Details

Time bar (total: 8.9s)

analyze172.0ms (1.9%)

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
25%25%75%0%0%0%0%3
28.6%25%62.5%0%0%0%12.5%4
30.8%25%56.2%0%0%0%18.7%5
36%28.1%50%0%0%0%21.9%6
38.8%29.7%46.9%0%0%0%23.4%7
40.2%30.5%45.3%0%0%0%24.2%8
40.7%30.8%44.9%0%0%0%24.2%9
41.2%31.2%44.5%0%0%0%24.2%10
41.4%31.3%44.4%0%0%0%24.2%11
41.5%31.4%44.3%0%0%0%24.3%12
Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.1s (23.7%)

Results
1.1s2719×body1024valid
459.0ms3899×body256valid
392.0ms1359×body512valid
137.0ms279×body2048valid
5.0ms45×body256infinite
0.0ms2×body256unsamplable
Bogosity

preprocess42.0ms (0.5%)

Algorithm
2×egg-herbie
Rules
633×associate-/l*_binary64
580×associate-*l*_binary64
568×associate-*r*_binary64
505×associate-/r*_binary64
380×fma-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
12513
23413
35913
412711
53498
613418
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify31.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
633×associate-/l*_binary64
580×associate-*l*_binary64
568×associate-*r*_binary64
505×associate-/r*_binary64
380×fma-def_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01113
12513
23413
35913
412711
53498
613418
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

eval1.0ms (0%)

Compiler

Compiled 18 to 14 computations (22.2% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.3b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.3b
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 6 to 5 computations (16.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (exp.f64 x))
✓0.2b
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 14 to 8 computations (42.9% saved)

series3.0ms (0%)

Counts
2 → 8
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(sqrt.f64 (+.f64 1 (exp.f64 x)))
1.0ms
x
@inf
(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0ms
x
@-inf
(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0ms
x
@0
(+.f64 1 (exp.f64 x))
0.0ms
x
@-inf
(+.f64 1 (exp.f64 x))

rewrite155.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
550×pow1_binary64
512×add-log-exp_binary64
512×log1p-expm1-u_binary64
512×expm1-log1p-u_binary64
500×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0614
111814
2142914
Stop Event
1×node limit
Counts
2 → 58
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 1 (exp.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (exp.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (/.f64 1 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (pow.f64 (exp.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (neg.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (neg.f64 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (exp.f64 (+.f64 x x)) 1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)))))

simplify124.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
586×fma-def_binary64
525×cancel-sign-sub-inv_binary64
434×fma-neg_binary64
433×associate-*r*_binary64
405×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
035169
1109137
2339131
31110103
45494103
Stop Event
1×node limit
Counts
66 → 71
Calls
Call 1
Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x)))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x)))) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(+.f64 (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))) (fma.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3))))))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 (fma.f64 1/2 x 1) x 2)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 2 (fma.f64 1/2 (*.f64 x x) x)))
(+.f64 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(+.f64 2 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x)))
(fma.f64 (fma.f64 1/2 x 1) x (fma.f64 1/6 (pow.f64 x 3) 2))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 (fma.f64 1/2 x 1) x 2))

eval19.0ms (0.2%)

Compiler

Compiled 818 to 581 computations (29% saved)

prune102.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New63871
Fresh000
Picked011
Done000
Total63972
Error
0.2b
Counts
72 → 9
Alt Table
Click to see full alt table
StatusErrorProgram
▶20.8b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
▶17.1b
(sqrt.f64 2)
▶0.9b
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
20.2b
(sqrt.f64 (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
✓0.3b
(sqrt.f64 (+.f64 1 (exp.f64 x)))
21.0b
(sqrt.f64 (+.f64 2 x))
20.8b
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3))))))
▶20.8b
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
▶20.4b
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))))
Compiler

Compiled 274 to 243 computations (11.3% saved)

localize112.0ms (1.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
0.0b
(+.f64 1 (exp.f64 x))
0.2b
(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓0.7b
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
Compiler

Compiled 30 to 20 computations (33.3% saved)

series2.0ms (0%)

Counts
2 → 16
Calls

6 calls:

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

rewrite65.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
889×pow1_binary64
832×add-log-exp_binary64
832×log1p-expm1-u_binary64
832×expm1-log1p-u_binary64
816×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0825
117919
2259019
Stop Event
1×node limit
Counts
2 → 79
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1)) (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)) 3)) (+.f64 1 (-.f64 (*.f64 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)) (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))) (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)) (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))) (-.f64 1 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (exp.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) -1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (/.f64 (+.f64 1 (exp.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 2) (*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (*.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)) (/.f64 1 (+.f64 1 (-.f64 (+.f64 1 (exp.f64 x)) (sqrt.f64 (+.f64 1 (exp.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 0 (exp.f64 x)) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (+.f64 1 (exp.f64 x)) (sqrt.f64 (+.f64 1 (exp.f64 x))))) (+.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 0 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 x) (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)) (+.f64 1 (-.f64 (+.f64 1 (exp.f64 x)) (sqrt.f64 (+.f64 1 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)) (+.f64 (+.f64 1 (exp.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (exp.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))) (neg.f64 (+.f64 1 (-.f64 (+.f64 1 (exp.f64 x)) (sqrt.f64 (+.f64 1 (exp.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 0 (exp.f64 x))) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)) 1) (+.f64 1 (-.f64 (+.f64 1 (exp.f64 x)) (sqrt.f64 (+.f64 1 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 0 (exp.f64 x)) 1) (-.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 1)))))

simplify86.0ms (1%)

Algorithm
1×egg-herbie
Rules
666×fma-def_binary64
525×cancel-sign-sub-inv_binary64
438×fma-neg_binary64
398×associate-*r*_binary64
359×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
040346
1118282
2354270
31117222
45443222
Stop Event
1×node limit
Counts
95 → 93
Calls
Call 1
Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (sqrt.f64 2) 1)
(+.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))))
Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x))) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(+.f64 (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))) (fma.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3) (sqrt.f64 2)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (sqrt.f64 2) 1)
(+.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) 1))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1)
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) 1))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2)))) 1))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x))) 1))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (+.f64 (sqrt.f64 2) 1))
(+.f64 (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))) (+.f64 (sqrt.f64 2) 1))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))))
(+.f64 (sqrt.f64 2) (+.f64 (fma.f64 1/2 (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))) 1))
(+.f64 (sqrt.f64 2) (+.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x))) 1)))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) 1))
(+.f64 (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))) (+.f64 (sqrt.f64 2) (fma.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3) 1)))

localize2.0ms (0%)

Compiler

Compiled 4 to 4 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
✓0.4b
(/.f64 x (sqrt.f64 2))
Compiler

Compiled 25 to 21 computations (16% saved)

series3.0ms (0%)

