Hyperbolic arcsine

Time bar (total: 6.5s)

analyze181.0ms (2.8%)

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)

sample3.5s (53.8%)

Results
1.6s2610×body1024valid
726.0ms1280×body2048valid
651.0ms3009×body256valid
479.0ms1310×body512valid
35.0ms47×body4096valid
Bogosity

preprocess281.0ms (4.3%)

Algorithm
1×egg-herbie
Rules
4550×fma-def
3750×associate-+r+
3054×associate-+l+
1272×distribute-lft-in
480×distribute-lft-out
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01673
13351
25951
310651
418151
527051
633551
738951
842251
949151
1071951
1198551
12121051
13139251
14140251
15140451
16140451
17219651
18245151
19269951
20283251
21284751
22284751
23454551
24454551
25454551
26454551
27454551
28762551
29767451
30785651
31794851
32795951
Stop Event
1×node limit
Calls
Call 1
Inputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (+.f64 (*.f64 (neg.f64 x) (neg.f64 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)))
(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)))
(log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (+.f64 (*.f64 (neg.f64 x) (neg.f64 x)) 1))))
(log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x 1))))
(log.f64 (-.f64 (hypot.f64 1 x) x))
Compiler

Compiled 10 to 7 computations (30% saved)

eval1.0ms (0%)

Compiler

Compiled 15 to 10 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶30.3%
(log.f64 (+.f64 x (hypot.f64 1 x)))
▶30.3%
(log.f64 (+.f64 x (hypot.f64 1 x)))
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize93.0ms (1.4%)

Localize:

Found 2 expressions with local error:

NewAccuracyProgram
✓78.3%
(+.f64 x (hypot.f64 1 x))
✓52.6%
(log.f64 (+.f64 x (hypot.f64 1 x)))
Compiler

Compiled 18 to 12 computations (33.3% saved)

series3.0ms (0%)

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))

rewrite88.0ms (1.3%)

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))

simplify235.0ms (3.6%)

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)))))
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(fma.f64 (cbrt.f64 (+.f64 1 (*.f64 x x))) (cbrt.f64 (hypot.f64 1 x)) x)
(fma.f64 (cbrt.f64 (fma.f64 x x 1)) (cbrt.f64 (hypot.f64 1 x)) x)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.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))
(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))

eval186.0ms (2.8%)

Compiler

Compiled 1915 to 1409 computations (26.4% saved)

prune70.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1315136
Fresh000
Picked011
Done000
Total1316137
Accuracy
100.0%
Counts
137 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶30.3%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
▶51.7%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
▶23.7%
(log.f64 (/.f64 -1/2 x))
✓30.3%
(log.f64 (+.f64 x (hypot.f64 1 x)))
▶26.0%
(log.f64 (+.f64 x x))
53.9%
x
▶30.3%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
▶51.7%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
▶23.7%
(log.f64 (/.f64 -1/2 x))
✓30.3%
(log.f64 (+.f64 x (hypot.f64 1 x)))
▶26.0%
(log.f64 (+.f64 x x))
53.9%
x
Compiler

Compiled 76 to 56 computations (26.3% saved)

localize396.0ms (6.1%)

Compiler

Compiled 71 to 47 computations (33.8% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune19.0ms (0.3%)

Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New000
Fresh011
Picked044
Done011
Total066
Accuracy
100.0%
Counts
6 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓30.3%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
✓51.7%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓23.7%
(log.f64 (/.f64 -1/2 x))
✓30.3%
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓26.0%
(log.f64 (+.f64 x x))
53.9%
x
✓30.3%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
✓51.7%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓23.7%
(log.f64 (/.f64 -1/2 x))
✓30.3%
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓26.0%
(log.f64 (+.f64 x x))
53.9%
x
Compiler

Compiled 76 to 56 computations (26.3% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune16.0ms (0.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done055
Total066
Accuracy
100.0%
Counts
6 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓30.3%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
✓51.7%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓23.7%
(log.f64 (/.f64 -1/2 x))
✓30.3%
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓26.0%
(log.f64 (+.f64 x x))
53.9%
x
✓30.3%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
✓51.7%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓23.7%
(log.f64 (/.f64 -1/2 x))
✓30.3%
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓26.0%
(log.f64 (+.f64 x x))
53.9%
x
Compiler

