Details

Time bar (total: 1.7s)

analyze4.0ms (0.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%50%50%2
0%50%50%3
12.5%25%62.5%4
18.7%12.5%68.8%5
21.9%6.2%71.9%6
23.4%3.1%73.5%7
24.2%1.6%74.2%8
24.6%0.8%74.6%9
24.8%0.4%74.8%10
24.9%0.2%74.9%11
24.9%0.1%75%12
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample863.0ms (52%)

Results
849.0ms8252×body64valid
1.0ms10×body64invalid
1.0ms4×body128valid

preprocess16.0ms (0.9%)

Algorithm
2×egg-herbie
Rules
1×+-commutative_binary64
1×*-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11311
21411
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
1×*-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11311
21411
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
0.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 31 to 22 computations (29% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

series3.0ms (0.2%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
1.0ms
x
@0
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
1.0ms
x
@inf
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

rewrite38.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
648×pow1_binary64
603×add-log-exp_binary64
602×log1p-expm1-u_binary64
602×expm1-log1p-u_binary64
587×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
11469
217539
Stop Event
1×node limit
Counts
1 → 14
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x -1) 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 x -1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))

simplify40.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
616×times-frac_binary64
527×fma-neg_binary64
498×associate-/r*_binary64
470×fma-def_binary64
384×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01834
14534
210234
325634
464134
5184234
6721734
Stop Event
1×node limit
Counts
18 → 21
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/8 x) (/.f64 (/.f64 1/16 x) x)))
(-.f64 (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)) (/.f64 1/16 (*.f64 x x)))
(+.f64 x (+.f64 -1/2 (-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 x (-.f64 -1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x))))

prune15.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New19221
Fresh000
Picked011
Done000
Total19322
Error
0b
Counts
22 → 3
Alt Table
StatusErrorProgram
✓0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
▶0.4b
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x))))
42.2b
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))
Compiler

Compiled 230 to 177 computations (23% saved)

localize11.0ms (0.6%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x)))

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x)))
1.0ms
x
@inf
(*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x)))
1.0ms
x
@-inf
(*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x)))

rewrite63.0ms (3.8%)

Algorithm
1×batch-egg-rewrite
Rules
587×unpow-prod-down_binary64
397×log-prod_binary64
310×exp-prod_binary64
300×prod-exp_binary64
231×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0910
119910
2248110
Stop Event
1×node limit
Counts
1 → 67
Calls
Call 1
Inputs
(*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/8 (/.f64 1 x)) (*.f64 (/.f64 -1/16 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 x) -1/8) (*.f64 (/.f64 1 x) (/.f64 -1/16 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 -1/8 x) (/.f64 (/.f64 1/16 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (+.f64 -1/8 (/.f64 -1/16 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (/.f64 x (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (/.f64 x (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 -1/512 (*.f64 1/4096 (pow.f64 x -3))) (*.f64 x (fma.f64 (/.f64 1/16 x) (+.f64 -1/8 (/.f64 1/16 x)) 1/64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/64 (*.f64 1/256 (pow.f64 x -2))) (*.f64 x (+.f64 -1/8 (/.f64 1/16 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 -1/512 (*.f64 1/4096 (pow.f64 x -3)))) (*.f64 (neg.f64 x) (fma.f64 (/.f64 1/16 x) (+.f64 -1/8 (/.f64 1/16 x)) 1/64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 1/64 (*.f64 1/256 (pow.f64 x -2)))) (*.f64 (neg.f64 x) (+.f64 -1/8 (/.f64 1/16 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1/512 (*.f64 1/4096 (pow.f64 x -3))) 1) (*.f64 (fma.f64 (/.f64 1/16 x) (+.f64 -1/8 (/.f64 1/16 x)) 1/64) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/64 (*.f64 1/256 (pow.f64 x -2))) 1) (*.f64 (+.f64 -1/8 (/.f64 1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1/512 (*.f64 1/4096 (pow.f64 x -3))) -1) (*.f64 (fma.f64 (/.f64 1/16 x) (+.f64 -1/8 (/.f64 1/16 x)) 1/64) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/64 (*.f64 1/256 (pow.f64 x -2))) -1) (*.f64 (+.f64 -1/8 (/.f64 1/16 x)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (+.f64 -1/8 (/.f64 -1/16 x))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1/512 (*.f64 1/4096 (pow.f64 x -3))) (/.f64 1 x)) (fma.f64 (/.f64 1/16 x) (+.f64 -1/8 (/.f64 1/16 x)) 1/64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/64 (*.f64 1/256 (pow.f64 x -2))) (/.f64 1 x)) (+.f64 -1/8 (/.f64 1/16 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (-.f64 -1/512 (*.f64 1/4096 (pow.f64 x -3)))) (fma.f64 (/.f64 1/16 x) (+.f64 -1/8 (/.f64 1/16 x)) 1/64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (-.f64 1/64 (*.f64 1/256 (pow.f64 x -2)))) (+.f64 -1/8 (/.f64 1/16 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 -1/8 (/.f64 -1/16 x)) -1) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 -1/8 (/.f64 -1/16 x)) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 -1/8 (/.f64 -1/16 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))) 2)) (cbrt.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))) (sqrt.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 -1/8 (/.f64 -1/16 x)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (*.f64 (log.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 x) -1) (log.f64 (+.f64 -1/8 (/.f64 -1/16 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (neg.f64 (log.f64 x)) 1) (log.f64 (+.f64 -1/8 (/.f64 -1/16 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (neg.f64 (log.f64 x)) (*.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 x) -1) (*.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (neg.f64 (log.f64 x)) 1) (*.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (neg.f64 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (*.f64 (log.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (*.f64 (log.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (*.f64 (neg.f64 (log.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (*.f64 (neg.f64 (log.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) -1/8 (*.f64 (/.f64 1 x) (/.f64 -1/16 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/8 (/.f64 1 x) (*.f64 (/.f64 -1/16 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))))

