ENA, Section 1.4, Mentioned, A

Details

Time bar (total: 3.5s)

analyze11.0ms (0.3%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%49.6%50.4%0%0%0%0
0%0%97.8%2.2%0%0%0%1
0%0%192.8%-92.8%0%0%0%2
33%94.9%192.8%-187.8%0%0%0%3
49.6%189.9%192.8%-282.8%0%0%0%4
59.6%284.9%192.8%-377.8%0%0%0%5
66.3%379.9%192.8%-472.8%0%0%0%6
71.1%474.9%192.8%-567.8%0%0%0%7
74.7%569.9%192.8%-662.7%0%0%0%8
77.5%664.9%192.8%-757.7%0%0%0%9
79.8%759.9%192.8%-852.7%0%0%0%10
81.6%854.9%192.8%-947.7%0%0%0%11
83.1%949.9%192.8%-1042.7%0%0%0%12
Compiler

Compiled 12 to 9 computations (25% saved)

sample2.7s (75.2%)

Results
1.1s2213×body1024valid
912.0ms4531×body256valid
363.0ms1066×body512valid
310.0ms446×body2048valid
Bogosity

preprocess14.0ms (0.4%)

Algorithm
2×egg-herbie
Rules
16×sub-neg
12×fma-def
8×+-commutative
6×associate--r+
6×associate-+l-
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11111
21511
32211
42911
53911
65011
76211
86511
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 1 (cos.f64 x))
Outputs
(-.f64 1 (cos.f64 x))
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify16.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
16×sub-neg
12×fma-def
8×+-commutative
6×associate--r+
6×associate-+l-
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11111
21511
32211
42911
53911
65011
76211
86511
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(-.f64 1 (cos.f64 x))
Outputs
(-.f64 1 (cos.f64 x))

eval0.0ms (0%)

Compiler

Compiled 5 to 4 computations (20% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Accurracy
54.3%
Counts
2 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶54.3%
(-.f64 1 (cos.f64 x))
▶54.3%
(-.f64 1 (cos.f64 x))
Compiler

Compiled 10 to 8 computations (20% saved)

localize82.0ms (2.3%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓54.3%
(-.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))

rewrite56.0ms (1.6%)

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))))

simplify53.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
1070×associate-/l*
998×div-sub
824×distribute-lft-in
782×distribute-rgt-in
724×associate-/r*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
093800
1231740
2679670
33306670
Stop Event
1×node limit
Counts
32 → 44
Calls
Call 1
Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(+.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 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (*.f64 1/2 (*.f64 x x)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (*.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))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/24 (pow.f64 x 4)) (+.f64 (*.f64 1/720 (pow.f64 x 6)) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (*.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/24 (pow.f64 x 4) (*.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 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) 1) (+.f64 1 (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.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 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) 1) (+.f64 1 (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.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 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) 1) (+.f64 1 (cos.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 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 x))) (neg.f64 (+.f64 1 (cos.f64 x))))
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) 1) (+.f64 1 (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.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 1 (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x)))) (-.f64 1 (neg.f64 (cos.f64 x))))
(/.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 x)) 1) (+.f64 1 (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.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))

eval10.0ms (0.3%)

Compiler

Compiled 491 to 309 computations (37.1% saved)

prune12.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New42244
Fresh000
Picked101
Done000
Total43245
Accurracy
100.0%
Counts
45 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶100.0%
(*.f64 1/2 (*.f64 x x))
▶100.0%
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶100.0%
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 28 to 20 computations (28.6% saved)

localize119.0ms (3.3%)

Local Accuracy

Found 2 expressions with local accuracy:

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

Compiled 30 to 17 computations (43.3% saved)