Counts
2 → 3
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 x (sqrt.f64 2))
1.0ms
x
@inf
(/.f64 x (sqrt.f64 2))
1.0ms
x
@-inf
(/.f64 x (sqrt.f64 2))
0.0ms
x
@0
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
0.0ms
x
@inf
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))

rewrite81.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
953×pow1_binary64
893×add-log-exp_binary64
892×log1p-expm1-u_binary64
892×expm1-log1p-u_binary64
90×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0820
117918
2238818
Stop Event
1×node limit
Counts
2 → 68
Calls
Call 1
Inputs
(/.f64 x (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (cbrt.f64 (/.f64 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 x x) 2)) (cbrt.f64 (/.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (sqrt.f64 2))) (sqrt.f64 (/.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 x (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 x (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 x) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 2 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 2 (-.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) 1/2))) (/.f64 (*.f64 (/.f64 (*.f64 x x) 2) 1/4) (-.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2) (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 2 3/2) (*.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8)) (/.f64 1 (+.f64 2 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2) (-.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 2 (*.f64 (/.f64 (*.f64 x x) 2) 1/4)) (/.f64 1 (-.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 2 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2) (-.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2) (sqrt.f64 2)))) (+.f64 (pow.f64 2 3/2) (*.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) 1/2)) (-.f64 2 (*.f64 (/.f64 (*.f64 x x) 2) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 2 3/2) (*.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8)) (+.f64 2 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2) (-.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 2 3/2) (*.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8)) (+.f64 (*.f64 (/.f64 (*.f64 x x) 2) 1/4) (-.f64 2 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 2 (*.f64 (/.f64 (*.f64 x x) 2) 1/4)) (-.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 2 3/2) (*.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8))) (neg.f64 (+.f64 2 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2) (-.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 2 (*.f64 (/.f64 (*.f64 x x) 2) 1/4))) (neg.f64 (-.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) 2) 1/4) 2) (-.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 x x) 2) 1/4)) (cbrt.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2)) (sqrt.f64 (*.f64 (/.f64 x (sqrt.f64 2)) 1/2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 2 1/4) (pow.f64 2 1/4) (*.f64 (/.f64 x (sqrt.f64 2)) 1/2))))))

simplify10.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
3×*-commutative_binary64
2×associate-/l*_binary64
1×associate-*r/_binary64
1×associate-*l/_binary64
1×associate-/r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0721
11021
21421
31821
41921
Stop Event
1×saturated
Counts
71 → 70
Calls
Call 1
Inputs
(sqrt.f64 2)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
Outputs
(sqrt.f64 2)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))))
✓0.1b
(*.f64 x (*.f64 x 3/8))
✓0.4b
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8))))
✓1.0b
(/.f64 1/2 (sqrt.f64 2))
Compiler

Compiled 53 to 40 computations (24.5% saved)

series6.0ms (0.1%)

Counts
4 → 36
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8))))
1.0ms
x
@0
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8))))
1.0ms
x
@inf
(*.f64 x (*.f64 x 3/8))
1.0ms
x
@-inf
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8))))
0.0ms
x
@inf
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))))

rewrite105.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
634×log-prod_binary64
532×fma-def_binary64
343×pow2_binary64
234×pow1/3_binary64
232×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01254
127839
2403839
Stop Event
1×node limit
Counts
4 → 201
Calls
Call 1
Inputs
(/.f64 1/2 (sqrt.f64 2))
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8))))
(*.f64 x (*.f64 x 3/8))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 1/8))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 1/8)))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 1/8) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 1/8)) (sqrt.f64 (sqrt.f64 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 1/8) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/16 (sqrt.f64 2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 2 -1/2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 2 3/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 2 3/2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1/16 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 1/8)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 1/8)))))))
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simplify138.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
1250×associate-/l/_binary64
773×associate-*l/_binary64
645×associate-*r/_binary64
642×fma-def_binary64
283×*-commutative_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
016545
134543
265531
3121531
4287441
51018395
62597395
74031395
84396395
94587395
104767395
115045395
126554395
Stop Event
1×node limit
Counts
237 → 214
Calls
Call 1
Inputs
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (pow.f64 x 2))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
Outputs
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 1/2 x) (sqrt.f64 2))
(*.f64 x (/.f64 1/2 (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x))
(*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 2)) 3/16))
(*.f64 x (/.f64 (*.f64 x 3/16) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x))
(*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 2)) 3/16))
(*.f64 x (/.f64 (*.f64 x 3/16) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(*.f64 3/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 3/8)
(*.f64 x (*.f64 x 3/8))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 x (/.f64 1/2 (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x) (sqrt.f64 2)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))
(fma.f64 (/.f64 x (sqrt.f64 2)) (fma.f64 x 3/16 1/2) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x) (sqrt.f64 2)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))
(fma.f64 (/.f64 x (sqrt.f64 2)) (fma.f64 x 3/16 1/2) (sqrt.f64 2))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x))
(*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 2)) 3/16))
(*.f64 x (/.f64 (*.f64 x 3/16) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x) (sqrt.f64 2)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))
(fma.f64 (/.f64 x (sqrt.f64 2)) (fma.f64 x 3/16 1/2) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x) (sqrt.f64 2)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))
(fma.f64 (/.f64 x (sqrt.f64 2)) (fma.f64 x 3/16 1/2) (sqrt.f64 2))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x))
(*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 2)) 3/16))
(*.f64 x (/.f64 (*.f64 x 3/16) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 x (sqrt.f64 2)) (*.f64 x 3/16)))
(*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16)))
(/.f64 (*.f64 x (fma.f64 x 3/16 1/2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x) (sqrt.f64 2)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))
(fma.f64 (/.f64 x (sqrt.f64 2)) (fma.f64 x 3/16 1/2) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (/.f64 (*.f64 1/2 x) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 3/16 (*.f64 (/.f64 x (sqrt.f64 2)) x) (sqrt.f64 2)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))
(fma.f64 (/.f64 x (sqrt.f64 2)) (fma.f64 x 3/16 1/2) (sqrt.f64 2))

localize295.0ms (3.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓1.0b
(pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)
1.0b
(/.f64 1/2 (sqrt.f64 2))
✓1.0b
(-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2))))
✓8.8b
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
Compiler

Compiled 335 to 316 computations (5.7% saved)

series6.0ms (0.1%)

Counts
3 → 12
Calls

3 calls:

TimeVariablePointExpression
3.0ms
x
@0
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
2.0ms
x
@inf
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
1.0ms
x
@-inf
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))

rewrite106.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
297×add-sqr-sqrt_binary64
290×pow1_binary64
286×*-un-lft-identity_binary64
281×add-log-exp_binary64
281×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02699
163033
Stop Event
1×node limit
Counts
3 → 46
Calls
Call 1
Inputs
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2))))
(pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)
Outputs
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(*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) 1/2 (*.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (*.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x))) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 (pow.f64 x 6) 49/9216) 2) 1/4)) (cbrt.f64 (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))) (*.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x))) 2)) (cbrt.f64 (*.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)))) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))) (sqrt.f64 (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))) (*.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)))) (sqrt.f64 (*.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)))) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))))
((#(struct:change #<rule egg-rr> (2) ((x . 7/96)))))
((#(struct:change #<rule egg-rr> (2) ((x . 1/8)))))

simplify45.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
625×distribute-rgt-out_binary64
431×cancel-sign-sub-inv_binary64
395×fma-neg_binary64
311×associate-*r*_binary64
279×times-frac_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
030697
197316
2308304
3785277
43835237
Stop Event
1×node limit
Counts
58 → 56
Calls
Call 1
Inputs
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
Outputs
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 1/2 x) (sqrt.f64 2))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x)))
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8))))
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 3/8 (*.f64 x x))))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (*.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))
(+.f64 (/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (/.f64 x (sqrt.f64 2))) (*.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3)))))
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x 7/96) 3/8)) x))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (*.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))
(+.f64 (/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (/.f64 x (sqrt.f64 2))) (*.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3)))))
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x 7/96) 3/8)) x))
(*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))
(*.f64 1/2 (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))))
(/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))
(/.f64 (*.f64 (pow.f64 x 3) 7/192) (sqrt.f64 2))
(*.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))))
(*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(+.f64 (/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))
(+.f64 (*.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x)) (/.f64 (*.f64 (pow.f64 x 3) 7/192) (sqrt.f64 2)))
(*.f64 (*.f64 x x) (+.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 (/.f64 7/192 (sqrt.f64 2)) x)))
(*.f64 1/2 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8)))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (*.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))
(+.f64 (/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (/.f64 x (sqrt.f64 2))) (*.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3)))))
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x 7/96) 3/8)) x))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (*.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))
(+.f64 (/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (/.f64 x (sqrt.f64 2))) (*.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3)))))
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x 7/96) 3/8)) x))
(*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))
(*.f64 1/2 (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))))
(/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))
(/.f64 (*.f64 (pow.f64 x 3) 7/192) (sqrt.f64 2))
(*.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))))
(*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(+.f64 (/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))
(+.f64 (*.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x)) (/.f64 (*.f64 (pow.f64 x 3) 7/192) (sqrt.f64 2)))
(*.f64 (*.f64 x x) (+.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 (/.f64 7/192 (sqrt.f64 2)) x)))
(*.f64 1/2 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8)))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (*.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))
(+.f64 (/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (/.f64 x (sqrt.f64 2))) (*.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3)))))
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x 7/96) 3/8)) x))
(+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (*.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 2))) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))))))
(+.f64 (/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (/.f64 x (sqrt.f64 2))) (*.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x)))
(fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3)))))
(*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x 7/96) 3/8)) x))

eval447.0ms (5%)