simplify45.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
513×distribute-neg-frac_binary64
490×associate-/l*_binary64
485×fma-neg_binary64
434×unswap-sqr_binary64
360×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
017150
137132
277132
3164132
4420132
51446132
63951132
77381132
Stop Event
1×node limit
Counts
79 → 72
Calls
Call 1
Inputs
(/.f64 -1/16 (pow.f64 x 2))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
Outputs
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))

prune282.0ms (17%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New72072
Fresh011
Picked011
Done011
Total72375
Error
0b
Counts
75 → 3
Alt Table
StatusErrorProgram
✓0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
✓0.4b
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x))))
▶42.2b
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))
Compiler

Compiled 1271 to 986 computations (22.4% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 x (+.f64 x -1))
✓0.0b
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3)
✓29.4b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓39.6b
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))

series6.0ms (0.4%)

Counts
4 → 36
Calls

12 calls:

TimeVariablePointExpression
2.0ms
x
@0
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3)
1.0ms
x
@-inf
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))
1.0ms
x
@0
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))
0.0ms
x
@inf
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3)
0.0ms
x
@-inf
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3)

rewrite72.0ms (4.3%)

Algorithm
1×batch-egg-rewrite
Rules
813×pow1_binary64
766×add-log-exp_binary64
766×log1p-expm1-u_binary64
766×expm1-log1p-u_binary64
749×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0935
119735
2215635
Stop Event
1×node limit
Counts
4 → 105
Calls
Call 1
Inputs
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3)
(*.f64 x (+.f64 x -1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (cbrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/4) 1/3) (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (cbrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/4) 1/3) (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (sqrt.f64 (*.f64 x (+.f64 x -1)))) (*.f64 (neg.f64 x) (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) (*.f64 x x)) (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 (+.f64 x -1) (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x -1) (*.f64 x (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (+.f64 x -1)) (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) (*.f64 x (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2) (*.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 (+.f64 x -1)) (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (*.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/4) (pow.f64 (*.f64 x (+.f64 x -1)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 x -1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x -1) 3/2) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 3/2) (pow.f64 (*.f64 x (+.f64 x -1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2) 3/2) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) 3) (pow.f64 (sqrt.f64 (+.f64 x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 3) (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x (+.f64 x -1)) (cbrt.f64 (*.f64 x (+.f64 x -1)))) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x (+.f64 x -1)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x (+.f64 x -1)) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) x) (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) (+.f64 x -1)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2)) (cbrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (+.f64 x -1))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) 1) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (neg.f64 x) 3)) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (*.f64 x x) (neg.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (neg.f64 x) (neg.f64 x))) (-.f64 (*.f64 x x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 -1 (pow.f64 x 3)) x) (fma.f64 x x (-.f64 1 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 x x -1) x) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 -1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (fma.f64 x x -1)) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (+.f64 x -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (+.f64 x -1))))))))

