Details

Time bar (total: 4.0s)

analyze770.0ms (19.2%)

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)

sample2.4s (60%)

Results
1.3s2664×body1024valid
415.0ms1362×body512valid
402.0ms3207×body128valid
176.0ms314×body2048valid
142.0ms709×body256valid
1.0ms5×body128invalid
Compiler

Compiled 28 to 24 computations (14.3% saved)

preprocess40.0ms (1%)

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)

simplify18.0ms (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)))

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶0.0b
(sqrt.f64 (+.f64 1 (exp.f64 x)))
44.3b
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Compiler

Compiled 56 to 46 computations (17.9% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series5.0ms (0.1%)

Counts
2 → 8
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@0
(sqrt.f64 (+.f64 1 (exp.f64 x)))
1.0ms
x
@0
(+.f64 1 (exp.f64 x))
0.0ms
x
@inf
(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0ms
x
@-inf
(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0ms
x
@inf
(+.f64 1 (exp.f64 x))

rewrite62.0ms (1.5%)

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

simplify24.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
733×times-frac_binary64
656×associate-/l*_binary64
268×fma-neg_binary64
177×associate-/r/_binary64
159×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
044180
1132166
2456142
31993130
Stop Event
1×node limit
Counts
66 → 71
Calls
Call 1
Inputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 x (*.f64 1/6 (pow.f64 x 3)))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
(-.f64 (+.f64 (*.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
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))
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 x (*.f64 1/6 (pow.f64 x 3)))))
(+.f64 2 (+.f64 (fma.f64 1/2 (*.f64 x x) x) (*.f64 1/6 (pow.f64 x 3))))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x)))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) 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 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
(+.f64 (fma.f64 1/4 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3))))
(-.f64 (fma.f64 1/4 (/.f64 x (/.f64 (sqrt.f64 2) x)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))) (*.f64 1/16 (/.f64 x (/.f64 (sqrt.f64 2) x))))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16))
(-.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) -3/16))
(-.f64 (+.f64 (*.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
(-.f64 (fma.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 1/4 (/.f64 (*.f64 x x) (sqrt.f64 2)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (*.f64 1/8 (+.f64 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3)) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)))))
(-.f64 (fma.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 1/4 (/.f64 x (/.f64 (sqrt.f64 2) x)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))))) (+.f64 (*.f64 1/16 (/.f64 x (/.f64 (sqrt.f64 2) x))) (*.f64 1/16 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(fma.f64 1/12 (/.f64 (pow.f64 x 3) (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)) (sqrt.f64 2))) (-.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 2)) 3/16) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 1/16))))
(-.f64 (+.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)) (sqrt.f64 2))) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/48))

prune63.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New68371
Fresh101
Picked101
Done000
Total70373
Error
0b
Counts
73 → 3
Alt Table
StatusErrorProgram
▶0.0b
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
43.2b
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x)))
17.3b
(sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))
Compiler

Compiled 897 to 634 computations (29.3% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series3.0ms (0.1%)

Counts
2 → 16
Calls

6 calls:

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

rewrite32.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
436×pow1_binary64
401×add-log-exp_binary64
400×log1p-expm1-u_binary64
400×expm1-log1p-u_binary64
390×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0613
110913
2115113
Stop Event
1×node limit
Counts
2 → 37
Calls
Call 1
Inputs
(sqrt.f64 (exp.f64 x))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) 1/4) (pow.f64 (exp.f64 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1/2) (pow.f64 (cbrt.f64 (exp.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 x))))))))
((#(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 1 (sqrt.f64 (+.f64 (exp.f64 x) 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 (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 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(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 (+.f64 (exp.f64 x) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3) 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 (sqrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x 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 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))))) (#(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 exp.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))))

