Hyperbolic arcsine

Time bar (total: 4.1s)

analyze64.0ms (1.5%)

Algorithm
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)

sample2.5s (60.1%)

Results
1.2s2545×body1024valid
547.0ms1306×body2048valid
411.0ms3113×body256valid
287.0ms1248×body512valid
25.0ms44×body4096valid
Bogosity

preprocess256.0ms (6.2%)

Algorithm
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
01650
13334
25934
310634
418134
527034
633534
738934
842234
949134
1071934
1198534
12121034
13139234
14140234
15140434
16140434
17219634
18245134
19269934
20283234
21284734
22284734
23454534
24454534
25454534
26454534
27454534
28762534
29767434
30785634
31794834
32795934
Stop Event
node limit
Calls
Call 1
Inputs
(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 (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 11 to 8 computations (27.3% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01023
11617
21717
Stop Event
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
31.8%
Counts
4 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
31.8%
(log.f64 (+.f64 x (hypot.f64 1 x)))
31.8%
(log.f64 (+.f64 x (hypot.f64 1 x)))
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize97.0ms (2.4%)

Local Accuracy

Found 2 expressions with local accuracy:

NewAccuracyProgram
75.3%
(+.f64 x (hypot.f64 1 x))
56.9%
(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))

rewrite61.0ms (1.5%)

Algorithm
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
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))

simplify81.0ms (2%)

Algorithm
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
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)))
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(+.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 1 (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 (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))

eval40.0ms (1%)

Compiler

Compiled 1915 to 1409 computations (26.4% saved)

prune23.0ms (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
46.6%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
26.5%
(log.f64 (/.f64 -1/2 x))
29.6%
(log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x))))
28.8%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
31.8%
(log.f64 (+.f64 x (hypot.f64 1 x)))
28.1%
(log.f64 (+.f64 x x))
48.9%
x
46.6%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
26.5%
(log.f64 (/.f64 -1/2 x))
29.6%
(log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x))))
28.8%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
31.8%
(log.f64 (+.f64 x (hypot.f64 1 x)))
28.1%
(log.f64 (+.f64 x x))
48.9%
x
Compiler

Compiled 170 to 128 computations (24.7% saved)

localize182.0ms (4.4%)

Compiler

Compiled 97 to 67 computations (30.9% 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
46.6%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
26.5%
(log.f64 (/.f64 -1/2 x))
29.6%
(log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x))))
28.8%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
31.8%
(log.f64 (+.f64 x (hypot.f64 1 x)))
28.1%
(log.f64 (+.f64 x x))
48.9%
x
46.6%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
26.5%
(log.f64 (/.f64 -1/2 x))
29.6%
(log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x))))
28.8%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
31.8%
(log.f64 (+.f64 x (hypot.f64 1 x)))
28.1%
(log.f64 (+.f64 x x))
48.9%
x
Compiler

Compiled 94 to 70 computations (25.5% saved)

localize0.0ms (0%)

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
Picked000
Done066
Total077
Accurracy
100.0%
Counts
7 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.6%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
26.5%
(log.f64 (/.f64 -1/2 x))
29.6%
(log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x))))
28.8%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
31.8%
(log.f64 (+.f64 x (hypot.f64 1 x)))
28.1%
(log.f64 (+.f64 x x))
48.9%
x
46.6%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
26.5%
(log.f64 (/.f64 -1/2 x))
29.6%
(log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x))))
28.8%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
31.8%
(log.f64 (+.f64 x (hypot.f64 1 x)))
28.1%
(log.f64 (+.f64 x x))
48.9%
x
Compiler

Compiled 94 to 70 computations (25.5% saved)

localize0.0ms (0%)

eval60.0ms (1.5%)

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
Picked000
Done066
Total077
Accurracy
100.0%
Counts
7 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.6%
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
26.5%
(log.f64 (/.f64 -1/2 x))
29.6%
(log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x))))
28.8%
(log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))
31.8%
(log.f64 (+.f64 x (hypot.f64 1 x)))
28.1%
(log.f64 (+.f64 x x))
48.9%
x
Compiler

Compiled 97 to 70 computations (27.8% saved)

regimes28.0ms (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 -1 (-.f64 x (hypot.f64 1 x))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
Outputs
(log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x))))
(+.f64 (*.f64 -1/6 (pow.f64 x 3)) x)
(log.f64 (+.f64 x (hypot.f64 1 x)))
Calls

3 calls:

14.0ms
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
89.0%3(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
89.0%3(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
Compiler