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

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

rewrite62.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
1822×pow1
1680×add-exp-log
1680×log1p-expm1-u
1680×expm1-log1p-u
1642×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01024
120924
2239224
Stop Event
1×node limit
Counts
2 → 31
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 x x))
(tan.f64 (/.f64 x 2))
Outputs
(-.f64 (+.f64 1 (*.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 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x))
(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))))
(-.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)
(*.f64 (tan.f64 (*.f64 1/2 x)) 1)
(*.f64 1 (tan.f64 (*.f64 1/2 x)))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))
(/.f64 1 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (neg.f64 (sin.f64 (*.f64 1/2 x))) (neg.f64 (cos.f64 (*.f64 1/2 x))))
(pow.f64 (tan.f64 (*.f64 1/2 x)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))
(exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 1/2 x))))

simplify53.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
1782×log-prod
1570×fma-def
1230×associate-*r*
1092×associate-*l*
758×distribute-rgt-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0941109
12091013
2706917
34127917
Stop Event
1×node limit
Counts
55 → 50
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 x)
(+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 17/40320 (pow.f64 x 7)) (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(-.f64 (+.f64 1 (*.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 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) x))
(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))))
(-.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)
(*.f64 (tan.f64 (*.f64 1/2 x)) 1)
(*.f64 1 (tan.f64 (*.f64 1/2 x)))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))
(/.f64 1 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (neg.f64 (sin.f64 (*.f64 1/2 x))) (neg.f64 (cos.f64 (*.f64 1/2 x))))
(pow.f64 (tan.f64 (*.f64 1/2 x)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))
(exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))
(log1p.f64 (expm1.f64 (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 x)
(+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(*.f64 x (fma.f64 x (*.f64 x 1/24) 1/2))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/240 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (*.f64 x 1/24) 1/2) (*.f64 1/240 (pow.f64 x 5)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 17/40320 (pow.f64 x 7)) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/240 (pow.f64 x 5) (*.f64 17/40320 (pow.f64 x 7)))))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (*.f64 x (fma.f64 x (*.f64 x 1/24) 1/2))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(-.f64 (+.f64 1 (*.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 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3) 1/3)
(*.f64 1/2 (*.f64 x x))
(pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)
(*.f64 1/2 (*.f64 x x))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(*.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))))
(cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3))
(*.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))
(log1p.f64 (expm1.f64 (*.f64 1/2 (*.f64 x x))))
(*.f64 1/2 (*.f64 x x))
(-.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (tan.f64 (*.f64 1/2 x)) 1)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 1 (tan.f64 (*.f64 1/2 x)))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 1 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (neg.f64 (sin.f64 (*.f64 1/2 x))) (neg.f64 (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(pow.f64 (tan.f64 (*.f64 1/2 x)) 1)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 1/2 x))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))

eval12.0ms (0.3%)

Compiler

Compiled 563 to 385 computations (31.6% saved)

prune14.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New49150
Fresh000
Picked112
Done000
Total50252
Accurracy
100.0%
Counts
52 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 (sin.f64 x) (*.f64 1/2 x))
✓100.0%
(*.f64 1/2 (*.f64 x x))
▶100.0%
(*.f64 (sin.f64 x) (*.f64 1/2 x))
✓100.0%
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 26 to 18 computations (30.8% saved)

localize59.0ms (1.6%)

Compiler

Compiled 15 to 9 computations (40% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Compiled 36 to 24 computations (33.3% saved)

regimes10.0ms (0.3%)

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

3 calls:

5.0ms
x
2.0ms
(-.f64 1 (cos.f64 x))
2.0ms
(cos.f64 x)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 1 (cos.f64 x))
100.0%1(cos.f64 x)
Compiler

Compiled 33 to 22 computations (33.3% saved)

regimes7.0ms (0.2%)

Accuracy

Total -29.2b remaining (-747947.9%)

Threshold costs -29.2b (-747947.9%)

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

3 calls:

3.0ms
x
2.0ms
(-.f64 1 (cos.f64 x))
2.0ms
(cos.f64 x)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 1 (cos.f64 x))
100.0%1(cos.f64 x)
Compiler

Compiled 20 to 14 computations (30% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01030
11330
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 1/2 (*.f64 x x))
Outputs
(*.f64 (sin.f64 x) (*.f64 1/2 x))
(*.f64 (sin.f64 x) (*.f64 x 1/2))
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 13 to 9 computations (30.8% saved)

soundness248.0ms (7%)

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
093800
1231740
2679670
33306670
093800
1231740
2679670
33306670
Stop Event
1×node limit
1×node limit
1×node limit
Compiler

Compiled 124 to 68 computations (45.2% saved)

end33.0ms (0.9%)

Compiler

Compiled 56 to 38 computations (32.1% saved)

Profiling

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