Compiler

Compiled 12864 to 10722 computations (16.7% saved)

prune118.0ms (1.3%)

Pruning

14 alts after pruning (11 fresh and 3 done)

PrunedKeptTotal
New5449553
Fresh123
Picked101
Done235
Total54814562
Error
0.2b
Counts
562 → 14
Alt Table
Click to see full alt table
StatusErrorProgram
✓20.8b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
20.8b
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x 7/96) 3/8)) x)))
▶20.7b
(+.f64 (sqrt.f64 2) (*.f64 x (/.f64 (*.f64 x 3/16) (sqrt.f64 2))))
20.8b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))))
▶21.0b
(sqrt.f64 (+.f64 2 x))
20.9b
(+.f64 (sqrt.f64 2) (expm1.f64 (log1p.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))))
▶21.3b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8))))
▶21.7b
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
20.4b
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/8) (+.f64 x (*.f64 x (*.f64 x 3/8)))))
▶17.7b
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
✓17.1b
(sqrt.f64 2)
20.2b
(sqrt.f64 (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
✓0.3b
(sqrt.f64 (+.f64 1 (exp.f64 x)))
62.2b
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
Compiler

Compiled 331 to 279 computations (15.7% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓1.0b
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
Compiler

Compiled 15 to 15 computations (0% saved)

series0.0ms (0%)

Counts
1 → 0

rewrite45.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
543×pow1_binary64
516×add-log-exp_binary64
515×log1p-expm1-u_binary64
515×expm1-log1p-u_binary64
507×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
066
11383
217493
Stop Event
1×node limit
Counts
1 → 42
Calls
Call 1
Inputs
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (sqrt.f64 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (sqrt.f64 2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (sqrt.f64 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (/.f64 1 (+.f64 (sqrt.f64 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (-.f64 (sqrt.f64 2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2)) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (sqrt.f64 2) 2) (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (-.f64 1 (*.f64 (+.f64 (sqrt.f64 2) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 2 3/2) (+.f64 2 (-.f64 0 (*.f64 (sqrt.f64 2) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (+.f64 (sqrt.f64 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (-.f64 (+.f64 (sqrt.f64 2) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2))) (neg.f64 (+.f64 (sqrt.f64 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 2 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 2 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 2 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 2)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 2 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (sqrt.f64 2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) 1)) 2) (cbrt.f64 (+.f64 (sqrt.f64 2) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 2 1/4) (pow.f64 2 1/4) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 2 1/4)) (hypot.f64 1 (pow.f64 2 1/4)) -1)))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
42 → 42
Calls
Call 1
Inputs
Outputs

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 2 x))
Compiler

Compiled 10 to 7 computations (30% saved)

series3.0ms (0%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(sqrt.f64 (+.f64 2 x))
1.0ms
x
@0
(sqrt.f64 (+.f64 2 x))
1.0ms
x
@-inf
(sqrt.f64 (+.f64 2 x))

rewrite55.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
554×pow1_binary64
522×add-log-exp_binary64
521×log1p-expm1-u_binary64
521×expm1-log1p-u_binary64
512×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11116
213816
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 2 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))))))

simplify113.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
1230×associate-/l/_binary64
989×fma-def_binary64
558×unswap-sqr_binary64
360×times-frac_binary64
349×sqr-pow_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02490
16782
218878
357870
4293966
5427966
6535266
7628766
8655766
9685566
Stop Event
1×node limit
Counts
26 → 29
Calls
Call 1
Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))))
(fma.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))))
(fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)))))
(fma.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (sqrt.f64 2)))

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
0.0b
(sqrt.f64 (+.f64 2 x))
✓0.7b
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
Compiler

Compiled 25 to 20 computations (20% saved)

series8.0ms (0.1%)

Counts
2 → 8
Calls

6 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
1.0ms
x
@inf
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
1.0ms
x
@0
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
1.0ms
x
@0
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
1.0ms
x
@-inf
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)

rewrite98.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
915×pow1_binary64
862×add-log-exp_binary64
861×log1p-expm1-u_binary64
861×expm1-log1p-u_binary64
95×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0821
118615
2261015
Stop Event
1×node limit
Counts
2 → 80
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 2 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 (sqrt.f64 (+.f64 2 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 (sqrt.f64 (+.f64 2 x)) 2)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 2) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 (sqrt.f64 (+.f64 2 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 (sqrt.f64 (+.f64 2 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1)) (neg.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))) (-.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 2 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) -1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (/.f64 (+.f64 2 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (*.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (/.f64 1 (+.f64 1 (-.f64 (+.f64 2 x) (sqrt.f64 (+.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 -1 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (+.f64 2 x) (sqrt.f64 (+.f64 2 x)))) (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))) (-.f64 -1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (+.f64 1 (-.f64 (+.f64 2 x) (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (+.f64 (+.f64 2 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (neg.f64 (+.f64 1 (-.f64 (+.f64 2 x) (sqrt.f64 (+.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 -1 x)) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 2 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) 1) (+.f64 1 (-.f64 (+.f64 2 x) (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1 x) 1) (-.f64 1 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4) 1)))))

simplify102.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
1221×associate-/l/_binary64
942×associate-/r/_binary64
558×unswap-sqr_binary64
548×fma-def_binary64
360×times-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
032192
190176
2251168
3744152
43437152
54069152
65142152
75401152
85644152
95945152
Stop Event
1×node limit
Counts
88 → 94
Calls
Call 1
Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) 1)
(+.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))))
Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 -1/16 x))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))))
(fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 -1/16 x)))))
(+.f64 (sqrt.f64 2) 1)
(+.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) 1))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) 1))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 1/2 (sqrt.f64 2)) x 1))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (+.f64 (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))) 1))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2))) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) 1)))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) 1)))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))) 1))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 -1/16 x))) 1))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))))
(+.f64 (sqrt.f64 2) (+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) 1))
(+.f64 (sqrt.f64 2) (+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))) 1))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) 1))))
(+.f64 (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) 1)))
(+.f64 (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 -1/16 x))) (+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) 1)))

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 x (/.f64 (*.f64 x 3/16) (sqrt.f64 2)))
✓0.5b
(/.f64 (*.f64 x 3/16) (sqrt.f64 2))
Compiler

