Details

Time bar (total: 3.9s)

analyze656.0ms (16.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%62.5%12.5%4
25%56.2%18.8%5
28.1%50%21.9%6
29.7%46.9%23.5%7
30.5%45.3%24.3%8
30.8%44.9%24.3%9
31.2%44.5%24.3%10
31.3%44.4%24.3%11
31.4%44.3%24.3%12
31.4%44.1%24.5%13
31.5%43.8%24.8%14
Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.6s (67.5%)

Results
1.5s2808×body1024valid
424.0ms1372×body512valid
342.0ms3142×body128valid
164.0ms288×body2048valid
137.0ms646×body256valid
1.0ms8×body128invalid

preprocess34.0ms (0.9%)

Algorithm
2×egg-herbie
Rules
590×associate-/l*_binary64
477×associate-/r*_binary64
380×fma-def_binary64
281×distribute-rgt-in_binary64
270×associate-/l/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
12513
23413
35913
412711
53498
613458
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 13 to 11 computations (15.4% saved)

simplify17.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
590×associate-/l*_binary64
477×associate-/r*_binary64
380×fma-def_binary64
281×distribute-rgt-in_binary64
270×associate-/l/_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01113
12513
23413
35913
412711
53498
613458
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)))

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.0b
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 30 to 24 computations (20% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series3.0ms (0.1%)

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))

rewrite39.0ms (1%)

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
2142314
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 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (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 (hypot.f64 1 (sqrt.f64 (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) (hypot.f64 1 (sqrt.f64 (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) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))))) (#(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 pow.f64 (+.f64 1 (exp.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (sqrt.f64 (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 (hypot.f64 1 (sqrt.f64 (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 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (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 expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (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 hypot.f64 1 (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (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 (pow.f64 (exp.f64 x) 2) (-.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 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (hypot.f64 1 (sqrt.f64 (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 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (hypot.f64 1 (sqrt.f64 (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) (hypot.f64 1 (sqrt.f64 (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 (pow.f64 (exp.f64 x) 2)) (/.f64 1 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (hypot.f64 1 (sqrt.f64 (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 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (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 (pow.f64 (exp.f64 x) 2))))))) (#(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 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.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 (pow.f64 (exp.f64 x) 2))) (neg.f64 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 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 (hypot.f64 1 (sqrt.f64 (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 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)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))))))

simplify18.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
586×fma-def_binary64
421×associate-*r*_binary64
412×associate-*l*_binary64
328×times-frac_binary64
315×associate-/l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
035169
1109137
2337131
31100103
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 (-.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)))
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 1/6 (pow.f64 x 3) (fma.f64 (fma.f64 1/2 x 1) x 2))

prune74.0ms (1.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New69271
Fresh000
Picked101
Done000
Total70272
Error
0b
Counts
72 → 2
Alt Table
StatusErrorProgram
0.7b
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
▶0.0b
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
Compiler

Compiled 848 to 600 computations (29.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(log1p.f64 (exp.f64 x))
✓0.0b
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
✓0.0b
(exp.f64 (log1p.f64 (exp.f64 x)))

series52.0ms (1.3%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
26.0ms
x
@inf
(exp.f64 (log1p.f64 (exp.f64 x)))
23.0ms
x
@-inf
(exp.f64 (log1p.f64 (exp.f64 x)))
1.0ms
x
@0
(exp.f64 (log1p.f64 (exp.f64 x)))
0.0ms
x
@0
(log1p.f64 (exp.f64 x))
0.0ms
x
@0
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))

rewrite44.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
459×pow1_binary64
421×add-log-exp_binary64
421×expm1-log1p-u_binary64
420×log1p-expm1-u_binary64
408×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0621
110919
2121519
Stop Event
1×node limit
Counts
3 → 65
Calls
Call 1
Inputs
(exp.f64 (log1p.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (exp.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (exp.f64 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (exp.f64 x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) (sqrt.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) 2) (cbrt.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 1/4) (*.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 1/4) (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) (pow.f64 (+.f64 (exp.f64 x) 1) 1/4)) (pow.f64 (+.f64 (exp.f64 x) 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) (cbrt.f64 (+.f64 (exp.f64 x) 1))) (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (exp.f64 x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2)) (cbrt.f64 (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (exp.f64 x)))) (sqrt.f64 (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (exp.f64 x) 1)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 (exp.f64 x) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (cbrt.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 1/4) (pow.f64 (+.f64 (exp.f64 x) 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (exp.f64 x) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(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 (exp.f64 x) 1))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2) (*.f64 (log1p.f64 (exp.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) 2)) (log.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log1p.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log1p.f64 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2) (cbrt.f64 (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) (sqrt.f64 (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (exp.f64 x))))))))

