Details

Time bar (total: 2.1s)

analyze4.0ms (0.2%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%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)

sample940.0ms (44.4%)

Results
929.0ms8256×body256valid
1.0ms12×body256invalid
Bogosity

preprocess136.0ms (6.4%)

Algorithm
2×egg-herbie
Rules
1222×+-commutative
1114×distribute-lft-in
1034×*-commutative
966×distribute-rgt-in
904×fma-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01239
12039
22839
33939
45539
59239
614639
732239
888439
9180939
10320339
11528739
12633539
13675139
14703939
15717539
16725239
17754739
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(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)))
Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify141.0ms (6.6%)

Algorithm
1×egg-herbie
Rules
1222×+-commutative
1114×distribute-lft-in
1034×*-commutative
966×distribute-rgt-in
904×fma-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01239
12039
22839
33939
45539
59239
614639
732239
888439
9180939
10320339
11528739
12633539
13675139
14703939
15717539
16725239
17754739
Stop Event
1×node limit
Counts
1 → 1
Calls
Call 1
Inputs
(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)))

eval0.0ms (0%)

Compiler

Compiled 14 to 10 computations (28.6% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0b
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize20.0ms (0.9%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓0.0b
(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
✓0.0b
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
Compiler

Compiled 53 to 29 computations (45.3% saved)

series3.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0ms
x
@-inf
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0ms
x
@0
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0ms
x
@inf
(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms
x
@-inf
(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite99.0ms (4.7%)

Algorithm
1×batch-egg-rewrite
Rules
1696×associate-/r*
970×associate-/l*
728×distribute-rgt-in
680×distribute-lft-in
536×associate-/r/
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01175
124575
2350375
Stop Event
1×node limit
Counts
3 → 247
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Outputs
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(*.f64 x x))) x) (pow.f64 x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -1) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 x -1) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (pow.f64 x -1)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2)) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 1 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (*.f64 x x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))))

simplify164.0ms (7.7%)

