2cos (problem 3.3.5)

Time bar (total: 8.1s)

start0.0ms (0.0%)

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

analyze48.0ms (0.6%)

Memory
-15.6MiB live, 39.6MiB allocated; 21ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0.0%0.0%50.6%49.4%0.0%0.0%0.0%0
0.0%0.0%50.6%49.4%0.0%0.0%0.0%1
0.0%0.0%50.6%49.4%0.0%0.0%0.0%2
0.0%0.0%25.3%49.4%0.0%25.3%0.0%3
0.0%0.0%25.3%49.4%0.0%25.3%0.0%4
0.0%0.0%19.0%49.4%0.0%31.6%0.0%5
0.0%0.0%15.8%49.4%0.0%34.8%0.0%6
0.0%0.0%11.1%49.4%0.0%39.5%0.0%7
0.0%0.0%8.7%49.4%0.0%41.9%0.0%8
0.0%0.0%5.9%49.4%0.0%44.6%0.0%9
0.0%0.0%4.5%49.4%0.0%46.0%0.0%10
0.0%0.0%3.1%49.4%0.0%47.5%0.0%11
0.0%0.0%2.7%49.4%0.0%47.9%0.0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample6.4s (79.3%)

Memory
-96.7MiB live, 7 836.1MiB allocated; 2.7s collecting garbage
Samples
2.5s25 547×0invalid
2.4s5 756×2valid
362.0ms2 432×1valid
20.0ms68×0valid
Precisions
Click to see histograms. Total time spent on operations: 4.1s
ival-cos: 2.8s (67.6% of total)
ival-fabs: 350.0ms (8.4% of total)
adjust: 344.0ms (8.3% of total)
ival-mult!: 170.0ms (4.1% of total)
ival-<: 150.0ms (3.6% of total)
ival-sub!: 128.0ms (3.1% of total)
ival-add!: 125.0ms (3.0% of total)
ival-and: 64.0ms (1.5% of total)
ival-assert: 12.0ms (0.3% of total)
Bogosity

preprocess34.0ms (0.4%)

Memory
-22.9MiB live, 28.9MiB allocated; 14ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02146
114342
2185142
Stop Event
node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 14 to 12 computations (14.3% saved)

sample0.0ms (0.0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Calls
Call 1
Inputs
Outputs

series12.0ms (0.2%)

Memory
19.1MiB live, 19.1MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0141506
Stop Event
iter-limit
Counts
6 → 33
Calls
Call 1
Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(cos.f64 x)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)))) (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps)))))) (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (cos (+ x eps)) (cos.f64 eps))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps)))))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (cos.f64 eps))) (sin.f64 eps)))))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps))))) (sin.f64 eps)))))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx x x)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x))))
#s(approx (cos x) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x))))
#s(approx (+ x eps) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 eps x)) #s(literal 1 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))))
#s(approx (+ x eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (cos.f64 x)))
#s(approx (cos (+ x eps)) (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))))
#s(approx (+ x eps) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1 binary64)))))
Calls

6 calls:

TimeVariablePoint
1.0ms
x
0
1.0ms
eps
inf
1.0ms
eps
-inf
1.0ms
x
-inf
0.0ms
eps
0

rewrite123.0ms (1.5%)

Memory
5.5MiB live, 138.6MiB allocated; 21ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
01018
17918
252818
0411918
Stop Event
iter-limit
node-limit
iter-limit
Counts
6 → 230
Calls
Call 1
Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(cos.f64 x)
Outputs
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x)))) (neg.f64 (cos.f64 x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (neg.f64 (cos.f64 x))) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (neg.f64 (cos.f64 x))) (cos.f64 (+.f64 eps x)))) (cos.f64 (+.f64 eps x)))
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))) (cos.f64 (+.f64 eps x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (cos.f64 (+.f64 eps x)))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fabs.f64 (+.f64 eps x)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fabs.f64 (+.f64 eps x)))) #s(literal 2 binary64)))))
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(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (neg.f64 eps) (neg.f64 eps) (*.f64 x (neg.f64 eps)))))
(/.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 x eps))))
(neg.f64 (-.f64 (neg.f64 eps) x))
(-.f64 eps (neg.f64 x))
(-.f64 x (neg.f64 eps))
(+.f64 eps x)
(+.f64 x (neg.f64 (neg.f64 eps)))
(+.f64 x eps)
x
eps
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) (*.f64 (sin.f64 x) #s(literal 0 binary64)))) (*.f64 (sin.f64 x) #s(literal 0 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (sin.f64 x) #s(literal 0 binary64))) (*.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))) (-.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (sin.f64 x) #s(literal 0 binary64)) (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))))))
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (neg.f64 (fabs.f64 x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (fabs.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(-.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) (sin.f64 (neg.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x))))
(cos.f64 (neg.f64 (neg.f64 (fabs.f64 x))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 (fabs.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 (fabs.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(+.f64 (*.f64 (sin.f64 (fabs.f64 x)) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))

eval47.0ms (0.6%)