Compiled 71 to 49 computations (31% saved)

regimes14.0ms (0.3%)

Counts
6 → 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)))
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:

12.0ms
x
Results
AccuracySegmentsBranch
99.9%3x
Compiler

Compiled 35 to 24 computations (31.4% saved)

regimes15.0ms (0.4%)

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:

13.0ms
x
Results
AccuracySegmentsBranch
99.7%3x
Compiler

Compiled 29 to 20 computations (31% saved)

regimes11.0ms (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:

10.0ms
x
Results
AccuracySegmentsBranch
99.7%3x
Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes10.0ms (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:

9.0ms
x
Results
AccuracySegmentsBranch
99.5%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:

5.0ms
x
Results
AccuracySegmentsBranch
74.9%2x
Compiler

Compiled 8 to 4 computations (50% saved)

regimes3.0ms (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:

2.0ms
x
Results
AccuracySegmentsBranch
48.9%1x
Compiler

Compiled 4 to 2 computations (50% saved)

bsearch40.0ms (1%)

Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
20.0ms
3.4596330331244965e-10
1.8657703578769296
20.0ms
-610175.9930587101
-1.1982556207107652e-5
Results
35.0ms320×body256valid
Compiler

Compiled 374 to 290 computations (22.5% saved)

bsearch40.0ms (1%)

Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
20.0ms
3.4596330331244965e-10
1.8657703578769296
20.0ms
-610175.9930587101
-1.1982556207107652e-5
Results
36.0ms320×body256valid
Compiler

Compiled 334 to 260 computations (22.2% saved)

bsearch40.0ms (1%)

Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
20.0ms
3.4596330331244965e-10
1.8657703578769296
19.0ms
-610175.9930587101
-1.1982556207107652e-5
Results
34.0ms320×body256valid
Compiler

Compiled 374 to 300 computations (19.8% saved)

bsearch40.0ms (1%)

Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
20.0ms
3.4596330331244965e-10
1.8657703578769296
19.0ms
-610175.9930587101
-1.1982556207107652e-5
Results
36.0ms320×body256valid
Compiler

Compiled 314 to 240 computations (23.6% saved)

bsearch44.0ms (1.1%)

Algorithm
binary-search
Stop Event
narrow-enough
narrow-enough
Steps
TimeLeftRight
23.0ms
3.4596330331244965e-10
1.8657703578769296
21.0ms
-610175.9930587101
-1.1982556207107652e-5
Results
40.0ms320×body256valid
Compiler

Compiled 194 to 140 computations (27.8% saved)

bsearch47.0ms (1.1%)

Algorithm
binary-search
Stop Event
narrow-enough
Steps
TimeLeftRight
47.0ms
3.4596330331244965e-10
1.8657703578769296
Results
45.0ms160×body256valid
Compiler

Compiled 104 to 70 computations (32.7% saved)

simplify11.0ms (0.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
051341
161341
264341
366341
467341
Stop Event
fuel
saturated
Calls
Call 1
Inputs
(if (<=.f64 x -5072854620270127/4611686018427387904) (log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x)))) (if (<=.f64 x 5072854620270127/4611686018427387904) (+.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 5072854620270127/4611686018427387904) (+.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 4278419646001971/4503599627370496) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.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 -5072854620270127/4611686018427387904) (log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x)))) (if (<=.f64 x 5072854620270127/4611686018427387904) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 x (hypot.f64 1 x)))))
(if (<=.f64 x -5072854620270127/4611686018427387904) (log.f64 (/.f64 -1 (-.f64 x (hypot.f64 1 x)))) (if (<=.f64 x 5072854620270127/4611686018427387904) (+.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 5072854620270127/4611686018427387904) (+.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 5072854620270127/4611686018427387904) (+.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 4278419646001971/4503599627370496) (+.f64 (*.f64 -1/6 (pow.f64 x 3)) x) (log.f64 (+.f64 (*.f64 2 x) (*.f64 1/2 (/.f64 1 x))))))
(if (<=.f64 x -5674535530486825/4503599627370496) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 4278419646001971/4503599627370496) (+.f64 x (*.f64 -1/6 (pow.f64 x 3))) (log.f64 (+.f64 (*.f64 x 2) (*.f64 1/2 (/.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 140 to 100 computations (28.6% saved)

soundness282.0ms (6.9%)

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

Useful iterations: 1 (0.0ms)

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

Compiled 281 to 171 computations (39.1% saved)

end0.0ms (0%)

preprocess120.0ms (2.9%)

Compiler

Compiled 338 to 228 computations (32.5% saved)

Profiling

Loading profile data...