Compiled 34 to 27 computations (20.6% saved)

series22.0ms (0.3%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
20.0ms
x
@0
(*.f64 x (/.f64 (*.f64 x 3/16) (sqrt.f64 2)))
1.0ms
x
@inf
(*.f64 x (/.f64 (*.f64 x 3/16) (sqrt.f64 2)))
1.0ms
x
@-inf
(/.f64 (*.f64 x 3/16) (sqrt.f64 2))
1.0ms
x
@0
(/.f64 (*.f64 x 3/16) (sqrt.f64 2))
1.0ms
x
@inf
(/.f64 (*.f64 x 3/16) (sqrt.f64 2))

rewrite61.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
848×pow1_binary64
795×add-log-exp_binary64
795×log1p-expm1-u_binary64
795×expm1-log1p-u_binary64
780×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0821
117121
2213721
Stop Event
1×node limit
Counts
2 → 64
Calls
Call 1
Inputs
(/.f64 (*.f64 x 3/16) (sqrt.f64 2))
(*.f64 x (/.f64 (*.f64 x 3/16) (sqrt.f64 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (*.f64 (sqrt.f64 2) 16/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 3/16 (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 3/16 (/.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 3/16 (*.f64 x (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 3/16) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (*.f64 (sqrt.f64 2) 16/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))) (cbrt.f64 (/.f64 (*.f64 (*.f64 x x) 9/256) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 x x) 9/256) 2)) (cbrt.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x 3/16)) 2) (*.f64 (cbrt.f64 (*.f64 x 3/16)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))) (sqrt.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x 3/16)) (*.f64 (sqrt.f64 (*.f64 x 3/16)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x -3/16) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (*.f64 x 3/16))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 1) (/.f64 3/16 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (cbrt.f64 2)) (/.f64 3/16 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (pow.f64 2 1/4)) (/.f64 3/16 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (sqrt.f64 2)) 3/16)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 x 3/16)) 2) 1) (/.f64 (cbrt.f64 (*.f64 x 3/16)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 x 3/16)) 1) (/.f64 (sqrt.f64 (*.f64 x 3/16)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 3/16 (cbrt.f64 2)) (/.f64 x (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (*.f64 x 3/16) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 x 3/16)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 x 3/16)) (cbrt.f64 2)) (/.f64 (sqrt.f64 (*.f64 x 3/16)) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 3/16 (pow.f64 2 1/4)) (/.f64 x (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (*.f64 x 3/16) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 x 3/16)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (*.f64 x 3/16)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 16/3 (/.f64 (sqrt.f64 2) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 x 3/16) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 (*.f64 x x) 9/256) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 x 3/16) 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (/.f64 x (*.f64 (sqrt.f64 2) 16/3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (*.f64 16/3 (/.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 x (*.f64 x 3/16))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x x) (*.f64 (sqrt.f64 2) 16/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (*.f64 x 3/16)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 x (*.f64 x 3/16))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x -3/16) x) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (*.f64 x -3/16)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x (*.f64 x 3/16)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x (*.f64 x 3/16)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x (*.f64 x 3/16)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (/.f64 x (*.f64 (sqrt.f64 2) 16/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (/.f64 x (*.f64 (sqrt.f64 2) 16/3))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (/.f64 x (*.f64 (sqrt.f64 2) 16/3)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (/.f64 x (*.f64 (sqrt.f64 2) 16/3)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (/.f64 x (*.f64 (sqrt.f64 2) 16/3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (/.f64 x (*.f64 (sqrt.f64 2) 16/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (/.f64 x (*.f64 (sqrt.f64 2) 16/3))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 x (*.f64 (sqrt.f64 2) 16/3)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (/.f64 x (*.f64 (sqrt.f64 2) 16/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (/.f64 x (*.f64 (sqrt.f64 2) 16/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (/.f64 x (*.f64 (sqrt.f64 2) 16/3)))))))))

simplify106.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
1372×associate-*l/_binary64
1103×associate-*r/_binary64
349×sqr-pow_binary64
314×*-commutative_binary64
242×unswap-sqr_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010252
121252
238252
370252
4192252
5691252
61809252
72827252
82937252
93078252
103256252
113526252
123852252
135336252
147988252
Stop Event
1×node limit
Counts
88 → 67
Calls
Call 1
Inputs
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
Outputs
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 x (sqrt.f64 2)))
(/.f64 (*.f64 3/16 x) (sqrt.f64 2))
(/.f64 3/16 (/.f64 (sqrt.f64 2) x))
(*.f64 (/.f64 3/16 (sqrt.f64 2)) x)
(*.f64 x (/.f64 3/16 (sqrt.f64 2)))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(/.f64 (*.f64 3/16 (*.f64 x x)) (sqrt.f64 2))
(*.f64 3/16 (/.f64 x (/.f64 (sqrt.f64 2) x)))
(*.f64 3/16 (*.f64 x (/.f64 x (sqrt.f64 2))))
(*.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))
(*.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))))

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8))))
✓0.2b
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8))
✓0.2b
(/.f64 (*.f64 x x) (sqrt.f64 2))
✓0.4b
(*.f64 x 7/96)
Compiler

Compiled 68 to 48 computations (29.4% saved)

series7.0ms (0.1%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@0
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8))
1.0ms
x
@inf
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8))
1.0ms
x
@0
(*.f64 x 7/96)
1.0ms
x
@inf
(*.f64 x 7/96)
1.0ms
x
@-inf
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8))

rewrite121.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
753×log-prod_binary64
371×fma-def_binary64
272×expm1-udef_binary64
272×log1p-udef_binary64
226×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01453
132151
2446951
Stop Event
1×node limit
Counts
4 → 205
Calls
Call 1
Inputs
(*.f64 x 7/96)
(/.f64 (*.f64 x x) (sqrt.f64 2))
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8))))
Outputs
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(#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 2))) (pow.f64 (pow.f64 (exp.f64 (fma.f64 x 7/96 3/8)) (*.f64 (/.f64 x (sqrt.f64 2)) x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 2)) (+.f64 1 (expm1.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 2))) (+.f64 1 (expm1.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2)))) (exp.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 x 7/96 3/8)) (*.f64 (/.f64 x (sqrt.f64 2)) x)) 1/2) (+.f64 1 (expm1.f64 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2)))) (+.f64 1 (expm1.f64 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 2) 1 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x 7/96 3/8) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 1/2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (fma.f64 x 7/96 3/8) (/.f64 (/.f64 (sqrt.f64 2) x) x)) 1/2 (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 (fma.f64 x 7/96 3/8) (/.f64 (/.f64 (sqrt.f64 2) x) x)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2)) 1 (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 2) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 x 4) 2) (pow.f64 (fma.f64 x 7/96 3/8) 2))) (*.f64 (cbrt.f64 (/.f64 (fma.f64 x 7/96 3/8) (/.f64 (/.f64 (sqrt.f64 2) x) x))) 1/2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2))) (cbrt.f64 (*.f64 (*.f64 (/.f64 (pow.f64 x 4) 2) (pow.f64 (fma.f64 x 7/96 3/8) 2)) 1/4)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 (/.f64 (pow.f64 x 4) 2) (pow.f64 (fma.f64 x 7/96 3/8) 2)) 1/4)) (cbrt.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 x (pow.f64 2 1/4)) (sqrt.f64 (fma.f64 x 7/96 3/8))) (*.f64 (*.f64 (/.f64 x (pow.f64 2 1/4)) (sqrt.f64 (fma.f64 x 7/96 3/8))) 1/2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (/.f64 x (pow.f64 2 1/4)) (sqrt.f64 (fma.f64 x 7/96 3/8))) (sqrt.f64 1/2)) (*.f64 (*.f64 (/.f64 x (pow.f64 2 1/4)) (sqrt.f64 (fma.f64 x 7/96 3/8))) (sqrt.f64 1/2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 2 1/4) (pow.f64 2 1/4) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) (*.f64 (fma.f64 x 7/96 3/8) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 1/2) (fma.f64 x 7/96 3/8) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (fma.f64 x 7/96 3/8)) (*.f64 (/.f64 x (sqrt.f64 2)) x) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (cbrt.f64 (*.f64 (/.f64 (pow.f64 x 4) 2) (pow.f64 (fma.f64 x 7/96 3/8) 2)))) (cbrt.f64 (/.f64 (fma.f64 x 7/96 3/8) (/.f64 (/.f64 (sqrt.f64 2) x) x))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (*.f64 (/.f64 x (pow.f64 2 1/4)) (sqrt.f64 (fma.f64 x 7/96 3/8)))) (*.f64 (/.f64 x (pow.f64 2 1/4)) (sqrt.f64 (fma.f64 x 7/96 3/8))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 1/2) 1) (fma.f64 x 7/96 3/8) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x 7/96 3/8)) 2)) (cbrt.f64 (fma.f64 x 7/96 3/8)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 1/2) (sqrt.f64 (fma.f64 x 7/96 3/8))) (sqrt.f64 (fma.f64 x 7/96 3/8)) (sqrt.f64 2))))))

