.f64 x))) (exp.f64 (log.f64 (sin.f64 x))))
(*.f64 (sin.f64 x) (sin.f64 x))
(pow.f64 (exp.f64 (log.f64 (sin.f64 x))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 x x)) (cos.f64 (+.f64 x x))) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 x (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
(+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (sin.f64 eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 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 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.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 #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 (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 x x)
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))
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#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (sin x) x)
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
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#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (sin.f64 eps))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
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#s(approx (* (sin eps) x) (*.f64 (sin.f64 eps) x))
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#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (fma.f64 (-.f64 (-.f64 (*.f64 (cos.f64 eps) #s(literal 2 binary64)) #s(literal 1 binary64)) (cos.f64 eps)) x (sin.f64 eps)))
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#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (fma.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 (cos.f64 eps) (sin.f64 eps)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (fma.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal -1 binary64) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) x (sin.f64 (+.f64 eps eps))) x (pow.f64 (sin.f64 eps) #s(literal 2 binary64))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (fma.f64 (fma.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 eps)) #s(literal -4/3 binary64)) x (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1 binary64)) x (sin.f64 (+.f64 eps eps))) x (pow.f64 (sin.f64 eps) #s(literal 2 binary64))))
#s(approx (pow (sin (+ eps x)) 2) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))
#s(approx (pow (sin (+ eps x)) 2) (fma.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 (cos.f64 eps) (sin.f64 eps)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))))
#s(approx (pow (sin (+ eps x)) 2) (fma.f64 (fma.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) x (sin.f64 (+.f64 eps eps))) x (pow.f64 (sin.f64 eps) #s(literal 2 binary64))))
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#s(approx (sin (+ eps x)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ eps x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)))
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#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (pow (sin x) 2) (*.f64 x x))
#s(approx (pow (sin x) 2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (pow (sin x) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x)))
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#s(approx (+ (sin x) (sin (+ eps x))) (sin.f64 eps))
#s(approx (+ (sin x) (sin (+ eps x))) (fma.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (+ (sin x) (sin (+ eps x))) (fma.f64 (+.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (+ (sin x) (sin (+ eps x))) (fma.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (cos.f64 eps) #s(literal -1/6 binary64)) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
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#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (cos x) (cos.f64 x))
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sin.f64 eps)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) (*.f64 x x)))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (-.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (+.f64 (/.f64 (sin.f64 eps) (*.f64 x x)) (/.f64 (cos.f64 eps) x))) (pow.f64 x #s(literal -1 binary64))) (*.f64 x x)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
#s(approx (pow (sin (+ eps x)) 2) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))
#s(approx (sin (+ eps x)) (sin.f64 (+.f64 eps x)))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (pow (sin x) 2) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
#s(approx (+ (sin x) (sin (+ eps x))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
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#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 eps) x) #s(literal -1 binary64) (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)))) x))) (*.f64 x x)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (neg.f64 x) (fma.f64 #s(literal 1/2 binary64) (sin.f64 eps) (/.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
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#s(approx (pow (sin (+ eps x)) 2) (pow.f64 (sin.f64 (-.f64 eps (neg.f64 x))) #s(literal 2 binary64)))
#s(approx (sin (+ eps x)) (sin.f64 (-.f64 eps (neg.f64 x))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (+ (sin x) (sin (+ eps x))) (+.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (cos.f64 x))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(approx eps eps)
#s(approx (sin eps) eps)
#s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps))
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) x)) eps (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) eps))