Algorithm
1×egg-herbie
Rules
1032×+-commutative
908×associate-*r*
700×associate-*l*
636×associate-/r*
550×fma-def
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
069614229
1189812847
2795912847
Stop Event
1×node limit
Counts
283 → 427
Calls
Call 1
Inputs
(/.f64 1 x)
(+.f64 (*.f64 -1/2 x) (/.f64 1 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 x) (/.f64 1 x)))
(+.f64 (*.f64 -1/8 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 x) (+.f64 (/.f64 1 x) (*.f64 -1/16 (pow.f64 x 5)))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 6)))))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(*.f64 -1 (sqrt.f64 -1))
(-.f64 (*.f64 -1 (sqrt.f64 -1)) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 -1 (sqrt.f64 -1)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4))))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 -1 (sqrt.f64 -1)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4))))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 6))))))
(/.f64 2 x)
(+.f64 (*.f64 -1/2 x) (*.f64 2 (/.f64 1 x)))
(+.f64 (*.f64 -1/8 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (*.f64 -1/8 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 x) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 -1/16 (pow.f64 x 5)))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (/.f64 1 x))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(*.f64 -1 (sqrt.f64 -1))
(+.f64 (/.f64 1 x) (*.f64 -1 (sqrt.f64 -1)))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 -1 (sqrt.f64 -1))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 1 x) (+.f64 (*.f64 -1 (sqrt.f64 -1)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 -1) x)
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(*.f64 -1 (*.f64 (sqrt.f64 -1) x))
(-.f64 (*.f64 -1 (*.f64 (sqrt.f64 -1) x)) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (*.f64 -1 (*.f64 (sqrt.f64 -1) x))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (*.f64 -1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x)))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 1)
(*.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
(*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 x -1))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 1)
(*.f64 (pow.f64 x -1) (sqrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 x -1)))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(*.f64 (pow.f64 x -1/2) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))
(*.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (pow.f64 x -1)))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (cbrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2))))
(*.f64 (cbrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (/.f64 -1 x))
(*.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 x -1/2)) (pow.f64 x -1/2))
(*.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (pow.f64 x -2))) (cbrt.f64 (pow.f64 x -1)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1) (pow.f64 x -1))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)) (pow.f64 x -1/2))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (pow.f64 x -1)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) -1)
(*.f64 (/.f64 -1 x) (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 1) (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) x))
(*.f64 (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) x) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(*.f64 (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (cbrt.f64 x)))
(*.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
(*.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x)))
(*.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1) 1) (pow.f64 x -1))
(*.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) x) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (/.f64 1 (/.f64 x (cbrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 1)
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) 2)
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) 3)
(pow.f64 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 3) 1/3)
(neg.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)))
(sqrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2)))
(log.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) 1))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(-.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1)))) 1)
(-.f64 (exp.f64 (log1p.f64 (pow.f64 x -1))) (-.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) (-.f64 1 (pow.f64 x -1)))
(-.f64 (*.f64 (/.f64 (pow.f64 x -2) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) x) (*.f64 (/.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) x))
(-.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (exp.f64 (log1p.f64 (pow.f64 x -1)))) 1)
(-.f64 (+.f64 (pow.f64 x -1) (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))) 1)
(*.f64 1 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1)))
(*.f64 (pow.f64 x -1) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1)) 1)
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(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) 1) 1) (*.f64 x x))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) 1) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) x))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) 1) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (pow.f64 x 4)))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) 1) (pow.f64 (cbrt.f64 x) 2)) (*.f64 (cbrt.f64 x) x))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) 1) (*.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) 1) (*.f64 x (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 x))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) x) (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) x) (sqrt.f64 (cbrt.f64 (pow.f64 x 4)))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (pow.f64 x 4))) 1) (pow.f64 (cbrt.f64 x) 2))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 x)) (cbrt.f64 x))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (pow.f64 x 4))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (cbrt.f64 (pow.f64 x 4)))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(/.f64 (/.f64 (/.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (pow.f64 x 4))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))
(/.f64 (/.f64 (+.f64 x (*.f64 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)) (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) x)
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1)) (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) (neg.f64 x))
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) 1) (neg.f64 (*.f64 x x)))
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) x) (neg.f64 x))
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) (cbrt.f64 (pow.f64 x 4))) (neg.f64 (pow.f64 (cbrt.f64 x) 2)))
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) (neg.f64 x)) x)
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) -1) (*.f64 x x))
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) (sqrt.f64 (neg.f64 (*.f64 x x)))) (sqrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) (*.f64 (cbrt.f64 (neg.f64 (*.f64 x x))) (cbrt.f64 (neg.f64 (*.f64 x x))))) (cbrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) (*.f64 (neg.f64 x) 1)) x)
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) (*.f64 (neg.f64 x) (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) (*.f64 (neg.f64 x) (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 x))