simplify135.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
926×fma-def_binary64
738×associate-*l/_binary64
572×associate-*r/_binary64
388×associate-/l*_binary64
385×*-commutative_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
023674
155672
2116660
3255660
4839570
52663524
64635524
75101524
85478524
95695524
105971524
116403524
Stop Event
1×node limit
Counts
253 → 224
Calls
Call 1
Inputs
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
Outputs
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(*.f64 7/96 x)
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(/.f64 (pow.f64 x 2) (sqrt.f64 2))
(/.f64 (*.f64 x x) (sqrt.f64 2))
(/.f64 x (/.f64 (sqrt.f64 2) x))
(*.f64 x (/.f64 x (sqrt.f64 2)))
(*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2)))
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/8)
(/.f64 3/8 (/.f64 (sqrt.f64 2) (*.f64 x x)))
(*.f64 (*.f64 x x) (/.f64 3/8 (sqrt.f64 2)))
(*.f64 x (*.f64 3/8 (/.f64 x (sqrt.f64 2))))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
(fma.f64 3/8 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (/.f64 3/8 (/.f64 (sqrt.f64 2) (*.f64 x x))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/8 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 3/8 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/8 (*.f64 7/96 x)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 7/96 x 3/8))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
(fma.f64 3/8 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (/.f64 3/8 (/.f64 (sqrt.f64 2) (*.f64 x x))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/8 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 3/8 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/8 (*.f64 7/96 x)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 7/96 x 3/8))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
(fma.f64 3/8 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (/.f64 3/8 (/.f64 (sqrt.f64 2) (*.f64 x x))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/8 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 3/8 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/8 (*.f64 7/96 x)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 7/96 x 3/8))
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2))
(/.f64 (pow.f64 x 3) (/.f64 (sqrt.f64 2) 7/96))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 3/8 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (/.f64 3/8 (/.f64 (sqrt.f64 2) (*.f64 x x))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/8 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 3/8 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/8 (*.f64 7/96 x)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 7/96 x 3/8))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 3/8 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (/.f64 3/8 (/.f64 (sqrt.f64 2) (*.f64 x x))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/8 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 3/8 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/8 (*.f64 7/96 x)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 7/96 x 3/8))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 3/8 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (/.f64 3/8 (/.f64 (sqrt.f64 2) (*.f64 x x))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/8 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 3/8 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/8 (*.f64 7/96 x)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 7/96 x 3/8))
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2))
(/.f64 (pow.f64 x 3) (/.f64 (sqrt.f64 2) 7/96))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 3/8 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (/.f64 3/8 (/.f64 (sqrt.f64 2) (*.f64 x x))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/8 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 3/8 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/8 (*.f64 7/96 x)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 7/96 x 3/8))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 3/8 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (/.f64 3/8 (/.f64 (sqrt.f64 2) (*.f64 x x))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/8 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 3/8 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/8 (*.f64 7/96 x)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 7/96 x 3/8))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 3/8 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (/.f64 3/8 (/.f64 (sqrt.f64 2) (*.f64 x x))))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/8 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 3/8 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/8 (*.f64 7/96 x)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 7/96 x 3/8))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16))
(fma.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16 (sqrt.f64 2))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16 (sqrt.f64 2))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) 3/16 (sqrt.f64 2))
(fma.f64 (*.f64 x x) (/.f64 3/16 (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 x (*.f64 x (/.f64 3/16 (sqrt.f64 2))) (sqrt.f64 2))
(fma.f64 x (*.f64 3/16 (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16 (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/16 (*.f64 x 7/192))))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 x 7/192 3/16) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16 (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/16 (*.f64 x 7/192))))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 x 7/192 3/16) (sqrt.f64 2))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)
(/.f64 (pow.f64 x 3) (/.f64 (sqrt.f64 2) 7/192))
(*.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192))
(fma.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16 (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16 (/.f64 (pow.f64 x 3) (/.f64 (sqrt.f64 2) 7/192)))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) 3/16 (*.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/16 (*.f64 x 7/192)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 x 7/192 3/16))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16 (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/16 (*.f64 x 7/192))))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 x 7/192 3/16) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16 (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/16 (*.f64 x 7/192))))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 x 7/192 3/16) (sqrt.f64 2))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)
(/.f64 (pow.f64 x 3) (/.f64 (sqrt.f64 2) 7/192))
(*.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192))
(fma.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16 (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16 (/.f64 (pow.f64 x 3) (/.f64 (sqrt.f64 2) 7/192)))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) 3/16 (*.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/16 (*.f64 x 7/192)))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 x 7/192 3/16))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16 (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/16 (*.f64 x 7/192))))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 x 7/192 3/16) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/16 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/16 (/.f64 (*.f64 x x) (sqrt.f64 2)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16 (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) 3/16 (fma.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192 (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (+.f64 3/16 (*.f64 x 7/192))))
(fma.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 x 7/192 3/16) (sqrt.f64 2))

eval436.0ms (4.9%)

Compiler

Compiled 8700 to 7308 computations (16% saved)

prune156.0ms (1.8%)

Pruning

14 alts after pruning (8 fresh and 6 done)

PrunedKeptTotal
New4814485
Fresh246
Picked011
Done257
Total48514499
Error
0.2b
Counts
499 → 14
Alt Table
Click to see full alt table
StatusErrorProgram
22.4b
(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) 1)
✓17.7b
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
▶62.5b
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
20.8b
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x 7/96) 3/8)) x)))
▶20.8b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))))
✓21.0b
(sqrt.f64 (+.f64 2 x))
62.1b
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 x 7/192 3/16))
▶20.9b
(+.f64 (sqrt.f64 2) (expm1.f64 (log1p.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))))
✓21.3b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8))))
✓21.7b
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
✓17.1b
(sqrt.f64 2)
✓0.3b
(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶21.3b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))))
▶62.2b
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
Compiler

Compiled 314 to 264 computations (15.9% saved)

localize114.0ms (1.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (pow.f64 x 3) (sqrt.f64 2))
✓0.3b
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
✓0.4b
(*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x))
✓8.8b
(+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
Compiler

Compiled 123 to 91 computations (26% saved)

series18.0ms (0.2%)

Counts
4 → 24
Calls

12 calls:

TimeVariablePointExpression
6.0ms
x
@inf
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
2.0ms
x
@0
(+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
1.0ms
x
@0
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
1.0ms
x
@inf
(+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
1.0ms
x
@-inf
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))

rewrite185.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
774×fma-def_binary64
376×fma-neg_binary64
309×expm1-udef_binary64
309×log1p-udef_binary64
248×log-pow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01761
139259
2514159
Stop Event
1×node limit
Counts
4 → 205
Calls
Call 1
Inputs
(+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x))
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(/.f64 (pow.f64 x 3) (sqrt.f64 2))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 7/96 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 7/96 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 7/96 (pow.f64 x 3)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 7/96 (pow.f64 x 3))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 7/96 (pow.f64 x 3)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (pow.f64 x 3)) 7/96) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 7/96 (neg.f64 (pow.f64 x 3))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x (cbrt.f64 (sqrt.f64 1/2))) (cbrt.f64 7/96)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) 3) 343/884736) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 (pow.f64 x 6) 1/2) 49/9216))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) (sqrt.f64 1/2)) 7/96))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) 3) 343/884736))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 (*.f64 x x) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (*.f64 (sqrt.f64 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (cbrt.f64 (sqrt.f64 1/2))) (cbrt.f64 (*.f64 (pow.f64 x 6) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 x 6) 1/2)) (*.f64 x (cbrt.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x 3/2) (pow.f64 2 1/4)) (/.f64 (pow.f64 x 3/2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 x 3)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3/2) (*.f64 (pow.f64 x 3/2) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 1) (/.f64 (*.f64 x x) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) 1) (/.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x 3/2) 1) (/.f64 (pow.f64 x 3/2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (cbrt.f64 2)) (/.f64 (*.f64 x x) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) (cbrt.f64 2)) (*.f64 x (cbrt.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 x 3) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x 3/2) (cbrt.f64 2)) (/.f64 (pow.f64 x 3/2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (pow.f64 2 1/4)) (/.f64 (*.f64 x x) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) (pow.f64 2 1/4)) (/.f64 x (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 x 3) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (cbrt.f64 (sqrt.f64 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 3/2) (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 x 3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 6) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x 3)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 x 3) 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))))