simplify25.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
736×fma-def_binary64
494×associate-*l*_binary64
485×associate-*r*_binary64
328×times-frac_binary64
316×associate-/l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
053366
1149334
2418328
31304294
Stop Event
1×node limit
Counts
101 → 88
Calls
Call 1
Inputs
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)))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(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)))
(log.f64 2)
(+.f64 (*.f64 1/2 x) (log.f64 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (log.f64 2)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/192 (pow.f64 x 4)) (log.f64 2))))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
Outputs
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))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) x))
(fma.f64 (fma.f64 x 1/2 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 x (*.f64 x 1/2) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 (fma.f64 x 1/2 1) x 2))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(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)))
(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)))
(log.f64 2)
(+.f64 (*.f64 1/2 x) (log.f64 2))
(fma.f64 1/2 x (log.f64 2))
(fma.f64 x 1/2 (log.f64 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (log.f64 2)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (log.f64 2)))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 x 1/2 (log.f64 2)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/8) (log.f64 2)))
(fma.f64 x (fma.f64 x 1/8 1/2) (log.f64 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/192 (pow.f64 x 4)) (log.f64 2))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 x 1/2 (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/8) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 x (fma.f64 x 1/8 1/2) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))

prune56.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New87188
Fresh101
Picked011
Done000
Total88290
Error
0b
Counts
90 → 2
Alt Table
StatusErrorProgram
▶0.7b
(sqrt.f64 (pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x))))
✓0.0b
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
Compiler

Compiled 942 to 679 computations (27.9% saved)

localize17.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(log1p.f64 (exp.f64 x))
✓0.0b
(sqrt.f64 (pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x))))
✓0.7b
(pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x)))

series15.0ms (0.4%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
13.0ms
x
@inf
(pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x)))
1.0ms
x
@0
(pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x)))
1.0ms
x
@-inf
(pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x)))
0.0ms
x
@inf
(sqrt.f64 (pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x))))
0.0ms
x
@0
(sqrt.f64 (pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x))))

rewrite41.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
573×pow1_binary64
529×add-log-exp_binary64
527×expm1-log1p-u_binary64
526×log1p-expm1-u_binary64
518×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0816
114514
2153714
Stop Event
1×node limit
Counts
2 → 47
Calls
Call 1
Inputs
(pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x)))
(sqrt.f64 (pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)))) (#(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 (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 (pow.f64 1 (log1p.f64 (exp.f64 x))) (+.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 2)) (log1p.f64 (exp.f64 x))) (pow.f64 (cbrt.f64 (E.f64)) (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (E.f64)) (log1p.f64 (exp.f64 x))) (pow.f64 (sqrt.f64 (E.f64)) (log1p.f64 (exp.f64 x))))))) (#(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 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (-.f64 (exp.f64 (+.f64 x x)) (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 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 -.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 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)) (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 2)) (*.f64 (log1p.f64 (exp.f64 x)) 1/2)) (pow.f64 (cbrt.f64 (E.f64)) (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (E.f64)) (*.f64 (log1p.f64 (exp.f64 x)) 1/2)) (pow.f64 (sqrt.f64 (E.f64)) (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))))) (#(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 pow.f64 (E.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 (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 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)))))))))

simplify23.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
586×fma-def_binary64
423×associate-*r*_binary64
408×associate-*l*_binary64
328×times-frac_binary64
314×associate-/l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
039281
1115249
2341243
31105215
Stop Event
1×node limit
Counts
71 → 61
Calls
Call 1
Inputs
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)))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(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)))
Outputs
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))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) x))
(fma.f64 (fma.f64 x 1/2 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 x (fma.f64 1/6 (pow.f64 x 3) (fma.f64 x (*.f64 x 1/2) 2)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 (fma.f64 x 1/2 1) x 2))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(+.f64 1 (exp.f64 x))
(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 (sqrt.f64 2) (fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 (pow.f64 x 3) 7/96)))))
(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)))

prune42.0ms (1.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New88088
Fresh000
Picked011
Done011
Total88290
Error
0b
Counts
90 → 2
Alt Table
StatusErrorProgram
✓0.7b
(sqrt.f64 (pow.f64 (exp.f64 1) (log1p.f64 (exp.f64 x))))
✓0.0b
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
Compiler

Compiled 1016 to 730 computations (28.1% saved)

regimes28.0ms (0.7%)

Accuracy

Total -0.6b remaining (-2829.1%)

Threshold costs -0.6b (-2829.1%)

Counts
16 → 1
Compiler

Compiled 164 to 121 computations (26.2% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
Outputs
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))

end66.0ms (1.7%)

Stop Event
1×done
Compiler

Compiled 24 to 14 computations (41.7% saved)

Profiling

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