Memory
6.7MiB live, 54.7MiB allocated; 19ms collecting garbage
Compiler

Compiled 5 792 to 1 321 computations (77.2% saved)

prune13.0ms (0.2%)

Memory
24.1MiB live, 24.1MiB allocated; 0ms collecting garbage
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New24415259
Fresh000
Picked011
Done000
Total24416260
Accuracy
99.8%
Counts
260 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.6%
(-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
50.6%
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
49.1%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
50.6%
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)))
80.7%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
5.5%
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))))
5.4%
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64)))))
5.5%
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 x (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 x (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64)))))
49.0%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))))
99.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))))
99.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))
77.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))
Compiler

Compiled 589 to 394 computations (33.1% saved)

sample0.0ms (0.0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Calls
Call 1
Inputs
-1/2
1/24
-1/6
1
(PI)
1/2
-2
2
Outputs
#s(literal -1/2 binary64)
#s(literal 6004799503160661/144115188075855872 binary64)
#s(literal -6004799503160661/36028797018963968 binary64)
#s(literal 1 binary64)
#s(literal 884279719003555/281474976710656 binary64)
#s(literal 1/2 binary64)
#s(literal -2 binary64)
#s(literal 2 binary64)
Samples
0.0ms0valid
Compiler

Compiled 10 to 10 computations (0.0% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
adjust: 0.0ms (0.0% of total)

series94.0ms (1.2%)

Memory
-7.8MiB live, 128.9MiB allocated; 13ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011078275
Stop Event
iter-limit
Counts
49 → 259
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
eps
(-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))
#s(literal -1/2 binary64)
(cos.f64 x)
x
(*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))
(*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))
#s(literal 1/24 binary64)
(*.f64 eps (cos.f64 x))
(*.f64 #s(literal -1/6 binary64) (sin.f64 x))
#s(literal -1/6 binary64)
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) x)
(PI.f64)
#s(literal 1/2 binary64)
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))))
(sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
(sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))
(*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))
(-.f64 (+.f64 eps x) x)
#s(literal -2 binary64)
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))))
#s(literal 2 binary64)
(*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))))
(sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))
(/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x))
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))
(cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))
(-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)))) (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps)))))) (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 x (fma.f64 eps (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal 1 binary64)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 eps (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) #s(literal 1 binary64)))))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))))))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x) (*.f64 eps (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 eps x))) #s(literal 1/2 binary64)))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) #s(literal 1/2 binary64)))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))))) #s(literal 1/2 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64)))))
#s(approx x x)
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))))
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 eps x))))
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x) (*.f64 #s(literal 1/6 binary64) eps)))))
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) eps (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))))
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/24 binary64) eps))
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x)))
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps x))))))
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x (fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps)))))))
#s(approx (* 1/24 (* eps (cos x))) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) eps)))
#s(approx (* 1/24 (* eps (cos x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/48 binary64) eps (*.f64 #s(literal 1/576 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (* 1/24 (* eps (cos x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/48 binary64) eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/17280 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/576 binary64) eps)))))))
#s(approx (* eps (cos x)) eps)
#s(approx (* eps (cos x)) (+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))))))
#s(approx (* eps (cos x)) (+.f64 eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1/24 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (* eps (cos x)) (+.f64 eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/720 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) eps)))))))
#s(approx (* -1/6 (sin x)) (*.f64 #s(literal -1/6 binary64) x))
#s(approx (* -1/6 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/6 binary64))))
#s(approx (* -1/6 (sin x)) (*.f64 x (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/36 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/6 binary64))))
#s(approx (* -1/6 (sin x)) (*.f64 x (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/36 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/30240 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/720 binary64))))) #s(literal 1/6 binary64))))
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 2 binary64))))))
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/6 binary64))))))
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/6 binary64))))))
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (cos.f64 eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (sin.f64 eps))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))) (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (sin.f64 eps))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (-.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/6 binary64) (sin.f64 eps)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) (*.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))) (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (sin.f64 eps))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (cos (+ x eps)) (cos.f64 eps))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps)))))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (cos.f64 eps))) (sin.f64 eps)))))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps))))) (sin.f64 eps)))))
#s(approx (+ x eps) (+.f64 eps x))
#s(approx (sin (+ (* (PI) 1/2) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#s(approx (sin (+ (* (PI) 1/2) x)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (sin (+ (* (PI) 1/2) x)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))))))
#s(approx (sin (+ (* (PI) 1/2) x)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))))))))
#s(approx (+ (* (PI) 1/2) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
#s(approx (+ (* (PI) 1/2) x) (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (fma.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))))))
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))))))))
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (* (+ (+ eps x) x) 1/2) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (+ (+ eps x) x) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 x (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))))))))))
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#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))))
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
#s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64))))
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/40320 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/720 binary64))))) #s(literal 1/2 binary64))))
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (cos.f64 x) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 x) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))))
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -2 binary64) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x))) (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))))))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x)))))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (fma.f64 #s(literal -1/48 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x)))))))))))
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)))))
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 eps (sin.f64 x)) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))))
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x)))))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/3840 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/48 binary64))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/3840 binary64) (*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/48 binary64))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal -1/48 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))))))))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal -1/48 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))))))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 eps (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))))
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))))))))
#s(approx (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))
#s(approx (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))
#s(approx (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))
#s(approx (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))
#s(approx (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))))))
#s(approx (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 eps (-.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))))
#s(approx (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 #s(literal 1/48 binary64) (*.f64 eps (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))) (*.f64 #s(literal 1/2 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))))
#s(approx (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
#s(approx (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (fma.f64 #s(literal -1/2 binary64) (PI.f64) (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 #s(literal -1 binary64) (PI.f64)))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (cos.f64 x))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (cos.f64 x))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (+ x eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))))
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
#s(approx (+ (+ eps x) x) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))))
#s(approx (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) eps)))))
#s(approx (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 x eps) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) eps))))))
#s(approx (+ (* (PI) 1/2) (+ eps x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (PI.f64) eps) (/.f64 x eps)))))
#s(approx (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) eps)))))
#s(approx (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (PI.f64) eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (cos.f64 x)))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x))))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x))))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x))))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal -1 binary64) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x))))))
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (cos (+ x eps)) (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))))
#s(approx (+ x eps) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1 binary64)))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps)))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps))))))
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps)))))
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)))))
#s(approx (+ (+ eps x) x) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 x eps)) #s(literal 1 binary64)))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps)))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps))))))
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps)))))
#s(approx (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) eps)) #s(literal 1/2 binary64)))))
#s(approx (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) eps)) #s(literal 1 binary64)))))
#s(approx (+ (* (PI) 1/2) (+ eps x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))) eps)) #s(literal 1 binary64)))))
#s(approx (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))))
#s(approx (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))))
#s(approx (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (/.f64 (PI.f64) eps) #s(literal 1 binary64)))))
Calls