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps))
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#s(approx (* (sin eps) x) (*.f64 eps x))
#s(approx (* (sin eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/6 binary64) x) eps))
#s(approx (* (sin eps) x) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 eps eps)) x (*.f64 #s(literal -1/6 binary64) x)) (*.f64 eps eps) x) eps))
#s(approx (* (sin eps) x) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 eps eps)) x (*.f64 #s(literal 1/120 binary64) x)) (*.f64 eps eps) (*.f64 #s(literal -1/6 binary64) x)) (*.f64 eps eps) x) eps))
#s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/40320 binary64) (*.f64 eps eps)) #s(literal 1/720 binary64)) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)))) eps (cos.f64 x)) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (fma.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal -4/3 binary64)) (sin.f64 x)) #s(literal 1/2 binary64)) (fma.f64 (*.f64 (cos.f64 x) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)))) (sin.f64 x))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/4 binary64) (cos.f64 x)))) eps (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (sin.f64 x))) (/.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (fma.f64 (-.f64 (fma.f64 (-.f64 (fma.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)))) (sin.f64 x)) (fma.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)))) (fma.f64 (*.f64 (cos.f64 x) (/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal -4/3 binary64)) (sin.f64 x)) #s(literal 1/2 binary64)) (fma.f64 (*.f64 (cos.f64 x) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)))) (sin.f64 x))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/4 binary64) (cos.f64 x)))) (sin.f64 x))) #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal -1/12 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))))) eps (*.f64 (/.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal -4/3 binary64)) (sin.f64 x)) #s(literal 1/2 binary64))) (fma.f64 (*.f64 (cos.f64 x) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)))) (sin.f64 x))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/4 binary64) (cos.f64 x)))) eps (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (sin.f64 x))) (/.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (*.f64 (*.f64 #s(literal 2 binary64) eps) (*.f64 (cos.f64 x) (sin.f64 x))))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (*.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps (sin.f64 (+.f64 x x))) eps))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (*.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal -4/3 binary64)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (sin.f64 (+.f64 x x))) eps))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (*.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal -4/3 binary64) (*.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (sin.f64 (+.f64 x x))) eps))
#s(approx (pow (sin (+ eps x)) 2) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
#s(approx (pow (sin (+ eps x)) 2) (fma.f64 (*.f64 #s(literal 2 binary64) eps) (*.f64 (cos.f64 x) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
#s(approx (pow (sin (+ eps x)) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps (sin.f64 (+.f64 x x))) eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
#s(approx (pow (sin (+ eps x)) 2) (fma.f64 (fma.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 x)) #s(literal -4/3 binary64)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (sin.f64 (+.f64 x x))) eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
#s(approx (sin (+ eps x)) (sin.f64 x))
#s(approx (sin (+ eps x)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ eps x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)))
#s(approx (sin (+ eps x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x)))
#s(approx (+ (sin x) (sin (+ eps x))) (*.f64 #s(literal 2 binary64) (sin.f64 x)))
#s(approx (+ (sin x) (sin (+ eps x))) (fma.f64 (cos.f64 x) eps (*.f64 #s(literal 2 binary64) (sin.f64 x))))
#s(approx (+ (sin x) (sin (+ eps x))) (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 #s(literal 2 binary64) (sin.f64 x))))
#s(approx (+ (sin x) (sin (+ eps x))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (*.f64 #s(literal 2 binary64) (sin.f64 x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (*.f64 #s(literal -1/6 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) (cos.f64 x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (*.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps))
#s(approx (sin eps) (sin.f64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))
#s(approx (- (cos eps) 1) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/6 binary64)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) #s(literal 1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) (*.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/6 binary64)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps)))))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (-.f64 (pow.f64 (sin.f64 (-.f64 x (neg.f64 eps))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))))
#s(approx (pow (sin (+ eps x)) 2) (pow.f64 (sin.f64 (-.f64 x (neg.f64 eps))) #s(literal 2 binary64)))
#s(approx (sin (+ eps x)) (sin.f64 (-.f64 x (neg.f64 eps))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (+ (sin x) (sin (+ eps x))) (+.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))