simplify100.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
1010×distribute-rgt-out_binary64
858×fma-def_binary64
716×associate-/r/_binary64
573×associate-*l*_binary64
536×unswap-sqr_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
020468
147468
2100420
3245388
4724386
53209382
67091382
Stop Event
1×node limit
Counts
229 → 216
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) x)
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(*.f64 (sqrt.f64 1/2) x)
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x))
(*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
Outputs
(*.f64 (sqrt.f64 1/2) x)
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x))
(*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/8 1)))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x)))
(fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x)))
(fma.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (fma.f64 x 3/8 1) (sqrt.f64 1/2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (fma.f64 x 3/8 1))))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x)))
(fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x)))
(fma.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (fma.f64 x 3/8 1) (sqrt.f64 1/2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (fma.f64 x 3/8 1))))
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 3/8 x) x) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x 3/8))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 1/2) 3/8) (*.f64 7/96 (/.f64 x (sqrt.f64 2)))))
(*.f64 x (*.f64 x (fma.f64 (sqrt.f64 1/2) 3/8 (*.f64 x (/.f64 7/96 (sqrt.f64 2))))))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x)))
(fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x)))
(fma.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (fma.f64 x 3/8 1) (sqrt.f64 1/2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (fma.f64 x 3/8 1))))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x)))
(fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x)))
(fma.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (fma.f64 x 3/8 1) (sqrt.f64 1/2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (fma.f64 x 3/8 1))))
(*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (*.f64 (*.f64 3/8 x) x) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x 3/8))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 1/2) 3/8) (*.f64 7/96 (/.f64 x (sqrt.f64 2)))))
(*.f64 x (*.f64 x (fma.f64 (sqrt.f64 1/2) 3/8 (*.f64 x (/.f64 7/96 (sqrt.f64 2))))))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x)))
(fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x)))
(fma.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (fma.f64 x 3/8 1) (sqrt.f64 1/2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (fma.f64 x 3/8 1))))
(+.f64 (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x)))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2))))
(fma.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x)))
(fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x)))
(fma.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (fma.f64 x 3/8 1) (sqrt.f64 1/2))))
(*.f64 x (fma.f64 (*.f64 x x) (/.f64 7/96 (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (fma.f64 x 3/8 1))))
(*.f64 (sqrt.f64 1/2) x)
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x))
(*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/8 1)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x))
(*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/8 1)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 (sqrt.f64 1/2) x))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x))
(*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/8 1)))
(*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x))
(*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 3/8 x) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x 3/8)))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x))
(*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/8 1)))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x))
(*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/8 1)))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x))
(*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/8 1)))
(*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x))
(*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 3/8 x) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x 3/8)))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x))
(*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/8 1)))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x))
(*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/8 1)))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (sqrt.f64 1/2)) (*.f64 x x)))
(fma.f64 (sqrt.f64 1/2) x (*.f64 (*.f64 3/8 (*.f64 x x)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (*.f64 3/8 x) x) x))
(*.f64 (sqrt.f64 1/2) (fma.f64 x (*.f64 x 3/8) x))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/8 1)))

localize16.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.4b
(/.f64 x (sqrt.f64 2))
Compiler

Compiled 16 to 13 computations (18.8% saved)

localize25.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (pow.f64 x 3) (sqrt.f64 2))
✓0.4b
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
Compiler

Compiled 24 to 20 computations (16.7% saved)

series3.0ms (0%)

Counts
1 → 0
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
1.0ms
x
@-inf
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
1.0ms
x
@0
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))

rewrite112.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
852×pow1_binary64
803×add-log-exp_binary64
802×log1p-expm1-u_binary64
802×expm1-log1p-u_binary64
787×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
119712
2221312
Stop Event
1×node limit
Counts
1 → 20
Calls
Call 1
Inputs
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 7/192 (sqrt.f64 (/.f64 (pow.f64 x 6) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 7/192 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 7/192 (pow.f64 x 3))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (pow.f64 x 3)) 7/192) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 7/192 (neg.f64 (pow.f64 x 3))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 7/192 (sqrt.f64 (/.f64 (pow.f64 x 6) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 7/192 (sqrt.f64 (/.f64 (pow.f64 x 6) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 x (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 7/192)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 7/192 (sqrt.f64 (/.f64 (pow.f64 x 6) 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 (pow.f64 x 6) 2) 49/36864))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 7/192) (sqrt.f64 (/.f64 (pow.f64 x 6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 7/192 (sqrt.f64 (/.f64 (pow.f64 x 6) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 7/192 (sqrt.f64 (/.f64 (pow.f64 x 6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 7/192 (sqrt.f64 (/.f64 (pow.f64 x 6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 7/192 (sqrt.f64 (/.f64 (pow.f64 x 6) 2)))))))))

simplify11.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
20 → 20
Calls
Call 1
Inputs
Outputs

localize92.0ms (1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))))
✓0.2b
(*.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))
✓0.2b
(*.f64 (pow.f64 2 -1/2) (*.f64 x x))
0.4b
(*.f64 x 7/96)
Compiler

Compiled 76 to 56 computations (26.3% saved)

series40.0ms (0.4%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
31.0ms
x
@inf
(*.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))
2.0ms
x
@0
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))))
1.0ms
x
@-inf
(*.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))
1.0ms
x
@0
(*.f64 (pow.f64 2 -1/2) (*.f64 x x))
1.0ms
x
@0
(*.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))