6 calls:

TimeVariablePoint
13.0ms
x
0
13.0ms
eps
-inf
7.0ms
x
-inf
7.0ms
eps
0
6.0ms
eps
inf

rewrite168.0ms (2.1%)

Memory
-51.0MiB live, 209.2MiB allocated; 24ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053457
092420
1481403
22709403
04050389
Stop Event
iter-limit
node-limit
iter-limit
Counts
49 → 824
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))))
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
eps
(-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))
#s(literal -1/2 binary64)
(cos.f64 x)
x
(*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))
(*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))
#s(literal 1/24 binary64)
(*.f64 eps (cos.f64 x))
(*.f64 #s(literal -1/6 binary64) (sin.f64 x))
#s(literal -1/6 binary64)
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) x)
(PI.f64)
#s(literal 1/2 binary64)
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))))
(sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
(sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))
(*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))
(-.f64 (+.f64 eps x) x)
#s(literal -2 binary64)
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))))
#s(literal 2 binary64)
(*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))))
(sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))
(/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x))
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))
(cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))
(-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps)
(*.f64 eps (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)))
(neg.f64 (*.f64 (-.f64 (sin.f64 x) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)) eps))
(neg.f64 (*.f64 eps (-.f64 (sin.f64 x) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps))))
(fma.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(fma.f64 eps (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 eps (neg.f64 (sin.f64 x))))
(+.f64 (*.f64 eps (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)) (*.f64 eps (neg.f64 (sin.f64 x))))
(+.f64 (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) eps) (*.f64 (neg.f64 (sin.f64 x)) eps))
eps
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps))) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps))) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps))
(/.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x)))) (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (neg.f64 (sin.f64 x))))
(/.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) #s(literal 3 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))) (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (neg.f64 (sin.f64 x))))))
(/.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)) (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)))))
(neg.f64 (-.f64 (sin.f64 x) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)))
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x))))
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x)))
(fma.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x))))
(fma.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x)))
(fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x))))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) eps) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) eps) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x)))
(fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x))))
(fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x)))
(fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) (neg.f64 (sin.f64 x)))
(-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (neg.f64 (neg.f64 (sin.f64 x))))
(-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x))
(+.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x))))
(+.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x)))
(+.f64 (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps))
(+.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (neg.f64 (sin.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
(*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)
(*.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)))) (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps))))))
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)))
(fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
(fma.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps) eps (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
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#s(literal -1/2 binary64)
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x
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(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 (-.f64 (-.f64 (+.f64 eps x) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (PI.f64)))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) (+.f64 x (-.f64 (neg.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) (-.f64 x (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (PI.f64))))
(+.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (neg.f64 (PI.f64)))
(+.f64 (-.f64 (-.f64 (+.f64 eps x) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(+.f64 (-.f64 (neg.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (-.f64 (+.f64 eps x) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x)) (-.f64 (neg.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))
(+.f64 (+.f64 eps x) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (-.f64 (neg.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))))
(+.f64 (+.f64 eps x) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (PI.f64))))

eval165.0ms (2.0%)