simplify28.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
795×times-frac_binary64
289×fma-neg_binary64
186×associate-/r/_binary64
168×fma-def_binary64
160×distribute-neg-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
049251
1139237
2468210
32110197
Stop Event
1×node limit
Counts
53 → 52
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/48 (pow.f64 x 3)))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
(-.f64 (+.f64 (*.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
(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
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/8 (*.f64 x x) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 1/2 x (*.f64 x (*.f64 x 1/8))))
(fma.f64 1/2 x (fma.f64 1/8 (*.f64 x x) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/8) 1))
(+.f64 1 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/48 (pow.f64 x 3)))))
(+.f64 1 (fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/48 (pow.f64 x 3)))))
(+.f64 1 (fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/48) 1/8))))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 (*.f64 x 1/48) 1/8)))))
(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 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
(+.f64 (fma.f64 1/4 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3))))
(-.f64 (fma.f64 1/4 (/.f64 x (/.f64 (sqrt.f64 2) x)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))) (*.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 1/16))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
(-.f64 (+.f64 (*.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
(-.f64 (fma.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 1/4 (/.f64 (*.f64 x x) (sqrt.f64 2)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (*.f64 1/8 (+.f64 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3)) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)))))
(-.f64 (fma.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 1/4 (/.f64 x (/.f64 (sqrt.f64 2) x)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))))) (+.f64 (*.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 1/16) (*.f64 1/16 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (fma.f64 1/12 (/.f64 (pow.f64 x 3) (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)) (sqrt.f64 2)))) (-.f64 (*.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 1/16)))
(-.f64 (+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (sqrt.f64 2))) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/48))
(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

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New52052
Fresh022
Picked011
Done000
Total52355
Error
0b
Counts
55 → 3
Alt Table
StatusErrorProgram
✓0.0b
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
43.2b
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x)))
▶17.3b
(sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))
Compiler

Compiled 596 to 445 computations (25.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓8.9b
(sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))

series4.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite39.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
840×pow1_binary64
783×log1p-expm1-u_binary64
783×expm1-log1p-u_binary64
85×add-sqr-sqrt_binary64
80×*-un-lft-identity_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
117213
2206913
Stop Event
1×node limit
Counts
1 → 25
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))) (cbrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))) (cbrt.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)) 1/4) (pow.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 4 (pow.f64 (fma.f64 x (*.f64 x 1/2) x) 2))) (sqrt.f64 (-.f64 2 (fma.f64 x (*.f64 x 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 8 (pow.f64 (fma.f64 x (*.f64 x 1/2) x) 3))) (sqrt.f64 (+.f64 4 (*.f64 (fma.f64 x (*.f64 x 1/2) x) (-.f64 (fma.f64 x (*.f64 x 1/2) x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))))))))

