Hyperbolic arcsine

Details

Time bar (total: 4.5s)

analyze212.0ms (4.7%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
50%50%50%0%0%0%0%2
50%50%50%0%0%0%0%3
62.5%62.5%37.5%0%0%0%0%4
68.8%68.7%31.2%0%0%0%0%5
71.9%71.8%28.1%0%0%0%0%6
73.4%73.4%26.5%0%0%0%0%7
74.2%74.2%25.8%0%0%0%0%8
74.6%74.6%25.4%0%0%0%0%9
74.8%74.8%25.2%0%0%0%0%10
74.9%74.9%25.1%0%0%0%0%11
75%74.9%25%0%0%0%0%12
Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.2s (70.6%)

Results
1.4s2603×body1024valid
683.0ms3125×body256valid
636.0ms1214×body2048valid
428.0ms1278×body512valid
18.0ms36×body4096valid
Bogosity

preprocess15.0ms (0.3%)

Algorithm
2×egg-herbie
Rules
4×+-commutative
2×1-exp
2×hypot-1-def
2×fma-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01023
11617
21717
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
Outputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x 1))))
(log.f64 (+.f64 x (hypot.f64 1 x)))
Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify12.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
4×+-commutative
2×1-exp
2×hypot-1-def
2×fma-def
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01023
11617
21717
Stop Event
1×saturated
Counts
1 → 3
Calls
Call 1
Inputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
Outputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x 1))))
(log.f64 (+.f64 x (hypot.f64 1 x)))

eval1.0ms (0%)

Compiler

Compiled 24 to 16 computations (33.3% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New213
Fresh101
Picked000
Done000
Total314
Accurracy
28.5%
Counts
4 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶28.5%
(log.f64 (+.f64 x (hypot.f64 1 x)))
▶28.5%
(log.f64 (+.f64 x (hypot.f64 1 x)))
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize95.0ms (2.1%)

Local Accuracy

Found 2 expressions with local accuracy:

NewAccuracyProgram
✓74.8%
(+.f64 x (hypot.f64 1 x))
✓54.2%
(log.f64 (+.f64 x (hypot.f64 1 x)))
Compiler

Compiled 18 to 12 computations (33.3% saved)

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(log.f64 (+.f64 x (hypot.f64 1 x)))
1.0ms
x
@-inf
(log.f64 (+.f64 x (hypot.f64 1 x)))
1.0ms
x
@inf
(log.f64 (+.f64 x (hypot.f64 1 x)))
0.0ms
x
@-inf
(+.f64 x (hypot.f64 1 x))
0.0ms
x
@inf
(+.f64 x (hypot.f64 1 x))

rewrite63.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
1590×pow1
1466×add-exp-log
1466×log1p-expm1-u
1466×expm1-log1p-u
1432×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0830
115830
2199930
Stop Event
1×node limit
Counts
2 → 56
Calls
Call 1
Inputs
(log.f64 (+.f64 x (hypot.f64 1 x)))
(+.f64 x (hypot.f64 1 x))
Outputs
(+.f64 0 (log.f64 (+.f64 x (hypot.f64 1 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2)) (log.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x)))))
(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
(-.f64 (log.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))) (log.f64 (-.f64 x (hypot.f64 1 x))))
(-.f64 (log.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3))) (log.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
(*.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x))))
(*.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1)
(*.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2)))
(*.f64 (cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2)) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(*.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1)
(pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 3)
(pow.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)
(sqrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2))
(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))
(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(log1p.f64 (-.f64 (+.f64 x (hypot.f64 1 x)) 1))
(-.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) 1)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (hypot.f64 1 x))) (/.f64 (+.f64 1 (*.f64 x x)) (-.f64 x (hypot.f64 1 x))))
(*.f64 1 (+.f64 x (hypot.f64 1 x)))
(*.f64 (+.f64 x (hypot.f64 1 x)) 1)
(*.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2) (cbrt.f64 (+.f64 x (hypot.f64 1 x))))
(*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
(*.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
(*.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x))) (/.f64 1 (-.f64 x (hypot.f64 1 x))))
(/.f64 1 (/.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x))) (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3))))
(/.f64 1 (/.f64 (-.f64 x (hypot.f64 1 x)) (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x))))
(/.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3)) (+.f64 (+.f64 1 (*.f64 x x)) (-.f64 (*.f64 x x) (*.f64 x (hypot.f64 1 x)))))
(/.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x))) (-.f64 x (hypot.f64 1 x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3))) (neg.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))) (neg.f64 (-.f64 x (hypot.f64 1 x))))
(/.f64 (-.f64 (+.f64 1 (*.f64 x x)) (*.f64 x x)) (-.f64 (hypot.f64 1 x) x))
(pow.f64 (+.f64 x (hypot.f64 1 x)) 1)
(pow.f64 (E.f64) (log.f64 (+.f64 x (hypot.f64 1 x))))
(pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 3)
(pow.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2)
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(sqrt.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2))
(log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x))))
(cbrt.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x))))
(exp.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))
(log1p.f64 (expm1.f64 (+.f64 x (hypot.f64 1 x))))
(fma.f64 1 x (hypot.f64 1 x))
(fma.f64 1 (hypot.f64 1 x) x)
(fma.f64 (cbrt.f64 (+.f64 1 (*.f64 x x))) (cbrt.f64 (hypot.f64 1 x)) x)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (hypot.f64 1 x))
(fma.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (hypot.f64 1 x))