rewrite311.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
799×log-prod_binary64
401×fma-def_binary64
287×expm1-udef_binary64
287×log1p-udef_binary64
230×log-pow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01652
136047
2460447
Stop Event
1×node limit
Counts
3 → 149
Calls
Call 1
Inputs
(*.f64 (pow.f64 2 -1/2) (*.f64 x x))
(*.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 1/2))) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 1/2))))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 1/2)))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (pow.f64 2 -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) 1/2) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) (*.f64 (sqrt.f64 1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x))))))))
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simplify250.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
868×fma-def_binary64
754×sqr-pow_binary64
549×cube-prod_binary64
532×*-commutative_binary64
372×pow-sqr_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
023626
157624
2143573
3441510
41586476
52829476
63587476
73698476
83858476
94051476
104304476
114705476
125125476
135655476
146319476
157149476
167548476
177912476
Stop Event
1×node limit
Counts
185 → 166
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
Outputs
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 (sqrt.f64 1/2) (pow.f64 x 2))
(*.f64 (sqrt.f64 1/2) (*.f64 x x))
(*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/8)
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) 3/8))
(*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x 3/8)))
(*.f64 x (*.f64 3/8 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/8 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/8)) (*.f64 7/96 (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 x 7/96 3/8))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (fma.f64 x 7/96 3/8)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/8 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/8)) (*.f64 7/96 (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 x 7/96 3/8))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (fma.f64 x 7/96 3/8)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/8 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/8)) (*.f64 7/96 (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 x 7/96 3/8))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (fma.f64 x 7/96 3/8)))
(*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(*.f64 (sqrt.f64 1/2) (*.f64 7/96 (pow.f64 x 3)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/8 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/8)) (*.f64 7/96 (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 x 7/96 3/8))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (fma.f64 x 7/96 3/8)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/8 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/8)) (*.f64 7/96 (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 x 7/96 3/8))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (fma.f64 x 7/96 3/8)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/8 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/8)) (*.f64 7/96 (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 x 7/96 3/8))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (fma.f64 x 7/96 3/8)))
(*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(*.f64 (sqrt.f64 1/2) (*.f64 7/96 (pow.f64 x 3)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/8 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/8)) (*.f64 7/96 (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 x 7/96 3/8))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (fma.f64 x 7/96 3/8)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/8 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/8)) (*.f64 7/96 (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 x 7/96 3/8))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (fma.f64 x 7/96 3/8)))
(+.f64 (*.f64 3/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 3/8 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/8 (*.f64 7/96 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/8)) (*.f64 7/96 (pow.f64 x 3))))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))))
(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 x 7/96 3/8))
(*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 x x) (fma.f64 x 7/96 3/8)))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(+.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16 (sqrt.f64 2))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x 3/16)) (sqrt.f64 2))
(fma.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 x 3/16) (sqrt.f64 2))
(fma.f64 x (*.f64 3/16 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16)))
(+.f64 (sqrt.f64 2) (fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) 7/192))))
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/16)) (*.f64 (pow.f64 x 3) 7/192))))
(fma.f64 x (*.f64 x (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x 7/192) 3/16))) (sqrt.f64 2))
(fma.f64 x (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 7/192 3/16)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16)))
(+.f64 (sqrt.f64 2) (fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) 7/192))))
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/16)) (*.f64 (pow.f64 x 3) 7/192))))
(fma.f64 x (*.f64 x (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x 7/192) 3/16))) (sqrt.f64 2))
(fma.f64 x (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 7/192 3/16)) (sqrt.f64 2))
(*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) 7/192)
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) 7/192))
(*.f64 (pow.f64 x 3) (*.f64 (sqrt.f64 1/2) 7/192))
(+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(fma.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) 7/192)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/16)) (*.f64 (pow.f64 x 3) 7/192)))
(*.f64 (*.f64 x x) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x 7/192) 3/16)))
(*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x (fma.f64 x 7/192 3/16))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16)))
(+.f64 (sqrt.f64 2) (fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) 7/192))))
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/16)) (*.f64 (pow.f64 x 3) 7/192))))
(fma.f64 x (*.f64 x (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x 7/192) 3/16))) (sqrt.f64 2))
(fma.f64 x (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 7/192 3/16)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16)))
(+.f64 (sqrt.f64 2) (fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) 7/192))))
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/16)) (*.f64 (pow.f64 x 3) 7/192))))
(fma.f64 x (*.f64 x (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x 7/192) 3/16))) (sqrt.f64 2))
(fma.f64 x (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 7/192 3/16)) (sqrt.f64 2))
(*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) 7/192)
(*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) 7/192))
(*.f64 (pow.f64 x 3) (*.f64 (sqrt.f64 1/2) 7/192))
(+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))
(fma.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16))
(fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) 7/192)))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/16)) (*.f64 (pow.f64 x 3) 7/192)))
(*.f64 (*.f64 x x) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x 7/192) 3/16)))
(*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x (fma.f64 x 7/192 3/16))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16)))
(+.f64 (sqrt.f64 2) (fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) 7/192))))
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/16)) (*.f64 (pow.f64 x 3) 7/192))))
(fma.f64 x (*.f64 x (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x 7/192) 3/16))) (sqrt.f64 2))
(fma.f64 x (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 7/192 3/16)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 7/192 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16)))
(+.f64 (sqrt.f64 2) (fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 x 3) 7/192))))
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x (*.f64 x 3/16)) (*.f64 (pow.f64 x 3) 7/192))))
(fma.f64 x (*.f64 x (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 x 7/192) 3/16))) (sqrt.f64 2))
(fma.f64 x (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 7/192 3/16)) (sqrt.f64 2))

localize208.0ms (2.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))
0.4b
(*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x))
✓0.5b
(/.f64 (sqrt.f64 2) (pow.f64 x 3))
✓8.8b
(fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))
Compiler

Compiled 148 to 111 computations (25% saved)

series9.0ms (0.1%)

Counts
3 → 24
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 (sqrt.f64 2) (pow.f64 x 3))
1.0ms
x
@0
(fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))
1.0ms
x
@-inf
(fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))
1.0ms
x
@-inf
(/.f64 (sqrt.f64 2) (pow.f64 x 3))
1.0ms
x
@inf
(fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))

rewrite124.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
837×log-prod_binary64
448×fma-def_binary64
311×expm1-udef_binary64
311×log1p-udef_binary64
267×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01850
140849
2505749
Stop Event
1×node limit
Counts
3 → 100
Calls
Call 1
Inputs
(fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3))))
(/.f64 (sqrt.f64 2) (pow.f64 x 3))
(/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))
Outputs
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((x pow.f64 (pow.f64 (fma.f64 (*.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (fma.f64 3/8 x 1)) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (*.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (fma.f64 3/8 x 1)) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (*.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (fma.f64 3/8 x 1)) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (*.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (fma.f64 3/8 x 1)) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (*.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (fma.f64 3/8 x 1)) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (*.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (fma.f64 3/8 x 1)) (/.f64 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2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (*.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (fma.f64 3/8 x 1)) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 (*.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (fma.f64 3/8 x 1)) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (*.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (fma.f64 3/8 x 1)) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 2) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x -3))) (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x -3))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x -3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (pow.f64 x -3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sqrt.f64 2) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) x) (cbrt.f64 (/.f64 2 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (pow.f64 x 6))) (/.f64 (cbrt.f64 (sqrt.f64 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 x 3/2)) (/.f64 (pow.f64 2 1/4) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (neg.f64 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -3) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (sqrt.f64 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) x) (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) x) (/.f64 (pow.f64 2 1/4) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (*.f64 x x)) (/.f64 (pow.f64 2 1/4) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 x x)) (/.f64 (sqrt.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (*.f64 x x)) (/.f64 (cbrt.f64 (sqrt.f64 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 x 3/2)) (/.f64 (sqrt.f64 2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (pow.f64 x 3/2)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 2 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (pow.f64 x 3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 7/192) (/.f64 (pow.f64 x 3) (sqrt.f64 2)))) (cbrt.f64 (pow.f64 (exp.f64 7/192) (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 7/192) (/.f64 (pow.f64 x 3) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 7/192) (/.f64 (pow.f64 x 3) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 7/192) (/.f64 (pow.f64 x 3) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (/.f64 7/192 (sqrt.f64 2))) x) (cbrt.f64 (/.f64 49/36864 (/.f64 2 (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 49/36864 (/.f64 2 (pow.f64 x 6)))) (*.f64 (cbrt.f64 (/.f64 7/192 (sqrt.f64 2))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))) (sqrt.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -7/192 (/.f64 1 (*.f64 (neg.f64 (sqrt.f64 2)) (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 7/192)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 7/192 (neg.f64 (sqrt.f64 2))) (neg.f64 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 7/192 (sqrt.f64 2)) x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 7/192 (sqrt.f64 2)) (*.f64 x x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 7/192 (sqrt.f64 2)) 1) (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3/2)) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 (/.f64 7/192 (sqrt.f64 2))) x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3)) 192/7) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 49/36864 (/.f64 2 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 7/192) (/.f64 (pow.f64 x 3) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))))))

