ENA, Section 1.4, Mentioned, A

Time bar (total: 5.5s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%49.6%50.4%0%0%0%0
100%49.6%0%50.4%0%0%0%1
Compiler

Compiled 12 to 9 computations (25% saved)

sample4.0s (72.6%)

Results
2.9s4399×body2048valid
675.0ms2100×body1024valid
278.0ms1014×body512valid
110.0ms743×body256valid
Bogosity

preprocess110.0ms (2%)

Algorithm
1×egg-herbie
Rules
22×sub-neg
16×fma-def
12×+-commutative
8×associate--r+
8×associate-+l-
Problems
134×(-.f64 1 (cos.f64 x))
122×No Errors
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01033
11733
22233
33133
44133
55533
67033
77933
88233
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 (neg.f64 x)))
Outputs
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 x))
(-.f64 1 (cos.f64 (neg.f64 x)))
(-.f64 1 (cos.f64 x))
Symmetry

(abs x)

Compiler

Compiled 15 to 10 computations (33.3% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶52.3%
(-.f64 1 (cos.f64 x))
▶52.3%
(-.f64 1 (cos.f64 x))
Compiler

Compiled 10 to 8 computations (20% saved)

localize85.0ms (1.6%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
✓52.3%
(-.f64 1 (cos.f64 x))
Compiler

Compiled 10 to 6 computations (40% saved)

series1.0ms (0%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(-.f64 1 (cos.f64 x))
0.0ms
x
@inf
(-.f64 1 (cos.f64 x))
0.0ms
x
@-inf
(-.f64 1 (cos.f64 x))

rewrite118.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
1386×pow1
1278×add-exp-log
1278×log1p-expm1-u
1278×expm1-log1p-u
1252×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
114011
2169111
Stop Event
1×node limit
Counts
1 → 28
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
Outputs
(+.f64 1 (neg.f64 (cos.f64 x)))
(+.f64 1 (*.f64 (neg.f64 (cos.f64 x)) 1))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(*.f64 1 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (neg.f64 (cos.f64 x)))))
(/.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x))))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))

simplify119.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
1068×associate-/l*
990×div-sub
824×distribute-lft-in
782×distribute-rgt-in
714×associate-/r*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
092800
1231740
2683670
33300670
Stop Event
1×node limit
Counts
32 → 48
Calls
Call 1
Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/2 (pow.f64 x 2)))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 -1/40320 (pow.f64 x 8)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2)))))
(+.f64 1 (neg.f64 (cos.f64 x)))
(+.f64 1 (*.f64 (neg.f64 (cos.f64 x)) 1))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(*.f64 1 (-.f64 1 (cos.f64 x)))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (neg.f64 (cos.f64 x)))))
(/.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x))))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
Outputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/2 (*.f64 x x)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 -1/40320 (pow.f64 x 8)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/2 (*.f64 x x) (*.f64 1/720 (pow.f64 x 6)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 1/2 (*.f64 x x) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(+.f64 1 (neg.f64 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(+.f64 1 (*.f64 (neg.f64 (cos.f64 x)) 1))
(-.f64 1 (cos.f64 x))
(+.f64 (neg.f64 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(*.f64 1 (-.f64 1 (cos.f64 x)))
(-.f64 1 (cos.f64 x))
(*.f64 (-.f64 1 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(*.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))
(-.f64 1 (cos.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(*.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (cos.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) 3) -1) (fma.f64 (cos.f64 x) (-.f64 -1 (cos.f64 x)) -1))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))) (-.f64 1 (pow.f64 (cos.f64 x) 3))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (cos.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) 3) -1) (fma.f64 (cos.f64 x) (-.f64 -1 (cos.f64 x)) -1))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (cos.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) 3) -1) (fma.f64 (cos.f64 x) (-.f64 -1 (cos.f64 x)) -1))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (cos.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) 3) -1) (fma.f64 (cos.f64 x) (-.f64 -1 (cos.f64 x)) -1))
(/.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (+.f64 1 (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (neg.f64 (cos.f64 x)))))
(*.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (+.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (cos.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (+.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) 3) -1) (fma.f64 (cos.f64 x) (-.f64 -1 (cos.f64 x)) -1))
(/.f64 (-.f64 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x))))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))) (sin.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(pow.f64 (-.f64 1 (cos.f64 x)) 1)
(-.f64 1 (cos.f64 x))
(pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)
(-.f64 1 (cos.f64 x))
(pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)
(-.f64 1 (cos.f64 x))
(pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)
(-.f64 1 (cos.f64 x))
(sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))
(-.f64 1 (cos.f64 x))
(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))
(-.f64 1 (cos.f64 x))
(expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))
(exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))
(log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))
(-.f64 1 (cos.f64 x))

eval13.0ms (0.2%)