(/.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)) (*.f64 x -1)) (neg.f64 (cbrt.f64 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 x) 2))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) 1) (neg.f64 (*.f64 x x)))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) x) (neg.f64 x))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) (cbrt.f64 (pow.f64 x 4))) (neg.f64 (pow.f64 (cbrt.f64 x) 2)))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) (neg.f64 x)) x)
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) -1) (*.f64 x x))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) (sqrt.f64 (neg.f64 (*.f64 x x)))) (sqrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) (*.f64 (cbrt.f64 (neg.f64 (*.f64 x x))) (cbrt.f64 (neg.f64 (*.f64 x x))))) (cbrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) (*.f64 (neg.f64 x) 1)) x)
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) (*.f64 (neg.f64 x) (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) (*.f64 (neg.f64 x) (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 x))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)) (neg.f64 (cbrt.f64 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 x) 2))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 x)) (*.f64 (neg.f64 x) -1)) (neg.f64 x)) (neg.f64 x))
(/.f64 (/.f64 (+.f64 x (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))) x) (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) 1) (neg.f64 (*.f64 x x)))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) x) (neg.f64 x))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (cbrt.f64 (pow.f64 x 4))) (neg.f64 (pow.f64 (cbrt.f64 x) 2)))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (neg.f64 x)) x)
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) -1) (*.f64 x x))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (sqrt.f64 (neg.f64 (*.f64 x x)))) (sqrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (*.f64 (cbrt.f64 (neg.f64 (*.f64 x x))) (cbrt.f64 (neg.f64 (*.f64 x x))))) (cbrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (*.f64 (neg.f64 x) 1)) x)
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (*.f64 (neg.f64 x) (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (*.f64 (neg.f64 x) (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 x))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (neg.f64 (cbrt.f64 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 x) 2))
(/.f64 (/.f64 (+.f64 (*.f64 (neg.f64 x) 1) (*.f64 -1 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (neg.f64 x)) (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) 1) (neg.f64 (*.f64 x x)))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) x) (neg.f64 x))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (pow.f64 x 4))) (neg.f64 (pow.f64 (cbrt.f64 x) 2)))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) (neg.f64 x)) x)
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) -1) (*.f64 x x))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) (sqrt.f64 (neg.f64 (*.f64 x x)))) (sqrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) (*.f64 (cbrt.f64 (neg.f64 (*.f64 x x))) (cbrt.f64 (neg.f64 (*.f64 x x))))) (cbrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) (*.f64 (neg.f64 x) 1)) x)
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) (*.f64 (neg.f64 x) (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) (*.f64 (neg.f64 x) (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 x))
(/.f64 (/.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))) (neg.f64 (cbrt.f64 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 x) 2))
(/.f64 (/.f64 (+.f64 x (*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (neg.f64 x)) (neg.f64 x))
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) 1) (neg.f64 (*.f64 x x)))
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) x) (neg.f64 x))
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (cbrt.f64 (pow.f64 x 4))) (neg.f64 (pow.f64 (cbrt.f64 x) 2)))
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (neg.f64 x)) x)
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) -1) (*.f64 x x))
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (sqrt.f64 (neg.f64 (*.f64 x x)))) (sqrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (*.f64 (cbrt.f64 (neg.f64 (*.f64 x x))) (cbrt.f64 (neg.f64 (*.f64 x x))))) (cbrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (*.f64 (neg.f64 x) 1)) x)
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (*.f64 (neg.f64 x) (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (*.f64 (neg.f64 x) (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 x))
(/.f64 (/.f64 (neg.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (neg.f64 (cbrt.f64 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 x) 2))
(pow.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1)) 1)
(pow.f64 (/.f64 (sqrt.f64 (+.f64 x (*.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))) x) 2)
(pow.f64 (cbrt.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))) 3)
(pow.f64 (pow.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1)) 3) 1/3)
(sqrt.f64 (pow.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1)) 2))
(log.f64 (exp.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1)))))
(cbrt.f64 (pow.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1)) 3))
(expm1.f64 (log1p.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))))
(exp.f64 (log.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))))
(exp.f64 (*.f64 (log.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))) 1))
(log1p.f64 (expm1.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))))
(fma.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) (pow.f64 x -1))
(fma.f64 1 (pow.f64 x -1) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
(fma.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 x -1) (pow.f64 x -1))
(fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (pow.f64 x -1))
(fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
(fma.f64 (cbrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (pow.f64 x -1))
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (pow.f64 x -1)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))) 1)
(*.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2)) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 1 (pow.f64 x 4)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
(pow.f64 (-.f64 1 (*.f64 x x)) 1/2)
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (*.f64 x x)))))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 (*.f64 x x))) 1/2))
(exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (*.f64 x x)))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
Outputs
(/.f64 1 x)
(+.f64 (*.f64 -1/2 x) (/.f64 1 x))
(fma.f64 -1/2 x (/.f64 1 x))
(fma.f64 x -1/2 (/.f64 1 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 x) (/.f64 1 x)))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 -1/2 x (/.f64 1 x)))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 x -1/2 (/.f64 1 x)))
(+.f64 (*.f64 -1/8 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 x) (+.f64 (/.f64 1 x) (*.f64 -1/16 (pow.f64 x 5)))))
(fma.f64 -1/8 (pow.f64 x 3) (+.f64 (fma.f64 -1/2 x (/.f64 1 x)) (*.f64 -1/16 (pow.f64 x 5))))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 x -1/2 (fma.f64 -1/16 (pow.f64 x 5) (/.f64 1 x))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
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(sqrt.f64 (exp.f64 (log1p.f64 (neg.f64 (*.f64 x x)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(sqrt.f64 (-.f64 1 (*.f64 x x)))