eval66.0ms (0.8%)

Memory
27.0MiB live, 115.6MiB allocated; 16ms collecting garbage
Compiler

Compiled 14 846 to 2 078 computations (86% saved)

prune64.0ms (0.8%)

Memory
-76.6MiB live, 46.0MiB allocated; 68ms collecting garbage
Pruning

26 alts after pruning (23 fresh and 3 done)

PrunedKeptTotal
New48221503
Fresh123
Picked325
Done011
Total48626512
Accuracy
100.0%
Counts
512 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.0%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓60.0%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
60.0%
(*.f64 (*.f64 (cos.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))
98.8%
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
▶99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
✓99.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #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))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
▶99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
✓99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
▶97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
▶96.8%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
Compiler

Compiled 1 465 to 961 computations (34.4% saved)

series65.0ms (0.8%)

Memory
-10.0MiB live, 37.4MiB allocated; 10ms collecting garbage
Counts
38 → 154
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(approx (* (cos x) eps) eps)
eps
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
(sin.f64 x)
x
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
(+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))
#s(literal 1/12 binary64)
(*.f64 eps eps)
#s(literal 1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
(*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 #s(approx (sin x) x) eps)
#s(approx (sin x) x)
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps))
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))
(*.f64 (sin.f64 x) eps)
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#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 (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))))
#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) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 eps))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2)))))))))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (- (* 1/12 (pow eps 2)) 1/2)))
#s(approx (* 1/12 (* eps eps)) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (* eps eps) -1/6) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* (pow eps 2) x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
Calls

6 calls:

TimeVariablePointExpression
43.0ms
x
@-inf
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) x (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) 1/2 (* -1/2 eps) (* (* eps eps) -1/6) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (* (* (* (sin x) eps) -1/2) eps) (* (* (sin x) eps) -1/2) (* (sin x) eps))
5.0ms
eps
@-inf
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) x (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) 1/2 (* -1/2 eps) (* (* eps eps) -1/6) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (* (* (* (sin x) eps) -1/2) eps) (* (* (sin x) eps) -1/2) (* (sin x) eps))
4.0ms
eps
@inf
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) x (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) 1/2 (* -1/2 eps) (* (* eps eps) -1/6) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (* (* (* (sin x) eps) -1/2) eps) (* (* (sin x) eps) -1/2) (* (sin x) eps))
4.0ms
x
@inf
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) x (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) 1/2 (* -1/2 eps) (* (* eps eps) -1/6) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (* (* (* (sin x) eps) -1/2) eps) (* (* (sin x) eps) -1/2) (* (sin x) eps))
3.0ms
eps
@0
((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) x (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) 1/2 (* -1/2 eps) (* (* eps eps) -1/6) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (* (* (* (sin x) eps) -1/2) eps) (* (* (sin x) eps) -1/2) (* (sin x) eps))

rewrite186.0ms (2.2%)

Memory
-0.3MiB live, 233.6MiB allocated; 27ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05994318
06424247
136234247
084573987
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
192 → 322
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(approx (* (cos x) eps) eps)
eps
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
(sin.f64 x)
x
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
(+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))
#s(literal 1/12 binary64)
(*.f64 eps eps)
#s(literal 1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
(*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 #s(approx (sin x) x) eps)
#s(approx (sin x) x)
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps))
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))
(*.f64 (sin.f64 x) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#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 (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))))
#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) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 eps))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2)))))))))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (- (* 1/12 (pow eps 2)) 1/2)))
#s(approx (* 1/12 (* eps eps)) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (* eps eps) -1/6) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* (pow eps 2) x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (*.f64 #s(literal -1/6 binary64) #s(approx (* (cos x) eps) eps))) eps (cos.f64 x)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (*.f64 #s(literal -1/6 binary64) #s(approx (* (cos x) eps) eps))) eps (cos.f64 x)) eps)
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#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (-.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/12 binary64)))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) x))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) (*.f64 eps eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 (fma.f64 (/.f64 x (*.f64 eps eps)) #s(literal -1/2 binary64) (-.f64 (*.f64 #s(literal 1/12 binary64) x) (/.f64 #s(literal 1/2 binary64) eps))) (*.f64 eps eps)))
#s(approx (- (* 1/12 (* eps eps)) 1/2) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))
#s(approx (- (* 1/12 (* eps eps)) 1/2) (*.f64 (-.f64 #s(literal 1/12 binary64) (*.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) (*.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))) eps))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/12 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) eps))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps)))))

eval54.0ms (0.6%)

Memory
5.4MiB live, 107.2MiB allocated; 9ms collecting garbage
Compiler

Compiled 17 456 to 1 984 computations (88.6% saved)

prune61.0ms (0.7%)

Memory
-4.8MiB live, 42.7MiB allocated; 2ms collecting garbage
Pruning

30 alts after pruning (25 fresh and 5 done)

PrunedKeptTotal
New38713400
Fresh61218
Picked325
Done033
Total39630426
Accuracy
100.0%
Counts
426 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.0%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓60.0%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
60.0%
(*.f64 (*.f64 (cos.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))
98.8%
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
▶99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
▶98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
✓99.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #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))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
✓99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
✓98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
▶97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
5.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
▶97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
✓96.8%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
Compiler