Compiler

Compiled 559 to 355 computations (36.5% saved)

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New46248
Fresh000
Picked101
Done000
Total47249
Accuracy
100.0%
Counts
49 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶99.7%
(*.f64 1/2 (*.f64 x x))
▶100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶99.7%
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 28 to 20 computations (28.6% saved)

localize91.0ms (1.7%)

Localize:

Found 2 expressions with local error:

NewAccuracyProgram
✓100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓100.0%
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 30 to 17 computations (43.3% saved)

series11.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
5.0ms
x
@0
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
4.0ms
x
@inf
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
1.0ms
x
@-inf
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
0.0ms
x
@0
(*.f64 1/2 (*.f64 x x))
0.0ms
x
@inf
(*.f64 1/2 (*.f64 x x))

rewrite68.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
1098×log-prod
734×prod-exp
650×pow-prod-down
552×pow-prod-up
484×pow-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01234
124834
2288134
Stop Event
1×node limit
Counts
2 → 60
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 x x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
Outputs
(+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 x x) 1/4))
(+.f64 0 (*.f64 1/2 (*.f64 x x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x)))) 1)
(pow.f64 (*.f64 1/2 (*.f64 x x)) 1)
(pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 6) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 1/2 x))) 3)
(pow.f64 (*.f64 (pow.f64 x 3) (pow.f64 (*.f64 1/2 x) 3)) 1/3)
(pow.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 1/2 x))) 2)
(pow.f64 (*.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 x 3)) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (*.f64 x x)))))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 6))
(expm1.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x))))
(exp.f64 (log.f64 (*.f64 1/2 (*.f64 x x))))
(exp.f64 (*.f64 (log.f64 (*.f64 1/2 (*.f64 x x))) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 1/2 (*.f64 x x))) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x)))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 6)) 1/3))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))) 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (*.f64 1/2 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (*.f64 1/2 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 (*.f64 1/2 x)) 1)))
(exp.f64 (+.f64 (log.f64 (*.f64 1/2 x)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 1/2 x)) 1) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 1/2 x)) 1) (*.f64 (log.f64 x) 1)))
(log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 x x))))
(+.f64 0 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 1)
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (/.f64 x -2)))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x)) (cos.f64 (/.f64 x -2)))
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 1)
(pow.f64 (cbrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 3)
(pow.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 2)
(sqrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 2))
(log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))))
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 3))
(expm1.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))))
(exp.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 2))
(exp.f64 (+.f64 (log.f64 (sin.f64 x)) (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (log.f64 (tan.f64 (*.f64 1/2 x)))))
(exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1)))
(exp.f64 (+.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) (*.f64 (log.f64 (sin.f64 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1) (log.f64 (sin.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1) (*.f64 (log.f64 (sin.f64 x)) 1)))
(log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))))