eval171.0ms (8.1%)

Compiler

Compiled 11039 to 7139 computations (35.3% saved)

prune65.0ms (3.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New4243427
Fresh000
Picked101
Done000
Total4253428
Error
0b
Counts
428 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
▶0b
(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
▶0.4b
(log.f64 (/.f64 2 x))
▶0.1b
(log.f64 (+.f64 (*.f64 -1/2 x) (*.f64 2 (/.f64 1 x))))
Compiler

Compiled 28 to 22 computations (21.4% saved)

localize14.0ms (0.7%)

Compiler

Compiled 35 to 27 computations (22.9% saved)

localize6.0ms (0.3%)

Compiler

Compiled 10 to 7 computations (30% saved)

localize16.0ms (0.8%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓0.0b
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
Compiler

Compiled 46 to 26 computations (43.5% saved)

series0.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite58.0ms (2.8%)

Algorithm
1×batch-egg-rewrite
Rules
1928×add-sqr-sqrt
1906×*-un-lft-identity
1780×add-cube-cbrt
1768×add-cbrt-cube
190×pow1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0923
119123
2252423
Stop Event
1×node limit
Counts
1 → 32
Calls
Call 1
Inputs
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) (hypot.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 0 (*.f64 x x)) (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (/.f64 1 (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (+.f64 0 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 0 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (+.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (-.f64 1 (*.f64 x x)) 1) (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 0 (*.f64 x x))) (neg.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))) (neg.f64 (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)))))

simplify63.0ms (3%)

Algorithm
1×egg-herbie
Rules
1048×associate-*r*
890×associate-/l*
850×associate-*l*
730×associate-*r/
516×+-commutative
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01211790
13191728
210651468
345371468
Stop Event
1×node limit
Counts
44 → 79
Calls
Call 1
Inputs
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 2 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 -1) x)
(+.f64 1 (*.f64 (sqrt.f64 -1) x))
(+.f64 1 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(*.f64 -1 (*.f64 (sqrt.f64 -1) x))
(+.f64 1 (*.f64 -1 (*.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 1 (*.f64 -1 (*.f64 (sqrt.f64 -1) x))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (*.f64 -1 (*.f64 (sqrt.f64 -1) x)))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) 1)
(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(*.f64 1 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(*.f64 (hypot.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) (hypot.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)))
(*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 2)))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(*.f64 (+.f64 0 (*.f64 x x)) (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(*.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (/.f64 1 (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))))
(/.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (+.f64 0 (*.f64 x x))))
(/.f64 1 (/.f64 (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))))
(/.f64 (+.f64 0 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(/.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x)))))))
(/.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (+.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (-.f64 (-.f64 1 (*.f64 x x)) 1) (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(/.f64 (neg.f64 (+.f64 0 (*.f64 x x))) (neg.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))) (neg.f64 (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))))
(pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(pow.f64 (hypot.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) 2)
(pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) 3)
(pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3) 1/3)
(sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 2))
(log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))
(cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3))
(expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(exp.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1))
(log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(fma.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(fma.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 1)
(fma.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
Outputs
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (*.f64 -1/2 (*.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 2)
(+.f64 2 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 2 (fma.f64 -1/2 (*.f64 x x) (*.f64 -1/8 (pow.f64 x 4))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) 2))
(+.f64 2 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/16 (pow.f64 x 6) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) (*.f64 -1/16 (pow.f64 x 6)))))
(+.f64 (fma.f64 -1/2 (*.f64 x x) 2) (fma.f64 -1/8 (pow.f64 x 4) (*.f64 -1/16 (pow.f64 x 6))))
(*.f64 (sqrt.f64 -1) x)
(*.f64 x (sqrt.f64 -1))
(+.f64 1 (*.f64 (sqrt.f64 -1) x))
(+.f64 (*.f64 x (sqrt.f64 -1)) 1)
(fma.f64 x (sqrt.f64 -1) 1)
(+.f64 1 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)))
(+.f64 1 (+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(+.f64 1 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(+.f64 (fma.f64 x (sqrt.f64 -1) 1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 1 (-.f64 (+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (+.f64 1 (/.f64 -1/8 (*.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3)))))
(+.f64 1 (+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))))))
(+.f64 1 (+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(*.f64 -1 (*.f64 (sqrt.f64 -1) x))
(neg.f64 (*.f64 x (sqrt.f64 -1)))
(*.f64 x (neg.f64 (sqrt.f64 -1)))
(*.f64 (sqrt.f64 -1) (neg.f64 x))
(+.f64 1 (*.f64 -1 (*.f64 (sqrt.f64 -1) x)))
(+.f64 1 (neg.f64 (*.f64 x (sqrt.f64 -1))))
(fma.f64 (neg.f64 (sqrt.f64 -1)) x 1)
(-.f64 1 (*.f64 x (sqrt.f64 -1)))
(-.f64 (+.f64 1 (*.f64 -1 (*.f64 (sqrt.f64 -1) x))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 1 (neg.f64 (*.f64 x (sqrt.f64 -1)))) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))
(+.f64 1 (fma.f64 (neg.f64 (sqrt.f64 -1)) x (/.f64 -1/2 (*.f64 x (sqrt.f64 -1)))))
(-.f64 1 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (*.f64 -1 (*.f64 (sqrt.f64 -1) x)))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (+.f64 1 (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (neg.f64 (*.f64 x (sqrt.f64 -1)))) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))
(+.f64 (-.f64 (/.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 (sqrt.f64 -1))) (*.f64 x (sqrt.f64 -1))) (+.f64 1 (/.f64 -1/2 (*.f64 x (sqrt.f64 -1)))))
(+.f64 (-.f64 1 (fma.f64 x (sqrt.f64 -1) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))))) (/.f64 -1/2 (*.f64 x (sqrt.f64 -1))))
(+.f64 (-.f64 1 (*.f64 x (sqrt.f64 -1))) (*.f64 (/.f64 -1 (*.f64 x (sqrt.f64 -1))) (+.f64 1/2 (/.f64 1/8 (*.f64 x x)))))
(-.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))) 1)
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
(*.f64 x (/.f64 x (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(*.f64 1 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (hypot.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) (hypot.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)))
(pow.f64 (hypot.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) 2)
(*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 2)))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 2)))
(*.f64 (+.f64 0 (*.f64 x x)) (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
(*.f64 x (/.f64 x (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(*.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (/.f64 1 (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) 1) (-.f64 2 (fma.f64 x x (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (-.f64 2 (fma.f64 x x (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (+.f64 0 (*.f64 x x))))
(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
(*.f64 x (/.f64 x (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 1 (/.f64 (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x)))))) (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) 1) (-.f64 2 (fma.f64 x x (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (-.f64 2 (fma.f64 x x (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (+.f64 0 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
(*.f64 x (/.f64 x (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x)))))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) 1) (-.f64 2 (fma.f64 x x (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (-.f64 2 (fma.f64 x x (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (+.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) 1) (-.f64 2 (fma.f64 x x (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (-.f64 2 (fma.f64 x x (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (-.f64 (-.f64 1 (*.f64 x x)) 1) (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
(*.f64 x (/.f64 x (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (neg.f64 (+.f64 0 (*.f64 x x))) (neg.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
(*.f64 x (/.f64 x (-.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))) (neg.f64 (+.f64 1 (-.f64 1 (+.f64 (*.f64 x x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) 1) (-.f64 2 (fma.f64 x x (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(/.f64 (+.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) (-.f64 2 (fma.f64 x x (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(pow.f64 (hypot.f64 1 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) 2)
(pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) 3)
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3) 1/3)
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 2))
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3))
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(exp.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1))
(exp.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(fma.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(fma.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 1)
(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(fma.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)