simplify109.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
863×distribute-lft-out_binary64
759×fma-def_binary64
735×associate-/r/_binary64
659×associate-*l*_binary64
495×distribute-rgt-out_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
021444
153444
2117423
3275402
4800386
52849382
66101382
Stop Event
1×node limit
Counts
124 → 107
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 (sqrt.f64 1/2) x))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
Outputs
(*.f64 1/2 (*.f64 (sqrt.f64 1/2) x))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)))
(fma.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)))
(fma.f64 1/2 (*.f64 (sqrt.f64 1/2) x) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))))
(*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 x) (*.f64 3/16 (*.f64 x x))))
(*.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 (*.f64 x 3/16) 1/2)))
(*.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/16 1/2)))
(*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 3/16 1/2))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 1/2 (*.f64 (sqrt.f64 1/2) x) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 x) (*.f64 3/16 (*.f64 x x)))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 (*.f64 x 3/16) 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/16 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)) (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 3/16 1/2)))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 1/2 (*.f64 (sqrt.f64 1/2) x) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 x) (*.f64 3/16 (*.f64 x x)))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 (*.f64 x 3/16) 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/16 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)) (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 3/16 1/2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))))
(fma.f64 (sqrt.f64 1/2) (*.f64 3/16 (*.f64 x x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x 3/16)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 1/2) 3/16) (*.f64 x (/.f64 7/192 (sqrt.f64 2)))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 1/2) 3/16 (/.f64 x (/.f64 (sqrt.f64 2) 7/192))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 1/2) 3/16 (*.f64 x (/.f64 7/192 (sqrt.f64 2)))))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 1/2 (*.f64 (sqrt.f64 1/2) x) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 x) (*.f64 3/16 (*.f64 x x)))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 (*.f64 x 3/16) 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/16 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)) (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 3/16 1/2)))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 1/2 (*.f64 (sqrt.f64 1/2) x) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 x) (*.f64 3/16 (*.f64 x x)))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 (*.f64 x 3/16) 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/16 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)) (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 3/16 1/2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))))
(fma.f64 (sqrt.f64 1/2) (*.f64 3/16 (*.f64 x x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x 3/16)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 1/2) 3/16) (*.f64 x (/.f64 7/192 (sqrt.f64 2)))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 1/2) 3/16 (/.f64 x (/.f64 (sqrt.f64 2) 7/192))))
(*.f64 (*.f64 x x) (fma.f64 (sqrt.f64 1/2) 3/16 (*.f64 x (/.f64 7/192 (sqrt.f64 2)))))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 1/2 (*.f64 (sqrt.f64 1/2) x) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 x) (*.f64 3/16 (*.f64 x x)))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 (*.f64 x 3/16) 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/16 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)) (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 3/16 1/2)))
(+.f64 (*.f64 3/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 1/2) x)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 3/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 1/2 (*.f64 (sqrt.f64 1/2) x) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/2 x) (*.f64 3/16 (*.f64 x x)))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 (*.f64 x 3/16) 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (*.f64 x (fma.f64 x 3/16 1/2)) (*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))
(fma.f64 (pow.f64 x 3) (/.f64 7/192 (sqrt.f64 2)) (*.f64 (*.f64 (sqrt.f64 1/2) x) (fma.f64 x 3/16 1/2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))

eval817.0ms (9.2%)

Compiler

Compiled 17131 to 14024 computations (18.1% saved)

prune179.0ms (2%)

Pruning

19 alts after pruning (13 fresh and 6 done)

PrunedKeptTotal
New64711658
Fresh123
Picked101
Done4610
Total65319672
Error
0.2b
Counts
672 → 19
Alt Table
Click to see full alt table
StatusErrorProgram
✓21.7b
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
21.0b
(+.f64 (sqrt.f64 2) (expm1.f64 (log1p.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x -3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x -3))))))))))
22.4b
(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) 1)
62.5b
(*.f64 7/192 (*.f64 (*.f64 x x) (*.f64 (sqrt.f64 1/2) x)))
62.2b
(*.f64 1/2 (*.f64 (pow.f64 2 -1/2) x))
✓17.7b
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
62.5b
(*.f64 7/192 (*.f64 (pow.f64 x 3) (sqrt.f64 1/2)))
20.8b
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x 7/96) 3/8)) x)))
20.9b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))))
20.8b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (*.f64 (pow.f64 x 3) (sqrt.f64 1/2))))))
✓21.0b
(sqrt.f64 (+.f64 2 x))
✓62.2b
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
21.3b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))))
62.1b
(*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x (fma.f64 x 7/192 3/16))))
20.8b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (pow.f64 2 1/4)) (pow.f64 2 1/4)))))
✓17.1b
(sqrt.f64 2)
✓0.3b
(sqrt.f64 (+.f64 1 (exp.f64 x)))
20.8b
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (*.f64 (*.f64 x x) (*.f64 (sqrt.f64 1/2) x))))))
42.3b
(+.f64 (sqrt.f64 2) (expm1.f64 (log1p.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3)))) 1))))))
Compiler

Compiled 312 to 263 computations (15.7% saved)

regimes58.0ms (0.7%)

Counts
34 → 1
Calls
Call 1
Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(*.f64 1/2 (*.f64 (pow.f64 2 -1/2) x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(*.f64 7/192 (*.f64 (*.f64 x x) (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 7/192 (*.f64 (pow.f64 x 3) (sqrt.f64 1/2)))
(*.f64 7/192 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(sqrt.f64 (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(*.f64 (sqrt.f64 1/2) (*.f64 x (*.f64 x (fma.f64 x 7/192 3/16))))
(*.f64 (*.f64 x (/.f64 x (sqrt.f64 2))) (fma.f64 x 7/192 3/16))
(+.f64 (sqrt.f64 2) (*.f64 x (/.f64 (*.f64 x 3/16) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/8) (+.f64 x (*.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (*.f64 x 7/96) 3/8))))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (*.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 x x)) (+.f64 (*.f64 x 7/96) 3/8))))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x 7/96) 3/8)) x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (*.f64 (*.f64 x x) (*.f64 (sqrt.f64 1/2) x))))))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (*.f64 (pow.f64 x 3) (sqrt.f64 1/2))))))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (/.f64 (pow.f64 x 3) (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3))))))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 (/.f64 (*.f64 7/96 (pow.f64 x 3)) (pow.f64 2 1/4)) (pow.f64 2 1/4)))))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (*.f64 7/96 (expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))))
(+.f64 (sqrt.f64 2) (expm1.f64 (log1p.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))))
(+.f64 (sqrt.f64 2) (expm1.f64 (log1p.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 x -3)))) 1))))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (expm1.f64 (log1p.f64 (fma.f64 1/2 (*.f64 (pow.f64 2 -1/2) (+.f64 (*.f64 3/8 (*.f64 x x)) x)) (/.f64 7/192 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x -3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x -3))))))))))
Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Calls

5 calls:

21.0ms
x
7.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
4.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
4.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
4.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Results
ErrorSegmentsBranch
0.3b1x
0.3b1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
0.3b1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
0.3b1(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
0.3b1(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
Compiler

Compiled 607 to 495 computations (18.5% saved)

regimes9.0ms (0.1%)

Accuracy

Total -45.6b remaining (-266.9%)

Threshold costs -45.6b (-266.9%)

Counts
8 → 1
Calls
Call 1
Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(*.f64 1/2 (*.f64 (pow.f64 2 -1/2) x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(*.f64 7/192 (*.f64 (*.f64 x x) (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) 1)
Outputs
(sqrt.f64 2)
Calls

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
17.1b1x
Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)
Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)
Compiler

Compiled 9 to 8 computations (11.1% saved)

soundness73.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
633×associate-/l*_binary64
580×associate-*l*_binary64
568×associate-*r*_binary64
505×associate-/r*_binary64
380×fma-def_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01113
12513
23413
35913
412711
53498
613418
Stop Event
1×node limit
Compiler

Compiled 92 to 70 computations (23.9% saved)

end27.0ms (0.3%)

Compiler

Compiled 8 to 7 computations (12.5% saved)

Profiling

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