arccos

Time bar (total: 1.6s)

analyze5.0ms (0.3%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%75%0%0%25%0%3
40%25%37.5%0%0%37.5%0%4
66.7%37.5%18.7%0%0%43.7%0%5
82.4%43.7%9.4%0%0%46.9%0%6
90.9%46.9%4.7%0%0%48.4%0%7
95.4%48.4%2.3%0%0%49.2%0%8
97.7%49.2%1.2%0%0%49.6%0%9
98.8%49.6%0.6%0%0%49.8%0%10
99.4%49.8%0.3%0%0%49.9%0%11
99.7%49.9%0.1%0%0%49.9%0%12
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.1s (67.1%)

Results
1.0s8256×body256valid
1.0ms16×body256invalid
Bogosity

preprocess61.0ms (3.9%)

Algorithm
1×egg-herbie
Rules
1490×fma-def
366×div-sub
250×times-frac
190×associate-/r*
174×distribute-lft-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01970
13766
26166
313366
435166
593166
6170266
7209766
8241766
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 (neg.f64 x)) (+.f64 1 (neg.f64 x))))))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 (neg.f64 x)) (+.f64 1 (neg.f64 x))))))
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 (neg.f64 x)) (-.f64 1 x)))))
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify57.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
1128×fma-def
554×div-sub
414×fma-neg
236×times-frac
194×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01233
12133
22733
33833
46133
58533
612333
719533
835633
958433
1079133
11116233
12160033
13199733
14223833
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

eval0.0ms (0%)

Compiler

Compiled 12 to 10 computations (16.7% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Accurracy
100.0%
Counts
2 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
▶100.0%
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Compiler

Compiled 24 to 20 computations (16.7% saved)

localize105.0ms (6.7%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(/.f64 (-.f64 1 x) (+.f64 1 x))
Compiler

Compiled 46 to 35 computations (23.9% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite57.0ms (3.6%)

Algorithm
1×batch-egg-rewrite
Rules
1814×pow1
1692×log1p-expm1-u
1692×expm1-log1p-u
1690×add-exp-log
1660×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0719
115519
2222119
Stop Event
1×node limit
Counts
1 → 35
Calls
Call 1
Inputs
(/.f64 (-.f64 1 x) (+.f64 1 x))
Outputs
(+.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (neg.f64 (/.f64 x (+.f64 1 x))))
(-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (/.f64 x (+.f64 1 x)))
(-.f64 (+.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(*.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(*.f64 (-.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (*.f64 (cbrt.f64 (-.f64 1 x)) (exp.f64 (neg.f64 (log1p.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (sqrt.f64 (-.f64 1 x)) (*.f64 (sqrt.f64 (-.f64 1 x)) (exp.f64 (neg.f64 (log1p.f64 x)))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (neg.f64 (-.f64 1 x)) (/.f64 1 (+.f64 (neg.f64 x) -1)))
(*.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 1 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (/.f64 (-.f64 1 x) (cbrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (sqrt.f64 (+.f64 1 x))) (/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) 1) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (/.f64 (sqrt.f64 (-.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x)))
(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)
(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2)
(pow.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) -1)
(neg.f64 (/.f64 (-.f64 1 x) (+.f64 (neg.f64 x) -1)))
(sqrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 2))
(log.f64 (exp.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (+.f64 1 x) 3)))
(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
(log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify64.0ms (4%)

