Hyperbolic arc-(co)secant

Time bar (total: 3.0s)

analyze3.0ms (0.1%)

Algorithm
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%50%0%0%50%0%3
33.3%12.5%25%0%0%62.5%0%4
60%18.7%12.5%0%0%68.7%0%5
77.8%21.9%6.2%0%0%71.8%0%6
88.2%23.4%3.1%0%0%73.4%0%7
93.9%24.2%1.6%0%0%74.2%0%8
96.9%24.6%0.8%0%0%74.6%0%9
98.4%24.8%0.4%0%0%74.8%0%10
99.2%24.9%0.2%0%0%74.9%0%11
99.6%24.9%0.1%0%0%74.9%0%12
Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.4s (45.8%)

Results
1.4s8256×body256valid
2.0ms26×body256invalid
Bogosity

preprocess529.0ms (17.7%)

Algorithm
egg-herbie
Rules
1654×fma-def
1206×sub-neg
1138×distribute-lft-out
846×associate-+r+
716×*-commutative
Problems
256×No Errors
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
022161
141157
263157
3121157
4176157
5258157
6385157
7659157
81279157
92150157
104775157
116458157
127223157
137521157
147577157
157609157
167862157
Stop Event
node limit
Calls
Call 1
Inputs
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(log.f64 (+.f64 (/.f64 1 (neg.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (neg.f64 x) (neg.f64 x)))) (neg.f64 x))))
Outputs
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 x x -1))) x)))
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 x x -1))) x)))
(log.f64 (+.f64 (/.f64 1 (neg.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (neg.f64 x) (neg.f64 x)))) (neg.f64 x))))
(log.f64 (+.f64 (/.f64 1 (neg.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x))))
(log.f64 (+.f64 (/.f64 -1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x))))
(log.f64 (+.f64 (/.f64 -1 x) (/.f64 (sqrt.f64 (neg.f64 (fma.f64 x x -1))) (neg.f64 x))))
Compiler

Compiled 68 to 40 computations (41.2% saved)

eval0.0ms (0%)

Compiler

Compiled 14 to 10 computations (28.6% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
100.0%
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
Compiler

Compiled 28 to 20 computations (28.6% saved)

localize243.0ms (8.1%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
100.0%
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
Compiler

Compiled 54 to 30 computations (44.4% saved)

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
1.0ms
x
@-inf
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
1.0ms
x
@0
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite468.0ms (15.6%)

Algorithm
batch-egg-rewrite
Rules
1033×log1p-expm1-u
1033×expm1-log1p-u
840×fma-def
346×fma-neg
322×expm1-udef
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01448
120245
2293545
Stop Event
node limit
Counts
1 → 22
Calls
Call 1
Inputs
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
Outputs
(+.f64 0 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)) 2))) (log.f64 (cbrt.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(+.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) (log.f64 (sqrt.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))))) 1)
(-.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (pow.f64 x 2))) x)) (*.f64 2 (log.f64 x)))
(-.f64 (log.f64 (fma.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/2) (pow.f64 x -3) (pow.f64 x -3))) (log.f64 (-.f64 (+.f64 (pow.f64 x -2) (*.f64 (-.f64 1 (pow.f64 x 2)) (pow.f64 x -2))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) (pow.f64 x 2)))))
(-.f64 (log.f64 (-.f64 (pow.f64 x -2) (*.f64 (-.f64 1 (pow.f64 x 2)) (pow.f64 x -2)))) (log.f64 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) x)))
(*.f64 1 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))))
(*.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 1)
(*.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 2))
(*.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 2) (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(*.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) (sqrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 1)
(pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 3)
(pow.f64 (pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 3) 1/3)
(pow.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 2)
(sqrt.f64 (pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 2))
(cbrt.f64 (pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 3))
(expm1.f64 (log1p.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(exp.f64 (log.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(exp.f64 (*.f64 (log.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 1))
(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) -1))

simplify55.0ms (1.8%)