Memory
44.5MiB live, 314.1MiB allocated; 57ms collecting garbage
Compiler

Compiled 37 463 to 5 705 computations (84.8% saved)

prune30.0ms (0.4%)

Memory
-0.2MiB live, 47.5MiB allocated; 2ms collecting garbage
Pruning

22 alts after pruning (20 fresh and 2 done)

PrunedKeptTotal
New91317930
Fresh7310
Picked415
Done011
Total92422946
Accuracy
100.0%
Counts
946 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.6%
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
50.5%
(-.f64 (sin.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
49.1%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
50.6%
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)))
36.5%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 eps #s(literal 0 binary64))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
99.3%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal -2 binary64))
99.6%
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64))
77.6%
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal -2 binary64))
5.7%
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))))
49.0%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)))
99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps))
41.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)))))))
99.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps #s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x))))
99.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))))
97.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
50.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
77.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))))
50.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
Compiler

Compiled 1 437 to 893 computations (37.9% saved)

sample1.0ms (0.0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Calls
Call 1
Inputs
1/2
-2
-1/2
2
-1
1/6
1
1/24
(PI)
(* 2 (PI))
Outputs
#s(literal 1/2 binary64)
#s(literal -2 binary64)
#s(literal -1/2 binary64)
#s(literal 2 binary64)
#s(literal -1 binary64)
#s(literal 6004799503160661/36028797018963968 binary64)
#s(literal 1 binary64)
#s(literal 6004799503160661/144115188075855872 binary64)
#s(literal 884279719003555/281474976710656 binary64)
#s(literal 884279719003555/140737488355328 binary64)
Samples
0.0ms0valid
Compiler

Compiled 14 to 12 computations (14.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
adjust: 0.0ms (0.0% of total)

series71.0ms (0.9%)

Memory
-18.4MiB live, 78.4MiB allocated; 11ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09507050
Stop Event
iter-limit
Counts
49 → 199
Calls
Call 1
Inputs
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))
(*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal -2 binary64) x)
#s(literal -2 binary64)
x
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
#s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))
(*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))
#s(literal -1/2 binary64)
(pow.f64 eps #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))))
(*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))
(*.f64 #s(literal -1 binary64) (sin.f64 x))
#s(literal -1 binary64)
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)))
#s(literal 1/6 binary64)
#s(literal 1 binary64)
(*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)))
#s(literal 1/24 binary64)
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))
(*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))
(-.f64 eps (PI.f64))
(PI.f64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))
(*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))
(-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))
(+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
Outputs
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (fma.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))))))))
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- eps (* -2 x)) eps)
#s(approx (- eps (* -2 x)) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
#s(approx (* -2 x) (*.f64 #s(literal -2 binary64) x))
#s(approx x x)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)))) (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps)))))) (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))
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#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 x (fma.f64 eps (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal 1 binary64)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 eps (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) #s(literal 1 binary64)))))
#s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))
#s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))
#s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/120 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64))))
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#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 2 binary64))))))
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/6 binary64))))))
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/6 binary64))))))
#s(approx (* x (- (* 1/6 (pow eps 2)) 1)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 x (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))))))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))
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#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))))))
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))))))))
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))
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#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))))
#s(approx (- eps (* -2 x)) (*.f64 #s(literal 2 binary64) x))
#s(approx (- eps (* -2 x)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
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#s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))
#s(approx (sin x) (sin.f64 x))
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#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))) x))))
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#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) x)))))
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (*.f64 x (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 (PI.f64) x) (/.f64 eps x)))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 1 binary64)))))
#s(approx (- eps (* -2 x)) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 eps x)) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x)))
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))) x))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))))
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) x)) #s(literal 1 binary64)))))
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) x)) #s(literal 2 binary64)))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))))
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#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x)))))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (fma.f64 #s(literal -1/48 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x)))))))))))
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/3840 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/48 binary64))))))
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/3840 binary64) (*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/48 binary64))))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 eps (sin.f64 x)) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x)))))))))
#s(approx (- eps (* -2 x)) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))))
#s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64))))
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/40320 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/720 binary64))))) #s(literal 1/2 binary64))))
#s(approx (pow eps 2) (pow.f64 eps #s(literal 2 binary64)))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal -1 binary64) (*.f64 eps x)))
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64))))))
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) #s(literal 1/2 binary64))))))
#s(approx (* x (- (* 1/6 (pow eps 2)) 1)) (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x))))
#s(approx (- (* 1/6 (pow eps 2)) 1) #s(literal -1 binary64))
#s(approx (- (* 1/6 (pow eps 2)) 1) (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))
#s(approx (* 1/6 (pow eps 2)) (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))))
#s(approx (- (* 1/24 (pow eps 2)) 1/2) #s(literal -1/2 binary64))
#s(approx (- (* 1/24 (pow eps 2)) 1/2) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (* 1/24 (pow eps 2)) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))))))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal -1/48 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))))))))))))
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#s(approx (* 1/2 (- eps (PI))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) eps)))))
#s(approx (- eps (PI)) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (PI.f64) eps)))))
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)) eps)))))
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (*.f64 eps (-.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) eps))) (*.f64 #s(literal -2 binary64) (/.f64 x eps)))))
#s(approx (+ eps (* 2 (PI))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) eps)))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps)))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps))))))
#s(approx (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps)))))
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)))))
#s(approx (- eps (* -2 x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 x eps)) #s(literal 1 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (cos.f64 x)))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x))))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x))))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x))))))
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) eps)))))
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps)))))
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps)))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps))))))
#s(approx (* (cos (* 1/2 (- eps (PI)))) (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps)))))))
#s(approx (cos (* 1/2 (- eps (PI)))) (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))))
#s(approx (* 1/2 (- eps (PI))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))))
#s(approx (- eps (PI)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (/.f64 (PI.f64) eps) #s(literal 1 binary64)))))
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps))))))
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)) eps)) #s(literal 1/2 binary64)))))
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)) eps)) #s(literal 1 binary64)))))
#s(approx (+ eps (* 2 (PI))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) eps)) #s(literal 1 binary64)))))
Calls