simplify30.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
887×times-frac_binary64
486×fma-neg_binary64
175×fma-def_binary64
163×associate-/r*_binary64
162×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
060388
1200372
2736334
33173332
Stop Event
1×node limit
Counts
37 → 48
Calls
Call 1
Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
(*.f64 (sqrt.f64 1/2) x)
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2))))
(-.f64 (+.f64 (*.f64 (sqrt.f64 1/2) x) (+.f64 (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) x))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 2)))) (+.f64 (*.f64 (sqrt.f64 1/2) x) (+.f64 (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) x)))))
(*.f64 -1 (*.f64 (sqrt.f64 1/2) x))
(neg.f64 (+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))))
(-.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) x))) (+.f64 (*.f64 (sqrt.f64 1/2) x) (+.f64 (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) x)))) (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 2)))) (+.f64 (*.f64 (sqrt.f64 1/2) x) (+.f64 (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))))
Outputs
(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))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
(+.f64 (fma.f64 1/4 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (sqrt.f64 2) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))) (*.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3))))
(-.f64 (fma.f64 1/4 (/.f64 (*.f64 x x) (sqrt.f64 2)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))) (*.f64 1/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
(-.f64 (fma.f64 1/4 (/.f64 (*.f64 x x) (sqrt.f64 2)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) (/.f64 (*.f64 1/2 x) (sqrt.f64 2))))) (*.f64 1/8 (+.f64 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3)) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)))))
(-.f64 (fma.f64 1/4 (/.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)) (sqrt.f64 2)))) (+.f64 (*.f64 1/16 (/.f64 (*.f64 x x) (sqrt.f64 2))) (*.f64 1/16 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (sqrt.f64 2))) (+.f64 (*.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (sqrt.f64 2))) (fma.f64 (/.f64 x (/.f64 (sqrt.f64 2) x)) 3/16 (*.f64 -1/16 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(*.f64 (sqrt.f64 1/2) x)
(*.f64 x (sqrt.f64 1/2))
(+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2))))
(fma.f64 (sqrt.f64 1/2) x (/.f64 1/2 (sqrt.f64 1/2)))
(fma.f64 x (sqrt.f64 1/2) (/.f64 1/2 (sqrt.f64 1/2)))
(-.f64 (+.f64 (*.f64 (sqrt.f64 1/2) x) (+.f64 (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) x))))
(-.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) x (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1 (*.f64 x (sqrt.f64 1/2)))) (/.f64 1/8 (*.f64 x (pow.f64 (sqrt.f64 1/2) 3))))
(-.f64 (+.f64 (fma.f64 x (sqrt.f64 1/2) (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1 (*.f64 x (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 (/.f64 2 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/2 (sqrt.f64 1/2)) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (fma.f64 x (sqrt.f64 1/2) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 2)))) (+.f64 (*.f64 (sqrt.f64 1/2) x) (+.f64 (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) x)))))
(+.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 5))) (-.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) x (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1 (*.f64 x (sqrt.f64 1/2)))) (+.f64 (/.f64 1/8 (*.f64 x (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))))
(+.f64 (+.f64 (fma.f64 x (sqrt.f64 1/2) (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1 (*.f64 x (sqrt.f64 1/2)))) (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 5))) (fma.f64 1/8 (/.f64 (/.f64 2 (sqrt.f64 1/2)) x) (*.f64 1/2 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x))))))
(+.f64 (fma.f64 x (sqrt.f64 1/2) (/.f64 1/16 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 5)))) (+.f64 (+.f64 (/.f64 1/2 (sqrt.f64 1/2)) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x))) (/.f64 (/.f64 -1 (sqrt.f64 1/2)) (*.f64 x x))))
(*.f64 -1 (*.f64 (sqrt.f64 1/2) x))
(neg.f64 (*.f64 x (sqrt.f64 1/2)))
(*.f64 x (neg.f64 (sqrt.f64 1/2)))
(neg.f64 (+.f64 (*.f64 (sqrt.f64 1/2) x) (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2)))))
(neg.f64 (fma.f64 (sqrt.f64 1/2) x (/.f64 1/2 (sqrt.f64 1/2))))
(-.f64 (/.f64 -1/2 (sqrt.f64 1/2)) (*.f64 x (sqrt.f64 1/2)))
(-.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) x))) (+.f64 (*.f64 (sqrt.f64 1/2) x) (+.f64 (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (/.f64 1/8 (*.f64 x (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (fma.f64 (sqrt.f64 1/2) x (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1 (*.f64 x (sqrt.f64 1/2)))))
(fma.f64 1/8 (/.f64 (/.f64 2 (sqrt.f64 1/2)) x) (neg.f64 (+.f64 (fma.f64 x (sqrt.f64 1/2) (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1 (*.f64 x (sqrt.f64 1/2))))))
(+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 -1 (*.f64 x (sqrt.f64 1/2))) (fma.f64 x (sqrt.f64 1/2) (/.f64 1/2 (sqrt.f64 1/2)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) x)))) (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 2)))) (+.f64 (*.f64 (sqrt.f64 1/2) x) (+.f64 (*.f64 1/2 (/.f64 1 (sqrt.f64 1/2))) (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))))
(+.f64 (/.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (-.f64 (/.f64 1/8 (*.f64 x (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (+.f64 (fma.f64 (sqrt.f64 1/2) x (/.f64 1/2 (sqrt.f64 1/2))) (/.f64 1 (*.f64 x (sqrt.f64 1/2)))) (/.f64 1/16 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 5))))))
(-.f64 (fma.f64 1/8 (/.f64 (/.f64 2 (sqrt.f64 1/2)) x) (*.f64 1/2 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)))) (+.f64 (fma.f64 x (sqrt.f64 1/2) (/.f64 1/2 (sqrt.f64 1/2))) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/16 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 5))))))
(+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (+.f64 (/.f64 1 (*.f64 x (*.f64 x (sqrt.f64 1/2)))) (+.f64 (-.f64 (/.f64 -1 (*.f64 x (sqrt.f64 1/2))) (fma.f64 x (sqrt.f64 1/2) (/.f64 1/2 (sqrt.f64 1/2)))) (/.f64 -1/16 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 5))))))

prune29.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New48048
Fresh011
Picked011
Done011
Total48351
Error
0b
Counts
51 → 3
Alt Table
StatusErrorProgram
✓0.0b
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
▶43.2b
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x)))
✓17.3b
(sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))
Compiler