Algorithm
egg-herbie
Rules
1320×times-frac
976×associate-*r*
886×associate-*l*
710×fma-def
560×log-prod
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01321866
13241688
210151653
354811603
Stop Event
node limit
Counts
34 → 82
Calls
Call 1
Inputs
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (+.f64 (*.f64 -1 (log.f64 x)) (*.f64 -1/4 (pow.f64 x 2))))
(+.f64 (log.f64 2) (+.f64 (*.f64 -1 (log.f64 x)) (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (*.f64 -3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (+.f64 (*.f64 -1 (log.f64 x)) (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (+.f64 (*.f64 -3/32 (pow.f64 x 4)) (*.f64 -5/96 (pow.f64 x 6))))))
(log.f64 (sqrt.f64 -1))
(+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(-.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1 (*.f64 x (sqrt.f64 -1)))) (*.f64 1/6 (/.f64 1 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(-.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (+.f64 (*.f64 3/40 (/.f64 1 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 1 (*.f64 x (sqrt.f64 -1))))) (*.f64 1/6 (/.f64 1 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(log.f64 (*.f64 -1 (sqrt.f64 -1)))
(-.f64 (log.f64 (*.f64 -1 (sqrt.f64 -1))) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(-.f64 (+.f64 (log.f64 (*.f64 -1 (sqrt.f64 -1))) (*.f64 1/6 (/.f64 1 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))))) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(-.f64 (+.f64 (log.f64 (*.f64 -1 (sqrt.f64 -1))) (*.f64 1/6 (/.f64 1 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))))) (+.f64 (*.f64 3/40 (/.f64 1 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 1 (*.f64 x (sqrt.f64 -1)))))
(+.f64 0 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)) 2))) (log.f64 (cbrt.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(+.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) (log.f64 (sqrt.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))))) 1)
(-.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (pow.f64 x 2))) x)) (*.f64 2 (log.f64 x)))
(-.f64 (log.f64 (fma.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/2) (pow.f64 x -3) (pow.f64 x -3))) (log.f64 (-.f64 (+.f64 (pow.f64 x -2) (*.f64 (-.f64 1 (pow.f64 x 2)) (pow.f64 x -2))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) (pow.f64 x 2)))))
(-.f64 (log.f64 (-.f64 (pow.f64 x -2) (*.f64 (-.f64 1 (pow.f64 x 2)) (pow.f64 x -2)))) (log.f64 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) x)))
(*.f64 1 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))))
(*.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 1)
(*.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 2))
(*.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 2) (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(*.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) (sqrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 1)
(pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 3)
(pow.f64 (pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 3) 1/3)
(pow.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 2)
(sqrt.f64 (pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 2))
(cbrt.f64 (pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 3))
(expm1.f64 (log1p.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(exp.f64 (log.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(exp.f64 (*.f64 (log.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 1))
(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) -1))
Outputs
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 2) (log.f64 x))
(+.f64 (log.f64 2) (+.f64 (*.f64 -1 (log.f64 x)) (*.f64 -1/4 (pow.f64 x 2))))
(+.f64 (log.f64 2) (fma.f64 -1 (log.f64 x) (*.f64 -1/4 (pow.f64 x 2))))
(+.f64 (log.f64 2) (-.f64 (*.f64 -1/4 (pow.f64 x 2)) (log.f64 x)))
(-.f64 (fma.f64 -1/4 (pow.f64 x 2) (log.f64 2)) (log.f64 x))
(+.f64 (log.f64 2) (+.f64 (*.f64 -1 (log.f64 x)) (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (*.f64 -3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (fma.f64 -1 (log.f64 x) (fma.f64 -1/4 (pow.f64 x 2) (*.f64 -3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (-.f64 (fma.f64 -1/4 (pow.f64 x 2) (*.f64 -3/32 (pow.f64 x 4))) (log.f64 x)))
(+.f64 (-.f64 (log.f64 2) (log.f64 x)) (fma.f64 -1/4 (pow.f64 x 2) (*.f64 -3/32 (pow.f64 x 4))))
(+.f64 (log.f64 2) (+.f64 (*.f64 -1 (log.f64 x)) (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (+.f64 (*.f64 -3/32 (pow.f64 x 4)) (*.f64 -5/96 (pow.f64 x 6))))))
(+.f64 (log.f64 2) (fma.f64 -1 (log.f64 x) (fma.f64 -1/4 (pow.f64 x 2) (fma.f64 -3/32 (pow.f64 x 4) (*.f64 -5/96 (pow.f64 x 6))))))
(+.f64 (log.f64 2) (-.f64 (fma.f64 -1/4 (pow.f64 x 2) (fma.f64 -3/32 (pow.f64 x 4) (*.f64 -5/96 (pow.f64 x 6)))) (log.f64 x)))
(+.f64 (-.f64 (log.f64 2) (log.f64 x)) (fma.f64 -1/4 (pow.f64 x 2) (fma.f64 -5/96 (pow.f64 x 6) (*.f64 -3/32 (pow.f64 x 4)))))
(+.f64 (-.f64 (fma.f64 -1/4 (pow.f64 x 2) (log.f64 2)) (log.f64 x)) (fma.f64 -5/96 (pow.f64 x 6) (*.f64 -3/32 (pow.f64 x 4))))
(log.f64 (sqrt.f64 -1))
(+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 (/.f64 1 x) (sqrt.f64 -1)))
(-.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1 (*.f64 x (sqrt.f64 -1)))) (*.f64 1/6 (/.f64 1 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(-.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 (/.f64 1 x) (sqrt.f64 -1))) (/.f64 1/6 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))))
(+.f64 (log.f64 (sqrt.f64 -1)) (+.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 -1/6 (*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 -1))))))
(+.f64 (log.f64 (sqrt.f64 -1)) (-.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 -1/6 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(-.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (+.f64 (*.f64 3/40 (/.f64 1 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 1 (*.f64 x (sqrt.f64 -1))))) (*.f64 1/6 (/.f64 1 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (log.f64 (sqrt.f64 -1)) (-.f64 (+.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 1/6 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (log.f64 (sqrt.f64 -1)) (+.f64 (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (+.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 -1/6 (*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 -1)))))))