Compiled 1 802 to 1 174 computations (34.9% saved)

series33.0ms (0.4%)

Memory
0.8MiB live, 46.5MiB allocated; 3ms collecting garbage
Counts
46 → 194
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
(fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps))
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal -1/2 binary64)
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(*.f64 (*.f64 eps x) #s(literal 1/12 binary64))
(*.f64 eps x)
#s(literal 1/12 binary64)
#s(literal 1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
(fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps))
(*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)
#s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps)
#s(approx (sin 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))
(*.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)
(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))
(-.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 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x))
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal 1/6 binary64)
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 eps))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (- (* 1/12 (* eps x)) 1/2)))
#s(approx (* (* eps x) 1/12) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 eps))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2)))))))))))
#s(approx (* (* eps x) -1/2) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 1/120))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow x 2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))))
#s(approx (* (* (sin x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* 1/12 (* eps (pow x 3)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* eps (pow x 2)))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1/5040 (pow x 7))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* -1/5040 (pow x 6))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* -1/5040 (pow x 2))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))))
Calls

6 calls:

TimeVariablePointExpression
5.0ms
x
@-inf
((- (sin (+ x eps)) (sin x)) (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) (* (* (sin x) eps) -1/2) (* (sin x) eps) (sin x) x eps -1/2 (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (- (* (* eps x) 1/12) 1/2) (* (* eps x) 1/12) (* eps x) 1/12 1/2 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (* (* (* (sin x) eps) -1/2) eps) (* (* (sin x) eps) -1/2) (* (* eps x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 1/6)
5.0ms
x
@inf
((- (sin (+ x eps)) (sin x)) (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) (* (* (sin x) eps) -1/2) (* (sin x) eps) (sin x) x eps -1/2 (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (- (* (* eps x) 1/12) 1/2) (* (* eps x) 1/12) (* eps x) 1/12 1/2 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (* (* (* (sin x) eps) -1/2) eps) (* (* (sin x) eps) -1/2) (* (* eps x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 1/6)
5.0ms
eps
@0
((- (sin (+ x eps)) (sin x)) (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) (* (* (sin x) eps) -1/2) (* (sin x) eps) (sin x) x eps -1/2 (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (- (* (* eps x) 1/12) 1/2) (* (* eps x) 1/12) (* eps x) 1/12 1/2 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (* (* (* (sin x) eps) -1/2) eps) (* (* (sin x) eps) -1/2) (* (* eps x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 1/6)
5.0ms
eps
@-inf
((- (sin (+ x eps)) (sin x)) (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) (* (* (sin x) eps) -1/2) (* (sin x) eps) (sin x) x eps -1/2 (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (- (* (* eps x) 1/12) 1/2) (* (* eps x) 1/12) (* eps x) 1/12 1/2 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (* (* (* (sin x) eps) -1/2) eps) (* (* (sin x) eps) -1/2) (* (* eps x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 1/6)
5.0ms
eps
@inf
((- (sin (+ x eps)) (sin x)) (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) (* (* (sin x) eps) -1/2) (* (sin x) eps) (sin x) x eps -1/2 (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (- (* (* eps x) 1/12) 1/2) (* (* eps x) 1/12) (* eps x) 1/12 1/2 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (* (* (* (sin x) eps) -1/2) eps) (* (* (sin x) eps) -1/2) (* (* eps x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 1/6)

rewrite205.0ms (2.4%)