simplify77.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
1522×fma-def
1096×fma-neg
724×unswap-sqr
698×log-prod
450×associate-+l+
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02142548
15482180
217102040
366102040
Stop Event
1×node limit
Counts
80 → 136
Calls
Call 1
Inputs
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (*.f64 3/32 (/.f64 1 (pow.f64 x 4))))) (+.f64 (*.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
1
(+.f64 1 x)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/8 (pow.f64 x 4)) x)))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 2 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 2 x) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(/.f64 -1/2 x)
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 5/128 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(+.f64 0 (log.f64 (+.f64 x (hypot.f64 1 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2)) (log.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x)))))
(+.f64 (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
(-.f64 (log.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))) (log.f64 (-.f64 x (hypot.f64 1 x))))
(-.f64 (log.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3))) (log.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
(*.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x))))
(*.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1)
(*.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2)))
(*.f64 (cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2)) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(*.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 1)
(pow.f64 (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 3)
(pow.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)
(sqrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2))
(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 3))
(expm1.f64 (log1p.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(log1p.f64 (-.f64 (+.f64 x (hypot.f64 1 x)) 1))
(-.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) 1)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (hypot.f64 1 x))) (/.f64 (+.f64 1 (*.f64 x x)) (-.f64 x (hypot.f64 1 x))))
(*.f64 1 (+.f64 x (hypot.f64 1 x)))
(*.f64 (+.f64 x (hypot.f64 1 x)) 1)
(*.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 2) (cbrt.f64 (+.f64 x (hypot.f64 1 x))))
(*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
(*.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
(*.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x))) (/.f64 1 (-.f64 x (hypot.f64 1 x))))
(/.f64 1 (/.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x))) (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3))))
(/.f64 1 (/.f64 (-.f64 x (hypot.f64 1 x)) (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3)) (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x))))
(/.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3)) (+.f64 (+.f64 1 (*.f64 x x)) (-.f64 (*.f64 x x) (*.f64 x (hypot.f64 1 x)))))
(/.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x))) (-.f64 x (hypot.f64 1 x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (hypot.f64 1 x) 3) (pow.f64 x 3))) (neg.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (+.f64 1 (*.f64 x x)))) (neg.f64 (-.f64 x (hypot.f64 1 x))))
(/.f64 (-.f64 (+.f64 1 (*.f64 x x)) (*.f64 x x)) (-.f64 (hypot.f64 1 x) x))
(pow.f64 (+.f64 x (hypot.f64 1 x)) 1)
(pow.f64 (E.f64) (log.f64 (+.f64 x (hypot.f64 1 x))))
(pow.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) 3)
(pow.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2)
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))) (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (+.f64 x (hypot.f64 1 x))) 2))) (cbrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
(sqrt.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 2))
(log.f64 (exp.f64 (+.f64 x (hypot.f64 1 x))))
(cbrt.f64 (pow.f64 (+.f64 x (hypot.f64 1 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 x (hypot.f64 1 x))))
(exp.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))
(log1p.f64 (expm1.f64 (+.f64 x (hypot.f64 1 x))))
(fma.f64 1 x (hypot.f64 1 x))
(fma.f64 1 (hypot.f64 1 x) x)
(fma.f64 (cbrt.f64 (+.f64 1 (*.f64 x x))) (cbrt.f64 (hypot.f64 1 x)) x)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (hypot.f64 1 x))
(fma.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (hypot.f64 1 x))
Outputs
x
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(fma.f64 -1/6 (pow.f64 x 3) x)
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) x))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) (+.f64 (*.f64 3/40 (pow.f64 x 5)) (+.f64 (*.f64 -5/112 (pow.f64 x 7)) x)))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 3/40 (pow.f64 x 5) (fma.f64 -5/112 (pow.f64 x 7) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (log.f64 2) (neg.f64 (neg.f64 (log.f64 x))))
(+.f64 (log.f64 2) (log.f64 x))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
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(+.f64 (+.f64 x (hypot.f64 1 x)) 0)
(+.f64 x (hypot.f64 1 x))
(fma.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)) x)
(+.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) -1)
(+.f64 (+.f64 x (hypot.f64 1 x)) 0)
(+.f64 x (hypot.f64 1 x))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (hypot.f64 1 x))
(+.f64 (+.f64 1 (+.f64 x (hypot.f64 1 x))) -1)
(+.f64 (+.f64 x (hypot.f64 1 x)) 0)
(+.f64 x (hypot.f64 1 x))

eval44.0ms (1%)