eval50.0ms (2.3%)

Compiler

Compiled 2548 to 1909 computations (25.1% saved)

prune18.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1430143
Fresh000
Picked011
Done022
Total1433146
Error
0b
Counts
146 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
✓0b
(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
✓0.4b
(log.f64 (/.f64 2 x))
✓0.1b
(log.f64 (+.f64 (*.f64 -1/2 x) (*.f64 2 (/.f64 1 x))))
Compiler

Compiled 28 to 22 computations (21.4% saved)

regimes12.0ms (0.5%)

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

3 calls:

4.0ms
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
4.0ms
(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
3.0ms
x
Results
ErrorSegmentsBranch
0b1x
0b1(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0b1(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
Compiler

Compiled 68 to 48 computations (29.4% saved)

regimes4.0ms (0.2%)

Accuracy

Total -0.3b remaining (-300.1%)

Threshold costs -0.3b (-300.1%)

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

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
0.1b1x
Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify5.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
12×+-commutative
10×*-commutative
4×sub-neg
4×neg-mul-1
4×cancel-sign-sub-inv
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02073
13173
23973
34373
44573
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
(log.f64 (+.f64 (*.f64 -1/2 x) (*.f64 2 (/.f64 1 x))))
(log.f64 (/.f64 2 x))
Outputs
(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
(log.f64 (+.f64 (*.f64 -1/2 x) (*.f64 2 (/.f64 1 x))))
(log.f64 (+.f64 (*.f64 x -1/2) (*.f64 2 (/.f64 1 x))))
(log.f64 (/.f64 2 x))
Compiler

Compiled 28 to 22 computations (21.4% saved)

soundness104.0ms (4.9%)

Algorithm
1×egg-herbie
Rules
1032×+-commutative
908×associate-*r*
700×associate-*l*
636×associate-/r*
550×fma-def
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
069614229
1189812847
2795912847
Stop Event
1×node limit
Compiler

Compiled 210 to 143 computations (31.9% saved)

end24.0ms (1.1%)

Compiler

Compiled 26 to 20 computations (23.1% saved)

Profiling

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