simplify48.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
592×fma-neg_binary64
524×fma-def_binary64
463×cancel-sign-sub-inv_binary64
395×distribute-rgt-neg-in_binary64
330×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
045338
1123317
2318305
3907297
42576296
55896296
Stop Event
1×node limit
Counts
141 → 116
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(pow.f64 x 3)
(+.f64 (*.f64 -3/2 (pow.f64 x 2)) (pow.f64 x 3))
(+.f64 (*.f64 -3/2 (pow.f64 x 2)) (+.f64 (*.f64 3/8 x) (pow.f64 x 3)))
(+.f64 1/16 (+.f64 (*.f64 -3/2 (pow.f64 x 2)) (+.f64 (*.f64 3/8 x) (pow.f64 x 3))))
(*.f64 -1 (pow.f64 x 3))
(+.f64 (*.f64 -1 (pow.f64 x 3)) (*.f64 3/2 (pow.f64 x 2)))
(+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 (*.f64 -3/8 x) (*.f64 3/2 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 (*.f64 -3/8 x) (*.f64 3/2 (pow.f64 x 2)))) 1/16)
(*.f64 -1 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(+.f64 -1/2 (-.f64 x (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(-.f64 (-.f64 (+.f64 x -1/2) (/.f64 1/8 x)) (/.f64 1/16 (*.f64 x x)))
(+.f64 x (-.f64 (-.f64 -1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(-.f64 (-.f64 (+.f64 x -1/2) (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (neg.f64 x))
(-.f64 1/2 x)
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1 x (/.f64 1/8 x)))
(+.f64 1/2 (-.f64 (/.f64 1/8 x) x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 1/2 (fma.f64 -1 x (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 1/2 (+.f64 (/.f64 1/16 (*.f64 x x)) (-.f64 (/.f64 1/8 x) x)))
(+.f64 1/2 (+.f64 (/.f64 1/8 x) (-.f64 (/.f64 1/16 (*.f64 x x)) x)))
(+.f64 1/2 (+.f64 (/.f64 1/8 x) (-.f64 (/.f64 (/.f64 1/16 x) x) x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(+.f64 -1/2 (-.f64 x (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(-.f64 (-.f64 (+.f64 x -1/2) (/.f64 1/8 x)) (/.f64 1/16 (*.f64 x x)))
(+.f64 x (-.f64 (-.f64 -1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(-.f64 (-.f64 (+.f64 x -1/2) (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (neg.f64 x))
(-.f64 1/2 x)
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1 x (/.f64 1/8 x)))
(+.f64 1/2 (-.f64 (/.f64 1/8 x) x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 1/2 (fma.f64 -1 x (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 1/2 (+.f64 (/.f64 1/16 (*.f64 x x)) (-.f64 (/.f64 1/8 x) x)))
(+.f64 1/2 (+.f64 (/.f64 1/8 x) (-.f64 (/.f64 1/16 (*.f64 x x)) x)))
(+.f64 1/2 (+.f64 (/.f64 1/8 x) (-.f64 (/.f64 (/.f64 1/16 x) x) x)))
(pow.f64 x 3)
(+.f64 (*.f64 -3/2 (pow.f64 x 2)) (pow.f64 x 3))
(fma.f64 -3/2 (*.f64 x x) (pow.f64 x 3))
(*.f64 (*.f64 x x) (+.f64 x -3/2))
(*.f64 x (*.f64 x (+.f64 x -3/2)))
(+.f64 (*.f64 -3/2 (pow.f64 x 2)) (+.f64 (*.f64 3/8 x) (pow.f64 x 3)))
(fma.f64 -3/2 (*.f64 x x) (fma.f64 3/8 x (pow.f64 x 3)))
(fma.f64 (*.f64 x x) -3/2 (fma.f64 x 3/8 (pow.f64 x 3)))
(*.f64 x (+.f64 (fma.f64 x x 3/8) (*.f64 x -3/2)))
(fma.f64 x (fma.f64 x -3/2 3/8) (pow.f64 x 3))
(+.f64 1/16 (+.f64 (*.f64 -3/2 (pow.f64 x 2)) (+.f64 (*.f64 3/8 x) (pow.f64 x 3))))