Algorithm
1×egg-herbie
Rules
864×associate-*r*
802×associate-*l*
698×div-sub
516×fma-neg
488×fma-def
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01221385
13291191
29801047
351831047
Stop Event
1×node limit
Counts
47 → 72
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 -2 x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 1 (*.f64 -2 x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 -2 x) (*.f64 -2 (pow.f64 x 3)))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(-.f64 (*.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(-.f64 (*.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (neg.f64 (/.f64 x (+.f64 1 x))))
(-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (/.f64 x (+.f64 1 x)))
(-.f64 (+.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(*.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(*.f64 (-.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (*.f64 (cbrt.f64 (-.f64 1 x)) (exp.f64 (neg.f64 (log1p.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (sqrt.f64 (-.f64 1 x)) (*.f64 (sqrt.f64 (-.f64 1 x)) (exp.f64 (neg.f64 (log1p.f64 x)))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (neg.f64 (-.f64 1 x)) (/.f64 1 (+.f64 (neg.f64 x) -1)))
(*.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 1 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (/.f64 (-.f64 1 x) (cbrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (sqrt.f64 (+.f64 1 x))) (/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) 1) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (/.f64 (sqrt.f64 (-.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x)))
(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)
(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2)
(pow.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) -1)
(neg.f64 (/.f64 (-.f64 1 x) (+.f64 (neg.f64 x) -1)))
(sqrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 2))
(log.f64 (exp.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (+.f64 1 x) 3)))
(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
(log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
Outputs
1
(+.f64 1 (*.f64 -2 x))
(fma.f64 -2 x 1)
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 1 (*.f64 -2 x)))
(fma.f64 2 (*.f64 x x) (+.f64 1 (*.f64 -2 x)))
(fma.f64 2 (*.f64 x x) (fma.f64 -2 x 1))
(fma.f64 x (*.f64 x 2) (fma.f64 -2 x 1))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 -2 x) (*.f64 -2 (pow.f64 x 3)))))
(fma.f64 2 (*.f64 x x) (+.f64 1 (*.f64 -2 (+.f64 x (pow.f64 x 3)))))
(fma.f64 2 (*.f64 x x) (fma.f64 -2 (+.f64 x (pow.f64 x 3)) 1))
(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (fma.f64 x (*.f64 x 2) 1))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(+.f64 (/.f64 2 x) -1)
(+.f64 -1 (/.f64 2 x))
(-.f64 (*.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (+.f64 1 (/.f64 2 (*.f64 x x))))
(-.f64 (+.f64 -1 (/.f64 2 x)) (/.f64 2 (*.f64 x x)))
(+.f64 -1 (+.f64 (/.f64 2 x) (/.f64 -2 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 2 (pow.f64 x 3)) (+.f64 1 (/.f64 2 (*.f64 x x)))))
(+.f64 (/.f64 2 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (+.f64 1 (/.f64 2 (*.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (+.f64 -1 (/.f64 -2 (*.f64 x x)))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(+.f64 (/.f64 2 x) -1)
(+.f64 -1 (/.f64 2 x))
(-.f64 (*.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (+.f64 1 (/.f64 2 (*.f64 x x))))
(-.f64 (+.f64 -1 (/.f64 2 x)) (/.f64 2 (*.f64 x x)))
(+.f64 -1 (+.f64 (/.f64 2 x) (/.f64 -2 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 2 (pow.f64 x 3)) (+.f64 1 (/.f64 2 (*.f64 x x)))))
(+.f64 (/.f64 2 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (+.f64 1 (/.f64 2 (*.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (+.f64 -1 (/.f64 -2 (*.f64 x x)))))
(+.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (neg.f64 (/.f64 x (+.f64 1 x))))
(-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (/.f64 x (+.f64 1 x)))
(-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (/.f64 x (+.f64 1 x)))
(-.f64 (+.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (-.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))
(*.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 1 x))
(/.f64 (-.f64 1 x) (exp.f64 (log1p.f64 x)))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (*.f64 (cbrt.f64 (-.f64 1 x)) (exp.f64 (neg.f64 (log1p.f64 x)))))
(*.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 1 x))
(/.f64 (-.f64 1 x) (exp.f64 (log1p.f64 x)))
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (sqrt.f64 (-.f64 1 x)) (*.f64 (sqrt.f64 (-.f64 1 x)) (exp.f64 (neg.f64 (log1p.f64 x)))))
(*.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 1 x))
(/.f64 (-.f64 1 x) (exp.f64 (log1p.f64 x)))
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (neg.f64 (-.f64 1 x)) (/.f64 1 (+.f64 (neg.f64 x) -1)))
(*.f64 (neg.f64 (-.f64 1 x)) (/.f64 1 (+.f64 -1 (neg.f64 x))))
(/.f64 (+.f64 -1 x) (-.f64 -1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(*.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 1 x))
(/.f64 (-.f64 1 x) (exp.f64 (log1p.f64 x)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (/.f64 (-.f64 1 x) (cbrt.f64 (+.f64 1 x))))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x)))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (sqrt.f64 (+.f64 1 x))) (/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) 1) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x)))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (/.f64 (sqrt.f64 (-.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(*.f64 (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))) (-.f64 1 x))
(*.f64 (-.f64 1 x) (/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x))))
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 6) (fma.f64 x (neg.f64 x) 1))
(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 6) (neg.f64 (fma.f64 x x -1)))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 x x) x)))
(/.f64 (-.f64 1 x) (/.f64 (+.f64 1 (pow.f64 x 3)) (+.f64 (*.f64 x x) (-.f64 1 x))))
(/.f64 (-.f64 1 x) (/.f64 (+.f64 1 (pow.f64 x 3)) (-.f64 (fma.f64 x x 1) x)))
(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3) 1/3)
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2)
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(pow.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) -1)
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(neg.f64 (/.f64 (-.f64 1 x) (+.f64 (neg.f64 x) -1)))
(*.f64 (neg.f64 (-.f64 1 x)) (/.f64 1 (+.f64 -1 (neg.f64 x))))
(/.f64 (+.f64 -1 x) (-.f64 -1 x))
(/.f64 (+.f64 x -1) (-.f64 -1 x))
(sqrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 2))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(log.f64 (exp.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (+.f64 1 x) 3)))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))
(exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
(log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(+.f64 1 (-.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1))
(+.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 0)
(/.f64 (-.f64 1 x) (+.f64 1 x))