simplify72.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
1456×log-prod
1436×associate-*r*
1202×associate-*l*
1028×fma-def
622×prod-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01851746
14241680
210941680
356641680
Stop Event
1×node limit
Counts
84 → 85
Calls
Call 1
Inputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/2 (pow.f64 x 2)))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 -1/40320 (pow.f64 x 8)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 x x) 1/4))
(+.f64 0 (*.f64 1/2 (*.f64 x x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x)))) 1)
(pow.f64 (*.f64 1/2 (*.f64 x x)) 1)
(pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 6) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 1/2 x))) 3)
(pow.f64 (*.f64 (pow.f64 x 3) (pow.f64 (*.f64 1/2 x) 3)) 1/3)
(pow.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 1/2 x))) 2)
(pow.f64 (*.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 x 3)) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (*.f64 x x)))))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 6))
(expm1.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x))))
(exp.f64 (log.f64 (*.f64 1/2 (*.f64 x x))))
(exp.f64 (*.f64 (log.f64 (*.f64 1/2 (*.f64 x x))) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 1/2 (*.f64 x x))) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x)))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 6)) 1/3))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))) 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (*.f64 1/2 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (*.f64 1/2 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 (*.f64 1/2 x)) 1)))
(exp.f64 (+.f64 (log.f64 (*.f64 1/2 x)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 1/2 x)) 1) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 1/2 x)) 1) (*.f64 (log.f64 x) 1)))
(log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 x x))))
(+.f64 0 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 1)
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (/.f64 x -2)))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x)) (cos.f64 (/.f64 x -2)))
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 1)
(pow.f64 (cbrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 3)
(pow.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 2)
(sqrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 2))
(log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))))
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 3))
(expm1.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))))
(exp.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 2))
(exp.f64 (+.f64 (log.f64 (sin.f64 x)) (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (log.f64 (tan.f64 (*.f64 1/2 x)))))
(exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1)))
(exp.f64 (+.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) (*.f64 (log.f64 (sin.f64 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1) (log.f64 (sin.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1) (*.f64 (log.f64 (sin.f64 x)) 1)))
(log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))))
Outputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/2 (*.f64 x x)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 -1/40320 (pow.f64 x 8)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/720 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/2 (*.f64 x x) (*.f64 1/720 (pow.f64 x 6)))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 1/2 (*.f64 x x) (*.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 x x) 1/4))
(*.f64 1/2 (*.f64 x x))
(+.f64 0 (*.f64 1/2 (*.f64 x x)))
(*.f64 1/2 (*.f64 x x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x))))
(*.f64 (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x))) 3)
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x)))) 1)
(*.f64 1/2 (*.f64 x x))
(pow.f64 (*.f64 1/2 (*.f64 x x)) 1)
(*.f64 1/2 (*.f64 x x))
(pow.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) 3)
(*.f64 1/2 (*.f64 x x))
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(fabs.f64 (*.f64 1/2 (*.f64 x x)))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 6) 1/3)
(*.f64 1/2 (*.f64 x x))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(*.f64 1/2 (*.f64 x x))
(pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 1/2 x))) 3)
(*.f64 1/2 (*.f64 x x))
(pow.f64 (*.f64 (pow.f64 x 3) (pow.f64 (*.f64 1/2 x) 3)) 1/3)
(*.f64 1/2 (*.f64 x x))
(pow.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 1/2 x))) 2)
(*.f64 1/2 (*.f64 x x))
(pow.f64 (*.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 x 3)) 1/3)
(*.f64 1/2 (*.f64 x x))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(fabs.f64 (*.f64 1/2 (*.f64 x x)))
(log.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 x (log.f64 (sqrt.f64 (exp.f64 x))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (*.f64 x x)))))
(*.f64 1/2 (*.f64 x x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 6))
(*.f64 1/2 (*.f64 x x))
(expm1.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (log.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (*.f64 1/2 (*.f64 x x))) 1))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 1/2 (*.f64 x x))) 1) 1))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x)))) 3))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 6)) 1/3))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))) 2))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (*.f64 1/2 x)) 1)))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (*.f64 1/2 x))))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 (*.f64 1/2 x)) 1)))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (+.f64 (log.f64 (*.f64 1/2 x)) (*.f64 (log.f64 x) 1)))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 1/2 x)) 1) (log.f64 x)))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 1/2 x)) 1) (*.f64 (log.f64 x) 1)))
(*.f64 1/2 (*.f64 x x))
(log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 1/2 (*.f64 x x))
(+.f64 0 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 1)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 1/2 x))) (cos.f64 (/.f64 x -2)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (/.f64 x -2)) (sin.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (/.f64 x -2))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (/.f64 x -2))))
(/.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) (sin.f64 x)) (cos.f64 (/.f64 x -2)))
(/.f64 (sin.f64 x) (/.f64 (cos.f64 (/.f64 x -2)) (sin.f64 (*.f64 1/2 x))))
(*.f64 (/.f64 (sin.f64 x) (cos.f64 (/.f64 x -2))) (sin.f64 (*.f64 1/2 x)))
(*.f64 (sin.f64 x) (/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (/.f64 x -2))))
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 1)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(pow.f64 (cbrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 3)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(pow.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 2) 1/2)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(pow.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 3) 1/3)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(pow.f64 (sqrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 2)
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(sqrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 2))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(log.f64 (pow.f64 (exp.f64 (sin.f64 x)) (tan.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))) 3))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(expm1.f64 (log1p.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 1))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))) 1) 1))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 3))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 1/3))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x))))) 2))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (+.f64 (log.f64 (sin.f64 x)) (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1)))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (log.f64 (tan.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sin.f64 x)) 1) (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1)))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (+.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) (*.f64 (log.f64 (sin.f64 x)) 1)))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1) (log.f64 (sin.f64 x))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 (tan.f64 (*.f64 1/2 x))) 1) (*.f64 (log.f64 (sin.f64 x)) 1)))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))
(log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))))
(*.f64 (sin.f64 x) (tan.f64 (*.f64 1/2 x)))

eval21.0ms (0.4%)