(+.f64 (log.f64 (sqrt.f64 -1)) (+.f64 (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (-.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 -1/6 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))))))
(log.f64 (*.f64 -1 (sqrt.f64 -1)))
(log.f64 (neg.f64 (sqrt.f64 -1)))
(-.f64 (log.f64 (*.f64 -1 (sqrt.f64 -1))) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 (/.f64 1 x) (sqrt.f64 -1)))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 -1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x))
(fma.f64 3 (log.f64 (sqrt.f64 -1)) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x))
(-.f64 (+.f64 (log.f64 (*.f64 -1 (sqrt.f64 -1))) (*.f64 1/6 (/.f64 1 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))))) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (/.f64 1/6 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (/.f64 (/.f64 1 x) (sqrt.f64 -1))))
(+.f64 (/.f64 1/6 (*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 -1)))) (+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 -1 (*.f64 x (sqrt.f64 -1)))))
(+.f64 (/.f64 -1/6 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x)))
(+.f64 (/.f64 -1/6 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (fma.f64 3 (log.f64 (sqrt.f64 -1)) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x)))
(-.f64 (+.f64 (log.f64 (*.f64 -1 (sqrt.f64 -1))) (*.f64 1/6 (/.f64 1 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))))) (+.f64 (*.f64 3/40 (/.f64 1 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 1 (*.f64 x (sqrt.f64 -1)))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (/.f64 1/6 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (/.f64 1/6 (*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 -1)))) (-.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (+.f64 (/.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (+.f64 (-.f64 (/.f64 -1/6 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x)))
(+.f64 (/.f64 -1/6 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (-.f64 (fma.f64 3 (log.f64 (sqrt.f64 -1)) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x)) (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))))
(+.f64 0 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)) 2))) (log.f64 (cbrt.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))) 2))) (log.f64 (cbrt.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) x) 2))) (log.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) x))))
(+.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) (log.f64 (sqrt.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))))) 1)
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(-.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (pow.f64 x 2))) x)) (*.f64 2 (log.f64 x)))
(+.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (pow.f64 x 2))) x)) (*.f64 -2 (log.f64 x)))
(+.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (pow.f64 x 2))) x)) (*.f64 (log.f64 x) -2))
(fma.f64 (log.f64 x) -2 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (pow.f64 x 2))) x)))
(fma.f64 (log.f64 x) -2 (+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x)))
(-.f64 (log.f64 (fma.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/2) (pow.f64 x -3) (pow.f64 x -3))) (log.f64 (-.f64 (+.f64 (pow.f64 x -2) (*.f64 (-.f64 1 (pow.f64 x 2)) (pow.f64 x -2))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) (pow.f64 x 2)))))
(-.f64 (log.f64 (fma.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/2) (pow.f64 x -3) (pow.f64 x -3))) (log.f64 (-.f64 (*.f64 (+.f64 (-.f64 1 (pow.f64 x 2)) 1) (pow.f64 x -2)) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) (pow.f64 x 2)))))
(-.f64 (log.f64 (*.f64 (+.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/2) 1) (pow.f64 x -3))) (log.f64 (-.f64 (*.f64 (pow.f64 x -2) (-.f64 1 (-.f64 (pow.f64 x 2) 1))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) (pow.f64 x 2)))))
(-.f64 (log.f64 (*.f64 (pow.f64 x -3) (+.f64 1 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/2)))) (log.f64 (-.f64 (*.f64 (pow.f64 x -2) (-.f64 2 (pow.f64 x 2))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) (pow.f64 x 2)))))
(-.f64 (+.f64 (log1p.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/2)) (*.f64 -3 (log.f64 x))) (log.f64 (+.f64 (pow.f64 x -2) (-.f64 (+.f64 -1 (pow.f64 x -2)) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) (pow.f64 x 2))))))
(-.f64 (log.f64 (-.f64 (pow.f64 x -2) (*.f64 (-.f64 1 (pow.f64 x 2)) (pow.f64 x -2)))) (log.f64 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) x)))
(-.f64 (log.f64 (*.f64 (+.f64 (neg.f64 (-.f64 1 (pow.f64 x 2))) 1) (pow.f64 x -2))) (log.f64 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) x)))
(-.f64 (log.f64 (*.f64 (pow.f64 x -2) (+.f64 1 (fma.f64 x x -1)))) (log.f64 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) x)))
(neg.f64 (log.f64 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) x)))
(*.f64 1 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(*.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 1)
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(*.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 2))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 2) (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(*.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) (sqrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 1)
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 3)
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(pow.f64 (pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 3) 1/3)
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(pow.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 2)
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(sqrt.f64 (pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 2))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(cbrt.f64 (pow.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1))) 3))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(expm1.f64 (log1p.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(exp.f64 (log.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(exp.f64 (*.f64 (log.f64 (log.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2))) 1)))) 1))
(log.f64 (*.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2))))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) (log.f64 x))
(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) -1))
(log1p.f64 (+.f64 -1 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (pow.f64 x 2)))) x)))