6 calls:

TimeVariablePoint
11.0ms
eps
0
5.0ms
eps
inf
5.0ms
x
-inf
5.0ms
x
inf
4.0ms
eps
-inf

rewrite220.0ms (2.7%)

Memory
-26.0MiB live, 146.7MiB allocated; 108ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
087615
0120611
1643607
23358607
04021556
Stop Event
iter-limit
node-limit
iter-limit
Counts
49 → 372
Calls
Call 1
Inputs
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))
(*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal -2 binary64) x)
#s(literal -2 binary64)
x
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
#s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))
(*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))
#s(literal -1/2 binary64)
(pow.f64 eps #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))))
(*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))
(*.f64 #s(literal -1 binary64) (sin.f64 x))
#s(literal -1 binary64)
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)))
#s(literal 1/6 binary64)
#s(literal 1 binary64)
(*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)))
#s(literal 1/24 binary64)
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))))
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))
(*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))
(-.f64 eps (PI.f64))
(PI.f64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))
(*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))
(-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))
(+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
Outputs
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(neg.f64 (*.f64 #s(literal 2 binary64) #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))))
(neg.f64 (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x eps))))) #s(literal 1/2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))))
(/.f64 (neg.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))))) #s(literal -2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x eps))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x eps))))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))))))
(neg.f64 (/.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x eps))))) #s(literal -2 binary64)))
(-.f64 (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))) #s(literal 2 binary64)) (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))) #s(literal 2 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
(/.f64 (*.f64 eps #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) eps) #s(literal 2 binary64))
(/.f64 eps #s(literal 2 binary64))
#s(literal 1/2 binary64)
eps
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 #s(literal -2 binary64) x) eps) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))
(neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal -2 binary64) x) eps)))
(neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
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(fma.f64 #s(literal 1/2 binary64) (+.f64 x eps) (*.f64 #s(literal 1/2 binary64) x))
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(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (fma.f64 eps eps (fma.f64 (PI.f64) (PI.f64) (*.f64 eps (PI.f64)))))
(neg.f64 (-.f64 (PI.f64) eps))
(fma.f64 (neg.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64)) eps)
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64))) eps)
(-.f64 eps (neg.f64 (neg.f64 (PI.f64))))
(-.f64 eps (PI.f64))
(+.f64 (neg.f64 (PI.f64)) eps)
(+.f64 eps (neg.f64 (PI.f64)))
(PI.f64)
(sin.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(/.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(literal 2 binary64))
(/.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 2 binary64))
(neg.f64 (*.f64 (-.f64 (*.f64 #s(literal -2 binary64) x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) #s(literal 1/2 binary64)))
(neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal -2 binary64) x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))))
(fma.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x))))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x))))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(+.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x))))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) eps)) eps)
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))
(/.f64 (-.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) (*.f64 (+.f64 x x) (+.f64 x x))) (-.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (+.f64 x x)))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)))) (-.f64 eps (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x))))
(/.f64 (+.f64 (pow.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) #s(literal 3 binary64)) (pow.f64 (+.f64 x x) #s(literal 3 binary64))) (fma.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (-.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (+.f64 x x)))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x))) (*.f64 eps (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x))))))
(/.f64 (-.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) (*.f64 (*.f64 #s(literal -2 binary64) x) (*.f64 #s(literal -2 binary64) x))) (+.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (pow.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 3 binary64))) (fma.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (fma.f64 (*.f64 #s(literal -2 binary64) x) (*.f64 #s(literal -2 binary64) x) (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (*.f64 #s(literal -2 binary64) x)))))
(neg.f64 (-.f64 (*.f64 #s(literal -2 binary64) x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)))
(fma.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64)) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 (cbrt.f64 (PI.f64)) (+.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 (neg.f64 x) #s(literal -2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))
(fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 #s(literal 2 binary64) (PI.f64) (fma.f64 #s(literal 2 binary64) x eps))
(fma.f64 #s(literal 2 binary64) x (fma.f64 (PI.f64) #s(literal 2 binary64) eps))
(fma.f64 #s(literal -2 binary64) (neg.f64 x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))
(fma.f64 x #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))
(-.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (*.f64 #s(literal -2 binary64) x))
(-.f64 eps (-.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (+.f64 x x)))
(-.f64 eps (fma.f64 (PI.f64) #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) x)))
(-.f64 eps (neg.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x))))
(+.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) eps)
(+.f64 (+.f64 x x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))
(+.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (+.f64 x x))
(+.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal 2 binary64) x eps))
(+.f64 eps (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 (PI.f64) (PI.f64)))) (+.f64 (PI.f64) (PI.f64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) eps)) eps)
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (PI.f64) (PI.f64)) eps)) eps)
(/.f64 (-.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (PI.f64))) (*.f64 eps eps)) (-.f64 (+.f64 (PI.f64) (PI.f64)) eps))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (PI.f64) #s(literal -2 binary64)))) (+.f64 eps (*.f64 (PI.f64) #s(literal -2 binary64))))
(/.f64 (+.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (+.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (PI.f64)) (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (PI.f64) (PI.f64)) eps))))
(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 binary64))) (fma.f64 eps eps (fma.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 eps (*.f64 (PI.f64) #s(literal -2 binary64))))))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 eps (+.f64 (PI.f64) (PI.f64))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (PI.f64))) (*.f64 eps (+.f64 (PI.f64) (PI.f64))))))
(neg.f64 (-.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) eps))
(fma.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64)) eps)
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) eps)
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) eps)
(fma.f64 (cbrt.f64 (PI.f64)) (+.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) eps)
(fma.f64 (PI.f64) #s(literal 2 binary64) eps)
(fma.f64 #s(literal 2 binary64) (PI.f64) eps)
(-.f64 (+.f64 (PI.f64) (PI.f64)) (neg.f64 eps))
(-.f64 eps (*.f64 (PI.f64) #s(literal -2 binary64)))
(+.f64 (+.f64 eps (PI.f64)) (PI.f64))
(+.f64 (+.f64 (PI.f64) (PI.f64)) eps)
(+.f64 (PI.f64) (+.f64 (PI.f64) eps))
(+.f64 eps (+.f64 (PI.f64) (PI.f64)))
(*.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (PI.f64)) (+.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64)))
(/.f64 (+.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64)))))
(neg.f64 (*.f64 (PI.f64) #s(literal -2 binary64)))
(fma.f64 (PI.f64) #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (PI.f64) (*.f64 #s(literal 1 binary64) (PI.f64)))
(-.f64 (PI.f64) (neg.f64 (PI.f64)))
(+.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 #s(literal 1 binary64) (PI.f64)))
(+.f64 (PI.f64) (PI.f64))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64)))
(log.f64 (*.f64 (exp.f64 (PI.f64)) (exp.f64 (PI.f64))))