Compiler

Compiled 932 to 640 computations (31.3% saved)

prune11.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New84185
Fresh000
Picked022
Done000
Total84387
Accuracy
100.0%
Counts
87 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.0%
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
✓100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓99.7%
(*.f64 1/2 (*.f64 x x))
▶99.0%
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
✓100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓99.7%
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 42 to 32 computations (23.8% saved)

localize33.0ms (0.6%)

Localize:

Found 2 expressions with local error:

NewAccuracyProgram
✓99.6%
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
✓99.3%
(*.f64 x (sqrt.f64 1/2))
Compiler

Compiled 17 to 14 computations (17.6% saved)

series2.0ms (0%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(*.f64 x (sqrt.f64 1/2))
0.0ms
x
@-inf
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
0.0ms
x
@inf
(*.f64 x (sqrt.f64 1/2))
0.0ms
x
@0
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
0.0ms
x
@-inf
(*.f64 x (sqrt.f64 1/2))

rewrite57.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
1456×pow1
1338×add-exp-log
1338×log1p-expm1-u
1338×expm1-log1p-u
1306×add-log-exp
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0928
118424
2195824
Stop Event
1×node limit
Counts
2 → 35
Calls
Call 1
Inputs
(*.f64 x (sqrt.f64 1/2))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
Outputs
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) 1)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 1)
(pow.f64 (*.f64 1/2 (*.f64 x x)) 1/2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) 2)
(sqrt.f64 (*.f64 1/2 (*.f64 x x)))
(fabs.f64 (*.f64 x (sqrt.f64 1/2)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 1/2)))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 1/2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (*.f64 1/2 (*.f64 x x))) 1)
(*.f64 x (*.f64 (sqrt.f64 1/2) (*.f64 x (sqrt.f64 1/2))))
(*.f64 1/2 (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x (sqrt.f64 1/2))))
(*.f64 (*.f64 x (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)))
(*.f64 (*.f64 1/2 (*.f64 x x)) 1)
(*.f64 1 (*.f64 1/2 (*.f64 x x)))
(*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)))
(*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) (*.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)) (cbrt.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 (*.f64 x x) 1/2)
(*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) (*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) (sqrt.f64 (*.f64 x (sqrt.f64 1/2)))) (sqrt.f64 (*.f64 x (sqrt.f64 1/2))))
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) x) (sqrt.f64 1/2))
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2)) x)
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) (cbrt.f64 (*.f64 1/2 (*.f64 x x)))) (cbrt.f64 (*.f64 x (sqrt.f64 1/2))))
(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4))
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 1/2))
(cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3))
(expm1.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x))))
(exp.f64 (log.f64 (*.f64 1/2 (*.f64 x x))))
(log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 x x))))