Compiled 76 to 56 computations (26.3% saved)

localize0.0ms (0%)

eval1.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune14.0ms (0.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done055
Total066
Accuracy
100.0%
Counts
6 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓30.3%
(-.f64 (+.f64 1 (log.f64 (+.f64 x (hypot.f64 1 x)))) 1)
✓51.7%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
✓23.7%
(log.f64 (/.f64 -1/2 x))
✓30.3%
(log.f64 (+.f64 x (hypot.f64 1 x)))
✓26.0%
(log.f64 (+.f64 x x))
53.9%
x
Compiler

Compiled 80 to 57 computations (28.8% saved)

regimes101.0ms (1.5%)

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 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)
(log.f64 (+.f64 x (hypot.f64 1 x)))
Calls

3 calls:

48.0ms
x
24.0ms
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
23.0ms
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
Results
AccuracySegmentsBranch
100.0%3x
89.4%3(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
89.4%3(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
Compiler

Compiled 63 to 43 computations (31.7% saved)

regimes42.0ms (0.6%)

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:

39.0ms
x
Results
AccuracySegmentsBranch
99.8%3x
Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes48.0ms (0.7%)

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:

45.0ms
x
Results
AccuracySegmentsBranch
99.7%3x
Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes25.0ms (0.4%)

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

1 calls:

22.0ms
x
Results
AccuracySegmentsBranch
77.9%2x
Compiler

Compiled 8 to 4 computations (50% saved)

regimes9.0ms (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:

8.0ms
x
Results
AccuracySegmentsBranch
53.9%1x
Compiler

Compiled 4 to 2 computations (50% saved)

bsearch63.0ms (1%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
36.0ms
9.428941008612768e-8
0.09559804729567148
27.0ms
-2017711538.8615599
-3.2760055226964108e-12
Results
57.0ms320×body256valid
Compiler

Compiled 332 to 259 computations (22% saved)

bsearch74.0ms (1.1%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
48.0ms
0.09559804729567148
24427625430346.29
25.0ms
-2017711538.8615599
-3.2760055226964108e-12
Results
66.0ms336×body256valid
Compiler

Compiled 329 to 252 computations (23.4% saved)

bsearch130.0ms (2%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
60.0ms
0.09559804729567148
24427625430346.29
69.0ms
-2017711538.8615599
-3.2760055226964108e-12
Results
118.0ms336×body256valid
Compiler

Compiled 203 to 147 computations (27.6% saved)

bsearch63.0ms (1%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
63.0ms
0.09559804729567148
24427625430346.29
Results
58.0ms160×body256valid
Compiler

Compiled 104 to 70 computations (32.7% saved)

simplify25.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
4×+-commutative
2×1-exp
2×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033187
138187
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x -5674535530486825/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 564931537257355/576460752303423488) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x (hypot.f64 1 x)))))
(if (<=.f64 x -5674535530486825/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 5/4) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x x))))
(if (<=.f64 x -5674535530486825/4503599627370496) (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 -5674535530486825/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 564931537257355/576460752303423488) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x (hypot.f64 1 x)))))
(if (<=.f64 x -5674535530486825/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 564931537257355/576460752303423488) (+.f64 x (*.f64 -1/6 (pow.f64 x 3))) (log.f64 (+.f64 x (hypot.f64 1 x)))))
(if (<=.f64 x -5674535530486825/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 5/4) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x x))))
(if (<=.f64 x -5674535530486825/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 5/4) (+.f64 x (*.f64 -1/6 (pow.f64 x 3))) (log.f64 (+.f64 x x))))
(if (<=.f64 x -5674535530486825/4503599627370496) (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 80 to 55 computations (31.3% saved)

soundness711.0ms (10.9%)

Rules
4550×fma-def
3750×associate-+r+
3054×associate-+l+
1522×fma-def
1272×distribute-lft-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01673
13351
25951
310651
418151
527051
633551
738951
842251
949151
1071951
1198551
12121051
13139251
14140251
15140451
16140451
17219651
18245151
19269951
20283251
21284751
22284751
23454551
24454551
25454551
26454551
27454551
28762551
29767451
30785651
31794851
32795951
02142548
15482180
217102040
366102040
Stop Event
1×node limit
1×node limit
Compiler

Compiled 56 to 34 computations (39.3% saved)

end0.0ms (0%)

preprocess143.0ms (2.2%)

Compiler

Compiled 222 to 142 computations (36% saved)

Profiling

Loading profile data...