eval85.0ms (1.0%)

Memory
-6.0MiB live, 137.5MiB allocated; 20ms collecting garbage
Compiler

Compiled 33 014 to 3 557 computations (89.2% saved)

prune31.0ms (0.4%)

Memory
17.6MiB live, 71.8MiB allocated; 3ms collecting garbage
Pruning

30 alts after pruning (28 fresh and 2 done)

PrunedKeptTotal
New54319562
Fresh6915
Picked505
Done022
Total55430584
Accuracy
100.0%
Counts
584 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.6%
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
50.5%
(-.f64 (sin.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
50.6%
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)))
99.3%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal -2 binary64))
99.4%
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (+.f64 x eps))) (+.f64 x eps)))))) #s(literal -2 binary64))
99.6%
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64))
99.4%
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))))) #s(literal -2 binary64))
99.3%
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64))
5.7%
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -2 binary64) x)))))))
49.0%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)))
99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps))
77.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps))
99.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps #s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x))))
99.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))))
9.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))))
9.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))))
76.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))))))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
50.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
50.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))))))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps))))
48.7%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps)))))))
24.0%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps)))))))
97.7%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64))))))))
97.7%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
49.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))))
Compiler

Compiled 2 407 to 1 579 computations (34.4% saved)

sample0.0ms (0.0%)

Memory
0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
Calls
Call 1
Inputs
1/2
-2
-1/2
1
2
(PI)
Outputs
#s(literal 1/2 binary64)
#s(literal -2 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal 884279719003555/281474976710656 binary64)
Samples
0.0ms0valid
Compiler

Compiled 8 to 8 computations (0.0% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
adjust: 0.0ms (0.0% of total)

series41.0ms (0.5%)