(+.f64 1/16 (fma.f64 -3/2 (*.f64 x x) (fma.f64 3/8 x (pow.f64 x 3))))
(+.f64 1/16 (fma.f64 (*.f64 x x) -3/2 (fma.f64 x 3/8 (pow.f64 x 3))))
(fma.f64 x (fma.f64 x x 3/8) (fma.f64 x (*.f64 x -3/2) 1/16))
(fma.f64 x (fma.f64 x -3/2 (fma.f64 x x 3/8)) 1/16)
(fma.f64 x (fma.f64 x x (fma.f64 x -3/2 3/8)) 1/16)
(*.f64 -1 (pow.f64 x 3))
(neg.f64 (pow.f64 x 3))
(pow.f64 (neg.f64 x) 3)
(+.f64 (*.f64 -1 (pow.f64 x 3)) (*.f64 3/2 (pow.f64 x 2)))
(fma.f64 -1 (pow.f64 x 3) (*.f64 (*.f64 x x) 3/2))
(-.f64 (*.f64 x (*.f64 x 3/2)) (pow.f64 x 3))
(*.f64 (*.f64 x x) (-.f64 3/2 x))
(*.f64 x (*.f64 x (-.f64 3/2 x)))
(+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 (*.f64 -3/8 x) (*.f64 3/2 (pow.f64 x 2))))
(fma.f64 -1 (pow.f64 x 3) (fma.f64 -3/8 x (*.f64 (*.f64 x x) 3/2)))
(-.f64 (fma.f64 x -3/8 (*.f64 x (*.f64 x 3/2))) (pow.f64 x 3))
(fma.f64 x -3/8 (*.f64 (*.f64 x x) (-.f64 3/2 x)))
(*.f64 x (+.f64 (*.f64 x (-.f64 3/2 x)) -3/8))
(*.f64 x (-.f64 -3/8 (*.f64 x (+.f64 x -3/2))))
(-.f64 (+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 (*.f64 -3/8 x) (*.f64 3/2 (pow.f64 x 2)))) 1/16)
(+.f64 (fma.f64 -1 (pow.f64 x 3) (fma.f64 -3/8 x (*.f64 (*.f64 x x) 3/2))) -1/16)
(+.f64 (-.f64 (fma.f64 x -3/8 (*.f64 x (*.f64 x 3/2))) (pow.f64 x 3)) -1/16)
(+.f64 (*.f64 (*.f64 x x) (-.f64 3/2 x)) (fma.f64 x -3/8 -1/16))
(-.f64 (fma.f64 x (fma.f64 x 3/2 -3/8) -1/16) (pow.f64 x 3))
(fma.f64 x (-.f64 -3/8 (*.f64 x (+.f64 x -3/2))) -1/16)
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(-.f64 (*.f64 x x) x)

prune104.0ms (6.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1160116
Fresh000
Picked011
Done022
Total1163119
Error
0b
Counts
119 → 3
Alt Table
StatusErrorProgram
✓0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
✓0.4b
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x))))
✓42.2b
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))
Compiler

Compiled 1421 to 1040 computations (26.8% saved)

regimes9.0ms (0.5%)

Accuracy

Total -42.3b remaining (-10432.6%)

Threshold costs -42.3b (-10432.6%)

Counts
3 → 1
Calls
Call 1
Inputs
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x))))
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x))))
Results
3.0ms0.4bx
4.0ms0.4b(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 40 to 30 computations (25% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
4×+-commutative_binary64
2×*-commutative_binary64
2×sub-neg_binary64
1×distribute-neg-frac_binary64
1×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01219
11919
22619
32819
42919
Stop Event
1×saturated
Calls
Call 1
Inputs
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x))))
Outputs
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 1 x) (-.f64 -1/8 (/.f64 1/16 x))))
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 1 x) (+.f64 -1/8 (/.f64 -1/16 x))))

end16.0ms (1%)

Stop Event
1×done
Compiler

Compiled 28 to 22 computations (21.4% saved)

Profiling

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