eval23.0ms (1.4%)

Compiler

Compiled 1152 to 924 computations (19.8% saved)

prune10.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New70272
Fresh000
Picked011
Done000
Total70373
Accurracy
100.0%
Counts
73 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
▶99.7%
(*.f64 2 (atan.f64 (sqrt.f64 (+.f64 1 (*.f64 -2 x)))))
▶99.5%
(*.f64 2 (atan.f64 (sqrt.f64 1)))
✓100.0%
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
▶99.7%
(*.f64 2 (atan.f64 (sqrt.f64 (+.f64 1 (*.f64 -2 x)))))
▶99.5%
(*.f64 2 (atan.f64 (sqrt.f64 1)))
Compiler

Compiled 56 to 50 computations (10.7% saved)

localize75.0ms (4.7%)

Compiler

Compiled 48 to 42 computations (12.5% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New000
Fresh000
Picked022
Done011
Total033
Accurracy
100.0%
Counts
3 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
✓99.7%
(*.f64 2 (atan.f64 (sqrt.f64 (+.f64 1 (*.f64 -2 x)))))
✓99.5%
(*.f64 2 (atan.f64 (sqrt.f64 1)))
Compiler

Compiled 54 to 48 computations (11.1% saved)

regimes12.0ms (0.8%)

Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 1)))
(*.f64 2 (atan.f64 (sqrt.f64 (+.f64 1 (*.f64 -2 x)))))
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Calls

5 calls:

4.0ms
x
2.0ms
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
2.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
2.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
100.0%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
100.0%1(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
100.0%1(/.f64 (-.f64 1 x) (+.f64 1 x))
Compiler

Compiled 67 to 55 computations (17.9% saved)

regimes4.0ms (0.2%)

Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 1)))
(*.f64 2 (atan.f64 (sqrt.f64 (+.f64 1 (*.f64 -2 x)))))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (+.f64 1 (*.f64 -2 x)))))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes3.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 1)))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 1)))
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
99.5%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify5.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
10×*-commutative
8×+-commutative
4×sub-neg
2×1-exp
2×neg-mul-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02171
13171
23571
33771
43871
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 2 (atan.f64 (sqrt.f64 (+.f64 1 (*.f64 -2 x)))))
(*.f64 2 (atan.f64 (sqrt.f64 1)))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 2 (atan.f64 (sqrt.f64 (+.f64 1 (*.f64 -2 x)))))
(*.f64 2 (atan.f64 (sqrt.f64 (+.f64 1 (*.f64 x -2)))))
(*.f64 2 (atan.f64 (sqrt.f64 1)))
(*.f64 2 (atan.f64 1))
Compiler

Compiled 27 to 24 computations (11.1% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess34.0ms (2.2%)

Compiler

Compiled 74 to 64 computations (13.5% saved)

Profiling

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