Memory
-2.2MiB live, 89.5MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06143872
Stop Event
iter-limit
Counts
39 → 134
Calls
Call 1
Inputs
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
x
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))
#s(literal 1 binary64)
(*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))
(pow.f64 eps #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))))
(*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))
(sin.f64 (+.f64 (PI.f64) x))
(+.f64 (PI.f64) x)
(PI.f64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))))
(*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))
(*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(cos.f64 x)
(sin.f64 x)
Outputs
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (fma.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))))))))
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx x x)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)))) (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps)))))) (sin.f64 eps)))) #s(literal 1 binary64)))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 x (fma.f64 eps (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal 1 binary64)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 eps (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) #s(literal 1 binary64)))))
#s(approx (sin (+ (PI) x)) (sin.f64 (PI.f64)))
#s(approx (sin (+ (PI) x)) (+.f64 (sin.f64 (PI.f64)) (*.f64 x (cos.f64 (PI.f64)))))
#s(approx (sin (+ (PI) x)) (+.f64 (sin.f64 (PI.f64)) (*.f64 x (+.f64 (cos.f64 (PI.f64)) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (PI.f64))))))))
#s(approx (sin (+ (PI) x)) (+.f64 (sin.f64 (PI.f64)) (*.f64 x (+.f64 (cos.f64 (PI.f64)) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (PI.f64)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (PI.f64))))))))))
#s(approx (+ (PI) x) (PI.f64))
#s(approx (+ (PI) x) (+.f64 x (PI.f64)))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))))))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x) (*.f64 eps (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 eps x))) #s(literal 1/2 binary64)))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) #s(literal 1/2 binary64)))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))))) #s(literal 1/2 binary64)))
#s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64))
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/1440 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/48 binary64))))) #s(literal 1/2 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64)))))
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 2 binary64))))))
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/6 binary64))))))
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/6 binary64))))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
#s(approx (sin (+ (PI) x)) (sin.f64 (+.f64 x (PI.f64))))
#s(approx (+ (PI) x) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x))))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))))
#s(approx (* -1/2 (cos x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 1 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x)))
#s(approx (sin (+ (PI) x)) (sin.f64 (-.f64 (PI.f64) (*.f64 #s(literal -1 binary64) x))))
#s(approx (+ (PI) x) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (PI.f64) x)) #s(literal 1 binary64)))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -2 binary64) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x))) (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))))))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x)))))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (fma.f64 #s(literal -1/48 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x)))))))))))
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/3840 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/48 binary64))))))
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/3840 binary64) (*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/48 binary64))))))
#s(approx eps eps)
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 eps (sin.f64 x)) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x)))))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))))
#s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64))))
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/40320 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/720 binary64))))) #s(literal 1/2 binary64))))
#s(approx (* eps eps) (pow.f64 eps #s(literal 2 binary64)))
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))))
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (+ 1 (* -1/2 (pow eps 2))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (cos.f64 x))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (cos.f64 x))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps)))))
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps)))))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps))))))
#s(approx (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps)))))
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (cos.f64 x)))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x))))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x))))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x))))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
Calls

6 calls:

TimeVariablePoint
5.0ms
eps
0
3.0ms
eps
inf
3.0ms
eps
-inf
2.0ms
x
-inf
2.0ms
x
inf

rewrite125.0ms (1.5%)

Memory
-7.5MiB live, 139.9MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068490
091490
1467482
22025482
04062447
Stop Event
iter-limit
node-limit
iter-limit
Counts
39 → 207
Calls
Call 1
Inputs
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
x
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)))
(-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))
#s(literal 1 binary64)
(*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))
(pow.f64 eps #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))))
(*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))
(sin.f64 (+.f64 (PI.f64) x))
(+.f64 (PI.f64) x)
(PI.f64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))))
(*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))
(*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(cos.f64 x)
(sin.f64 x)
Outputs
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 1/2 binary64))
(*.f64 (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))))) #s(literal -2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))))))
(neg.f64 (/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -2 binary64)))
(-.f64 (/.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (/.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
(neg.f64 (*.f64 #s(literal -1/2 binary64) eps))
#s(literal 1/2 binary64)
eps
(sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) eps) x)) x)
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)) x)
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 #s(literal -1/2 binary64) eps))) (+.f64 x (*.f64 #s(literal -1/2 binary64) eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) eps) (-.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 #s(literal -1/2 binary64) eps) (*.f64 x (*.f64 #s(literal -1/2 binary64) eps)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) eps))) (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))
(neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 eps #s(literal 1/2 binary64) x)
(-.f64 (*.f64 #s(literal 1/2 binary64) eps) (neg.f64 x))
(-.f64 x (*.f64 #s(literal -1/2 binary64) eps))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps))
x
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos eps) 1) (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps))
(*.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 eps)) (neg.f64 eps))
(*.f64 (*.f64 #s(literal -1/2 binary64) (fabs.f64 eps)) (fabs.f64 eps))
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal -1/2 binary64)))
(*.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))
(neg.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(*.f64 (pow.f64 eps #s(literal 1 binary64)) eps)
(*.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)))
(*.f64 (neg.f64 (fabs.f64 eps)) (neg.f64 (fabs.f64 eps)))
(*.f64 (fabs.f64 (fabs.f64 eps)) (fabs.f64 (fabs.f64 eps)))
(*.f64 (pow.f64 eps (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 eps (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 (fabs.f64 eps) (fabs.f64 eps))
(*.f64 eps eps)
(pow.f64 (neg.f64 eps) #s(literal 2 binary64))
(pow.f64 (fabs.f64 eps) #s(literal 2 binary64))
(pow.f64 eps #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -2 binary64)))
(neg.f64 (*.f64 eps (neg.f64 eps)))
(neg.f64 (*.f64 (neg.f64 eps) eps))
(fabs.f64 (*.f64 eps eps))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
#s(literal -1/2 binary64)
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(/.f64 (+.f64 (pow.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))) (*.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (neg.f64 (sin.f64 x))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))))
(neg.f64 (-.f64 (sin.f64 x) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)))
(fma.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x)))
(fma.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(-.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (neg.f64 (neg.f64 (sin.f64 x))))
(-.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(+.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (neg.f64 (sin.f64 x)))
(+.f64 (neg.f64 (sin.f64 x)) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))
(*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
(neg.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(neg.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
(fma.f64 (sin.f64 x) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 (fabs.f64 x)))
(cos.f64 (fabs.f64 (fabs.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 (fabs.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
(sin.f64 x)