simplify67.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
1238×fma-def
1220×distribute-rgt-in
1210×distribute-lft-in
1076×log-prod
606×associate-+r+
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0781121
1193723
2675637
32254637
47394637
Stop Event
1×node limit
Counts
47 → 44
Calls
Call 1
Inputs
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) 1)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 1)
(pow.f64 (*.f64 1/2 (*.f64 x x)) 1/2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) 2)
(sqrt.f64 (*.f64 1/2 (*.f64 x x)))
(fabs.f64 (*.f64 x (sqrt.f64 1/2)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 1/2)))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 1/2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (*.f64 1/2 (*.f64 x x))) 1)
(*.f64 x (*.f64 (sqrt.f64 1/2) (*.f64 x (sqrt.f64 1/2))))
(*.f64 1/2 (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x (sqrt.f64 1/2))))
(*.f64 (*.f64 x (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)))
(*.f64 (*.f64 1/2 (*.f64 x x)) 1)
(*.f64 1 (*.f64 1/2 (*.f64 x x)))
(*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)))
(*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) (*.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)) (cbrt.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 (*.f64 x x) 1/2)
(*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) (*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) (sqrt.f64 (*.f64 x (sqrt.f64 1/2)))) (sqrt.f64 (*.f64 x (sqrt.f64 1/2))))
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) x) (sqrt.f64 1/2))
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2)) x)
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) (cbrt.f64 (*.f64 1/2 (*.f64 x x)))) (cbrt.f64 (*.f64 x (sqrt.f64 1/2))))
(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4))
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 1/2))
(cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3))
(expm1.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x))))
(exp.f64 (log.f64 (*.f64 1/2 (*.f64 x x))))
(log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 x x))))
Outputs
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) 1)
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 1)
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(pow.f64 (*.f64 1/2 (*.f64 x x)) 1/2)
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) 3)
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 3) 1/3)
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) 2)
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(sqrt.f64 (*.f64 1/2 (*.f64 x x)))
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(fabs.f64 (*.f64 x (sqrt.f64 1/2)))
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 1/2)))
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 3))
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (+.f64 1 (*.f64 x (sqrt.f64 1/2))) -1)
(+.f64 (*.f64 x (sqrt.f64 1/2)) 0)
(*.f64 x (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/2 (*.f64 x x))) 1)
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 (sqrt.f64 1/2) (*.f64 x (sqrt.f64 1/2))))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x (sqrt.f64 1/2))))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (*.f64 x (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (*.f64 1/2 (*.f64 x x)) 1)
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 1 (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)))
(*.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/2))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)))
(*.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/2))) (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))))
(*.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) (cbrt.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 (cbrt.f64 (*.f64 1/2 (*.f64 x x))) (*.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)) (cbrt.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/2))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4)))
(*.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/2))) (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))))
(*.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 x 4))) (cbrt.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 (*.f64 x x) 1/2)
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) (*.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) (*.f64 x (sqrt.f64 1/2))))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) (sqrt.f64 (*.f64 x (sqrt.f64 1/2)))) (sqrt.f64 (*.f64 x (sqrt.f64 1/2))))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) x) (sqrt.f64 1/2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2)) x)
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(*.f64 (*.f64 (*.f64 x (sqrt.f64 1/2)) (cbrt.f64 (*.f64 1/2 (*.f64 x x)))) (cbrt.f64 (*.f64 x (sqrt.f64 1/2))))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) 4))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 1/2))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(expm1.f64 (log1p.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(exp.f64 (log.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
(log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 x (*.f64 x (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))

eval10.0ms (0.2%)

Compiler

Compiled 412 to 313 computations (24% saved)

prune6.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New43144
Fresh000
Picked101
Done112
Total45247
Accuracy
100.0%
Counts
47 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶99.7%
(*.f64 x (*.f64 x 1/2))
✓100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶99.7%
(*.f64 x (*.f64 x 1/2))
Compiler

Compiled 28 to 20 computations (28.6% saved)

localize20.0ms (0.4%)

Compiler

Compiled 12 to 8 computations (33.3% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Accuracy
100.0%
Counts
2 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓99.7%
(*.f64 x (*.f64 x 1/2))
Compiler

Compiled 42 to 30 computations (28.6% saved)

regimes9.0ms (0.2%)

Counts
5 → 1
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(-.f64 1 (cos.f64 x))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
Outputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
Calls

3 calls:

4.0ms
x
2.0ms
(cos.f64 x)
2.0ms
(-.f64 1 (cos.f64 x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 1 (cos.f64 x))
100.0%1(cos.f64 x)
Compiler

Compiled 38 to 27 computations (28.9% saved)

regimes14.0ms (0.3%)

Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 x x))
(*.f64 x (*.f64 x 1/2))
(-.f64 1 (cos.f64 x))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
Outputs
(*.f64 x (*.f64 x 1/2))
Calls

3 calls:

6.0ms
(cos.f64 x)
4.0ms
x
2.0ms
(-.f64 1 (cos.f64 x))
Results
AccuracySegmentsBranch
99.7%1x
99.7%1(-.f64 1 (cos.f64 x))
99.7%1(cos.f64 x)
Compiler

Compiled 31 to 22 computations (29% saved)

regimes4.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 x x))
Outputs
(*.f64 1/2 (*.f64 x x))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
8×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01447
11847
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
Outputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(*.f64 x (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 20 to 14 computations (30% saved)

soundness482.0ms (8.8%)

Rules
1386×pow1
1278×add-exp-log
1278×log1p-expm1-u
1278×expm1-log1p-u
1252×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
114011
2169111
092800
1231740
2683670
33300670
092800
1231740
2683670
33300670
01234
124834
2288134
0781121
1193723
2675637
32254637
47394637
Stop Event
1×node limit
1×node limit
1×node limit
1×node limit
1×node limit
Compiler

Compiled 220 to 132 computations (40% saved)

end0.0ms (0%)

preprocess61.0ms (1.1%)

Remove

(abs x)

Compiler

Compiled 84 to 58 computations (31% saved)

Profiling

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