Memory
-0.8MiB live, 182.2MiB allocated; 21ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07145593
07665428
140445428
082795124
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
240 → 370
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
(fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps))
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal -1/2 binary64)
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
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#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
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#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) #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)))))
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#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
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#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
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#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
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#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 1/120))
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#s(approx (sin x) #s(hole binary64 (sin x)))
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#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* 1/12 (* eps (pow x 3)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
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#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* eps (pow x 2)))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))))
#s(approx (* (* (* (sin x) eps) -1/2) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1/5040 (pow x 7))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* -1/5040 (pow x 6))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* -1/5040 (pow x 2))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (* (* (sin x) eps) -1/2) eps) (* (cos x) eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))))
#s(approx (- (* (* eps x) 1/12) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(*.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) (*.f64 (cos.f64 x) eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) (*.f64 (cos.f64 x) eps)))))
(fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps))
(fma.f64 (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) eps) (*.f64 (cos.f64 x) eps))
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps))
(fma.f64 eps (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) eps))
(fma.f64 eps (cos.f64 x) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps))
(-.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) (*.f64 (neg.f64 (cos.f64 x)) eps))
(-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (neg.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
(+.f64 (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) (*.f64 (cos.f64 x) eps))
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps))
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x))
(*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))
(*.f64 (sin.f64 x) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 (sin.f64 x) eps)
(*.f64 eps (sin.f64 x))
(sin.f64 x)
x
eps
#s(literal -1/2 binary64)
(*.f64 (cos.f64 x) eps)
(*.f64 eps (cos.f64 x))
(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 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps)
(*.f64 eps #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
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#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (+.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)))
#s(approx (* -1/2 eps) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (*.f64 #s(literal -1/6 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) (cos.f64 x)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (*.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) (pow.f64 eps #s(literal -2 binary64))))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (pow.f64 eps #s(literal -1 binary64)))) eps))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (* (* eps x) 1/12) 1/2) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) eps))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x)))))
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)))))
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) (*.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps)))))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (neg.f64 eps) (*.f64 (fma.f64 #s(literal -1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)))
#s(approx (+ (* (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) x) 1) (*.f64 (neg.f64 eps) (fma.f64 (fma.f64 #s(literal -1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) (*.f64 #s(literal -1/12 binary64) (*.f64 x x))) #s(literal 1/2 binary64))))
#s(approx (- (* (* eps x) 1/12) 1/2) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/12 binary64) x (/.f64 #s(literal 1/2 binary64) eps))))

eval108.0ms (1.3%)

Memory
-12.5MiB live, 133.4MiB allocated; 37ms collecting garbage
Compiler

Compiled 19 856 to 2 615 computations (86.8% saved)

prune106.0ms (1.2%)

Memory
6.7MiB live, 146.9MiB allocated; 48ms collecting garbage
Pruning

38 alts after pruning (28 fresh and 10 done)

PrunedKeptTotal
New4749483
Fresh11920
Picked055
Done055
Total47538513
Accuracy
100.0%
Counts
513 → 38
Alt Table
Click to see full alt table
StatusAccuracyProgram
60.0%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓60.0%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
60.0%
(*.f64 (*.f64 (cos.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))
98.8%
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
✓99.6%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
✓98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
98.4%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
✓99.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #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))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
99.2%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
✓99.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
✓99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
99.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
✓98.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.4%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
98.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
✓97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
5.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
5.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
✓97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
96.8%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
97.6%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
✓96.8%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
Compiler

Compiled 3 080 to 1 228 computations (60.1% saved)

regimes47.0ms (0.6%)

Memory
8.7MiB live, 97.7MiB allocated; 14ms collecting garbage
Counts
52 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (*.f64 (cos.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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #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))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
Calls

3 calls:

16.0ms
x
12.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms
eps
Results
AccuracySegmentsBranch
99.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.8%1x
99.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes42.0ms (0.5%)

Memory
43.2MiB live, 87.0MiB allocated; 8ms collecting garbage
Counts
49 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(*.f64 (*.f64 (cos.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))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #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))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
Calls

3 calls:

17.0ms
x
12.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
11.0ms
eps
Results
AccuracySegmentsBranch
99.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes45.0ms (0.5%)

Memory
-39.6MiB live, 59.1MiB allocated; 23ms collecting garbage
Counts
42 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
Calls

3 calls:

17.0ms
eps
16.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms
x
Results
AccuracySegmentsBranch
99.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.4%)

Memory
27.8MiB live, 71.9MiB allocated; 7ms collecting garbage
Counts
41 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Calls

3 calls:

14.0ms
x
10.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms
eps
Results
AccuracySegmentsBranch
99.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.5%1x
99.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes39.0ms (0.5%)

Memory
-13.7MiB live, 87.6MiB allocated; 14ms collecting garbage
Counts
39 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
Calls

3 calls:

16.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms
eps
9.0ms
x
Results
AccuracySegmentsBranch
99.2%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.2%1x
99.2%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes76.0ms (0.9%)