Compiler

Compiled 1915 to 1409 computations (26.4% saved)

prune26.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1306136
Fresh000
Picked011
Done000
Total1307137
Accurracy
100.0%
Counts
137 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶28.5%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
▶50.2%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
▶27.2%
(log.f64 (/.f64 -1/2 x))
▶24.3%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
✓28.5%
(log.f64 (+.f64 x (hypot.f64 1 x)))
▶23.4%
(log.f64 (+.f64 x x))
52.4%
x
▶28.5%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
▶50.2%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
▶27.2%
(log.f64 (/.f64 -1/2 x))
▶24.3%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
✓28.5%
(log.f64 (+.f64 x (hypot.f64 1 x)))
▶23.4%
(log.f64 (+.f64 x x))
52.4%
x
Compiler

Compiled 178 to 136 computations (23.6% saved)

localize157.0ms (3.5%)

Compiler

Compiled 105 to 73 computations (30.5% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune5.0ms (0.1%)

Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New000
Fresh011
Picked055
Done011
Total077
Accurracy
100.0%
Counts
7 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓28.5%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
✓50.2%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓27.2%
(log.f64 (/.f64 -1/2 x))
✓24.3%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
✓28.5%
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓23.4%
(log.f64 (+.f64 x x))
52.4%
x
✓28.5%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
✓50.2%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓27.2%
(log.f64 (/.f64 -1/2 x))
✓24.3%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
✓28.5%
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓23.4%
(log.f64 (+.f64 x x))
52.4%
x
Compiler

Compiled 98 to 74 computations (24.5% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune6.0ms (0.1%)

Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done066
Total077
Accurracy
100.0%
Counts
7 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓28.5%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
✓50.2%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓27.2%
(log.f64 (/.f64 -1/2 x))
✓24.3%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
✓28.5%
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓23.4%
(log.f64 (+.f64 x x))
52.4%
x
✓28.5%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
✓50.2%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓27.2%
(log.f64 (/.f64 -1/2 x))
✓24.3%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
✓28.5%
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓23.4%
(log.f64 (+.f64 x x))
52.4%
x
Compiler

Compiled 98 to 74 computations (24.5% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune4.0ms (0.1%)

Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done066
Total077
Accurracy
100.0%
Counts
7 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓28.5%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
✓50.2%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓27.2%
(log.f64 (/.f64 -1/2 x))
✓24.3%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
✓28.5%
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓23.4%
(log.f64 (+.f64 x x))
52.4%
x
Compiler

Compiled 101 to 74 computations (26.7% saved)

regimes31.0ms (0.7%)

Counts
8 → 3
Calls
Call 1
Inputs
x
(log.f64 (+.f64 x x))
(log.f64 (/.f64 -1/2 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
(log.f64 (+.f64 x (hypot.f64 1 x)))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
Outputs
(log.f64 (/.f64 -1/2 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
Calls

3 calls:

15.0ms
x
6.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
Results
AccuracySegmentsBranch
100.0%3x
90.2%3(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
90.2%3(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
Compiler

Compiled 73 to 51 computations (30.1% saved)

regimes18.0ms (0.4%)

Counts
7 → 3
Calls
Call 1
Inputs
x
(log.f64 (+.f64 x x))
(log.f64 (/.f64 -1/2 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
(log.f64 (+.f64 x (hypot.f64 1 x)))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
Outputs
(log.f64 (/.f64 -1/2 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (+.f64 x (hypot.f64 1 x)))
Calls

1 calls:

15.0ms
x
Results
AccuracySegmentsBranch
100.0%3x
Compiler

Compiled 44 to 30 computations (31.8% saved)

regimes14.0ms (0.3%)

Counts
5 → 3
Calls
Call 1
Inputs
x
(log.f64 (+.f64 x x))
(log.f64 (/.f64 -1/2 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
Outputs
(log.f64 (/.f64 -1/2 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
Calls

1 calls:

12.0ms
x
Results
AccuracySegmentsBranch
99.4%3x
Compiler

Compiled 29 to 20 computations (31% saved)

regimes14.0ms (0.3%)

Counts
4 → 3
Calls
Call 1
Inputs
x
(log.f64 (+.f64 x x))
(log.f64 (/.f64 -1/2 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
Outputs
(log.f64 (/.f64 -1/2 x))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (+.f64 x x))
Calls

1 calls:

12.0ms
x
Results
AccuracySegmentsBranch
99.3%3x
Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes11.0ms (0.3%)

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

1 calls:

11.0ms
x
Results
AccuracySegmentsBranch
99.1%3x
Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes6.0ms (0.1%)

Counts
2 → 2
Calls
Call 1
Inputs
x
(log.f64 (+.f64 x x))
Outputs
x
(log.f64 (+.f64 x x))
Calls

1 calls:

6.0ms
x
Results
AccuracySegmentsBranch
74.0%2x
Compiler

Compiled 8 to 4 computations (50% saved)

regimes4.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
x
Outputs
x
Calls

1 calls:

4.0ms
x
Results
AccuracySegmentsBranch
52.4%1x
Compiler

Compiled 4 to 2 computations (50% saved)

bsearch35.0ms (0.8%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
15.0ms
6.0854792779133984e-5
0.013866100007939329
20.0ms
-1120620188.924475
-4.4214709382780475e-8
Results
32.0ms272×body256valid
Compiler

Compiled 311 to 249 computations (19.9% saved)

bsearch38.0ms (0.8%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
15.0ms
6.0854792779133984e-5
0.013866100007939329
22.0ms
-1120620188.924475
-4.4214709382780475e-8
Results
34.0ms272×body256valid
Compiler

Compiled 283 to 221 computations (21.9% saved)

bsearch37.0ms (0.8%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
17.0ms
0.013866100007939329
2.505164392450688
21.0ms
-1120620188.924475
-4.4214709382780475e-8
Results
34.0ms272×body256valid
Compiler

Compiled 311 to 249 computations (19.9% saved)

bsearch35.0ms (0.8%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
14.0ms
0.013866100007939329
2.505164392450688
20.0ms
-1120620188.924475
-4.4214709382780475e-8
Results
31.0ms272×body256valid
Compiler

Compiled 269 to 207 computations (23% saved)

bsearch33.0ms (0.7%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
14.0ms
0.013866100007939329
2.505164392450688
19.0ms
-1120620188.924475
-4.4214709382780475e-8
Results
30.0ms272×body256valid
Compiler

Compiled 167 to 122 computations (26.9% saved)

bsearch13.0ms (0.3%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
13.0ms
0.013866100007939329
2.505164392450688
Results
12.0ms112×body256valid
Compiler

Compiled 77 to 52 computations (32.5% saved)

simplify13.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
12×+-commutative
8×*-commutative
4×unsub-neg
4×sub-neg
4×neg-mul-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
054341
165341
269341
372341
475341
578341
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 662929865148937/576460752303423488) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 4150517416584649/4611686018427387904) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x (hypot.f64 1 x)))))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 1080863910568919/1125899906842624) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 5854679515581645/4503599627370496) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x x))))
(if (<=.f64 x -5/4) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 5/4) x (log.f64 (+.f64 x x))))
(if (<=.f64 x 5/4) x (log.f64 (+.f64 x x)))
x
Outputs
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 662929865148937/576460752303423488) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 662929865148937/576460752303423488) (+.f64 x (*.f64 -1/6 (pow.f64 x 3))) (-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 662929865148937/576460752303423488) (+.f64 x (*.f64 -1/6 (pow.f64 x 3))) (+.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) -1)))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 4150517416584649/4611686018427387904) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x (hypot.f64 1 x)))))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 4150517416584649/4611686018427387904) (+.f64 x (*.f64 -1/6 (pow.f64 x 3))) (log.f64 (+.f64 x (hypot.f64 1 x)))))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 1080863910568919/1125899906842624) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 1080863910568919/1125899906842624) (+.f64 x (*.f64 -1/6 (pow.f64 x 3))) (log.f64 (+.f64 (*.f64 x 2) (*.f64 1/2 (/.f64 1 x))))))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 5854679515581645/4503599627370496) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x x))))
(if (<=.f64 x -5854679515581645/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 5854679515581645/4503599627370496) (+.f64 x (*.f64 -1/6 (pow.f64 x 3))) (log.f64 (+.f64 x x))))
(if (<=.f64 x -5/4) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 5/4) x (log.f64 (+.f64 x x))))
(if (<=.f64 x 5/4) x (log.f64 (+.f64 x x)))
x
Compiler

Compiled 140 to 101 computations (27.9% saved)

soundness186.0ms (4.2%)

Rules
1590×pow1
1522×fma-def
1466×add-exp-log
1466×log1p-expm1-u
1466×expm1-log1p-u
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01023
11617
21717
0830
115830
2199930
02142548
15482180
217102040
366102040
Stop Event
1×node limit
1×node limit
1×saturated
Compiler

Compiled 81 to 59 computations (27.2% saved)

end102.0ms (2.3%)

Compiler

Compiled 338 to 230 computations (32% saved)

Profiling

Loading profile data...