eval99.0ms (3.3%)

Compiler

Compiled 1628 to 1380 computations (15.2% saved)

prune12.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New80282
Fresh000
Picked011
Done000
Total80383
Accuracy
100.0%
Counts
83 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(-.f64 (log.f64 2) (log.f64 x))
100.0%
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.0%
(log.f64 (sqrt.f64 -1))
99.6%
(-.f64 (log.f64 2) (log.f64 x))
100.0%
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.0%
(log.f64 (sqrt.f64 -1))
Compiler

Compiled 48 to 38 computations (20.8% saved)

localize44.0ms (1.5%)

Compiler

Compiled 19 to 15 computations (21.1% 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
Accuracy
100.0%
Counts
3 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(-.f64 (log.f64 2) (log.f64 x))
100.0%
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.0%
(log.f64 (sqrt.f64 -1))
Compiler

Compiled 46 to 36 computations (21.7% saved)

regimes12.0ms (0.4%)

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

3 calls:

4.0ms
(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
4.0ms
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
3.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
100.0%1(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
Compiler

Compiled 51 to 37 computations (27.5% saved)

regimes29.0ms (1%)

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

1 calls:

29.0ms
x
Results
AccuracySegmentsBranch
99.6%1x
Compiler

Compiled 11 to 9 computations (18.2% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(log.f64 (sqrt.f64 -1))
Outputs
(log.f64 (sqrt.f64 -1))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
0.0%1x
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
12×+-commutative
10×sub-neg
neg-mul-1
*-commutative
neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02178
13178
24078
34678
44978
Stop Event
done
saturated
Calls
Call 1
Inputs
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(-.f64 (log.f64 2) (log.f64 x))
(log.f64 (sqrt.f64 -1))
Outputs
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(-.f64 (log.f64 2) (log.f64 x))
(log.f64 (sqrt.f64 -1))
Compiler

Compiled 24 to 19 computations (20.8% saved)

soundness81.0ms (2.7%)

Rules
1320×times-frac
976×associate-*r*
886×associate-*l*
710×fma-def
560×log-prod
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01321866
13241688
210151653
354811603
Stop Event
node limit
Compiler

Compiled 19 to 14 computations (26.3% saved)

end0.0ms (0%)

preprocess36.0ms (1.2%)

Compiler

Compiled 72 to 54 computations (25% saved)

Profiling

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