Memory
-11.3MiB live, 81.4MiB allocated; 7ms collecting garbage
Counts
34 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Calls

3 calls:

53.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
13.0ms
eps
8.0ms
x
Results
AccuracySegmentsBranch
99.1%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.1%1x
99.1%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes50.0ms (0.6%)

Memory
5.8MiB live, 51.5MiB allocated; 5ms collecting garbage
Counts
32 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
Calls

3 calls:

33.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms
x
8.0ms
eps
Results
AccuracySegmentsBranch
99.1%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.1%1x
99.1%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes41.0ms (0.5%)

Memory
-4.9MiB live, 53.2MiB allocated; 36ms collecting garbage
Counts
30 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Calls

3 calls:

25.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
eps
7.0ms
x
Results
AccuracySegmentsBranch
99.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.0%1x
99.0%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes29.0ms (0.3%)

Memory
6.5MiB live, 50.1MiB allocated; 9ms collecting garbage
Counts
29 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
Calls

3 calls:

13.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
x
7.0ms
eps
Results
AccuracySegmentsBranch
98.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.9%1x
98.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.3%)

Memory
12.1MiB live, 54.5MiB allocated; 11ms collecting garbage
Counts
28 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
Calls

3 calls:

12.0ms
x
7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
eps
Results
AccuracySegmentsBranch
98.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.9%1x
98.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes24.0ms (0.3%)

Memory
-2.1MiB live, 43.5MiB allocated; 5ms collecting garbage
Counts
26 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (pow (sin (+ eps x)) 2) (pow (sin x) 2)) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
Calls

3 calls:

9.0ms
x
7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
eps
Results
AccuracySegmentsBranch
98.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.8%1x
98.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.3%)

Memory
-21.1MiB live, 38.2MiB allocated; 9ms collecting garbage
Counts
23 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
Calls

3 calls:

10.0ms
x
6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
eps
Results
AccuracySegmentsBranch
98.4%1x
98.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.2%)

Memory
10.0MiB live, 56.5MiB allocated; 2ms collecting garbage
Counts
21 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
Calls

3 calls:

7.0ms
x
5.0ms
eps
5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Results
AccuracySegmentsBranch
98.4%1x
98.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.2%)

Memory
-3.9MiB live, 43.3MiB allocated; 1ms collecting garbage
Counts
17 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (*.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 #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))) eps (*.f64 #s(approx (* (* (sin x) eps) -1/2) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
Calls

3 calls:

5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
98.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.0%1x
98.0%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.2%)

Memory
-7.5MiB live, 36.3MiB allocated; 4ms collecting garbage
Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
Calls

3 calls:

4.0ms
eps
4.0ms
x
4.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Results
AccuracySegmentsBranch
97.6%1eps
97.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.6%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory
30.2MiB live, 30.2MiB allocated; 0ms collecting garbage
Counts
10 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (cos x) eps) (* (* (* (sin x) eps) -1/2) eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* (* eps x) 1/12) 1/2) x) (* -1/2 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/12 binary64))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
Calls

3 calls:

3.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
97.6%1x
97.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory
-35.1MiB live, 20.1MiB allocated; 2ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
Calls

3 calls:

16.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
97.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.6%1x
97.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory
15.4MiB live, 15.4MiB allocated; 0ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
Calls

3 calls:

2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
97.5%1x
97.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory
9.7MiB live, 9.7MiB allocated; 0ms collecting garbage
Accuracy

Total -58.8b remaining (-2870%)

Threshold costs -58.8b (-2870%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
Calls

3 calls:

1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms
eps
1.0ms
x
Results
AccuracySegmentsBranch
96.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
96.8%1x
96.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify56.0ms (0.7%)

Memory
-1.7MiB live, 45.6MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0160576
1219576
2360576
3750576
41587576
54701576
Stop Event
1×node limit
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps (*.f64 (cos.f64 x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 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)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

derivations604.0ms (7.1%)

Memory
-7.4MiB live, 702.5MiB allocated; 90ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 576 to 165 computations (71.4% saved)

preprocess130.0ms (1.5%)

Memory
13.2MiB live, 199.3MiB allocated; 29ms collecting garbage
Compiler

Compiled 1 196 to 368 computations (69.2% saved)

end0.0ms (0%)

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

Profiling

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