eval36.0ms (0.4%)

Memory
3.0MiB live, 49.0MiB allocated; 3ms collecting garbage
Compiler

Compiled 12 218 to 1 756 computations (85.6% saved)

prune21.0ms (0.3%)

Memory
-16.2MiB live, 31.4MiB allocated; 1ms collecting garbage
Pruning

31 alts after pruning (26 fresh and 5 done)

PrunedKeptTotal
New2878295
Fresh51823
Picked235
Done022
Total29431325
Accuracy
100.0%
Counts
325 → 31
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.6%
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
50.5%
(-.f64 (sin.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
50.5%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
50.6%
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)))
99.4%
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (+.f64 x eps))) (+.f64 x eps)))))) #s(literal -2 binary64))
99.6%
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -2 binary64))
99.4%
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))))) #s(literal -2 binary64))
99.3%
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64))
5.7%
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -2 binary64) x)))))))
49.0%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps))
77.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps))
99.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps #s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x))))
99.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))))
98.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (sin.f64 x))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x))))
9.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 x x)) (-.f64 (PI.f64) x))))))
9.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))))
9.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)) x)))))
9.2%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (PI.f64))) (PI.f64))))))
9.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))))
76.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))))))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
50.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps))))
48.7%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps)))))))
97.7%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64))))))))
97.7%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))))
77.0%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
49.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))))
Compiler

Compiled 1 260 to 819 computations (35.0% saved)

regimes182.0ms (2.2%)

Memory
37.4MiB live, 279.5MiB allocated; 12ms collecting garbage
Counts
1 → 1
3 → 1
6 → 1
13 → 1
21 → 1
29 → 1
30 → 1
39 → 1
60 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
Call 2
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
Call 3
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))))
Call 4
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps)))))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64))))))))
Call 5
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps))))
Call 6
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x))))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (PI.f64))) (PI.f64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 x x)) (-.f64 (PI.f64) x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (sin.f64 x))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x))))
Call 7
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x))))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (PI.f64))) (PI.f64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 x x)) (-.f64 (PI.f64) x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x))))
Call 8
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x))))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (PI.f64))) (PI.f64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 x x)) (-.f64 (PI.f64) x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x))))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal -2 binary64))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
Outputs
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64))
Call 9
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x))))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (PI.f64))) (PI.f64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)) x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 x x)) (-.f64 (PI.f64) x))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x))))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal -2 binary64))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -2 binary64))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64))
(-.f64 (sin.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -2 binary64) x)))))))
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (+.f64 x eps))) (+.f64 x eps)))))) #s(literal -2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 x (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 x (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps #s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 eps #s(literal 0 binary64))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))))) #s(literal -2 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x)))
(-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)))))))
Outputs
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -2 binary64))
Calls

27 calls:

16.0ms
x
14.0ms
eps
10.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
10.0ms
eps
10.0ms
x
Results
AccuracySegmentsBranch
50.3%1x
50.3%1eps
50.3%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
77.0%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
77.0%1x
77.0%1eps
97.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.7%1x
97.7%1eps
97.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.7%1eps
97.7%1x
97.9%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.9%1x
97.9%1eps
98.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.5%1x
98.5%1eps
98.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.5%1x
98.5%1eps
99.3%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.3%1x
99.3%1eps
99.6%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 2 318 to 546 computations (76.4% saved)

derivations65.0ms (0.8%)

Memory
-21.9MiB live, 72.5MiB allocated; 2ms collecting garbage
Stop Event
fuel
Compiler

Compiled 420 to 124 computations (70.5% saved)

preprocess71.0ms (0.9%)

Memory
-16.2MiB live, 130.0MiB allocated; 7ms collecting garbage
Compiler

Compiled 457 to 155 computations (66.1% saved)

end0.0ms (0.0%)

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

Profiling

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