Compiled 913 to 742 computations (18.7% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x))
✓0.0b
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x)))
✓0.0b
(pow.f64 (exp.f64 x) 2)
✓4.4b
(-.f64 (pow.f64 (exp.f64 x) 2) 1)

series19.0ms (0.5%)

Counts
4 → 32
Calls

12 calls:

TimeVariablePointExpression
13.0ms
x
@0
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x)))
1.0ms
x
@inf
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x)))
1.0ms
x
@-inf
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x)))
1.0ms
x
@0
(-.f64 (pow.f64 (exp.f64 x) 2) 1)
1.0ms
x
@-inf
(-.f64 (pow.f64 (exp.f64 x) 2) 1)

rewrite67.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
435×log-prod_binary64
182×prod-diff_binary64
163×expm1-udef_binary64
163×log1p-udef_binary64
150×pow3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01045
121236
2262636
Stop Event
1×node limit
Counts
4 → 188
Calls
Call 1
Inputs
(-.f64 (pow.f64 (exp.f64 x) 2) 1)
(pow.f64 (exp.f64 x) 2)
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x)))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (exp.f64 x) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (pow.f64 (exp.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (expm1.f64 (+.f64 x x)))) (cbrt.f64 (exp.f64 (expm1.f64 (+.f64 x x)))))) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (+.f64 x x))))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (+.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (cbrt.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (*.f64 6 x)) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (*.f64 4 x)) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (exp.f64 x) 1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)) (expm1.f64 (*.f64 6 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 (*.f64 4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 6 x)) (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 6 x)) (+.f64 (pow.f64 (exp.f64 x) 4) (-.f64 1 (*.f64 (pow.f64 (exp.f64 x) 2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 4 x)) (+.f64 (pow.f64 (exp.f64 x) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (*.f64 6 x))) (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (*.f64 4 x))) (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 (pow.f64 (exp.f64 x) 2) 1)) (expm1.f64 (*.f64 6 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 (*.f64 4 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (expm1.f64 (+.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 x) (exp.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 x) 2) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (exp.f64 x) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (pow.f64 (exp.f64 x) 4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (*.f64 (cbrt.f64 (exp.f64 x)) (exp.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) (pow.f64 (cbrt.f64 (exp.f64 x)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) (*.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (exp.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) 3) (sqrt.f64 (exp.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (cbrt.f64 (exp.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (+.f64 x x) 1))))))
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pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) (pow.f64 (expm1.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 x) 2) (/.f64 1 (expm1.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 x))) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 x)))) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 x))) (sqrt.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (pow.f64 (exp.f64 x) 2) (cbrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (pow.f64 (exp.f64 x) 2) (sqrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (exp.f64 x) 1) (/.f64 (exp.f64 x) (expm1.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) 1) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (expm1.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) (sqrt.f64 (expm1.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))))

simplify34.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
743×times-frac_binary64
278×fma-def_binary64
275×fma-neg_binary64
191×associate-+l+_binary64
154×distribute-neg-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
068519
1199488
2619414
32489369
Stop Event
1×node limit
Counts
220 → 220
Calls
Call 1
Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 2 x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 4/3 (pow.f64 x 3)) (*.f64 2 x)))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 4/3 (pow.f64 x 3)) (*.f64 2 x))))
1
(+.f64 1 (*.f64 2 x))
(+.f64 1 (+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 2 x)))
(+.f64 1 (+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2 x) (*.f64 4/3 (pow.f64 x 3)))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
(-.f64 (+.f64 (*.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 x (*.f64 1/6 (pow.f64 x 3)))))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
Outputs
(*.f64 2 x)
(+.f64 x x)
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 2 x))
(*.f64 2 (+.f64 (*.f64 x x) x))
(*.f64 2 (fma.f64 x x x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 4/3 (pow.f64 x 3)) (*.f64 2 x)))
(fma.f64 2 (*.f64 x x) (fma.f64 2 x (*.f64 4/3 (pow.f64 x 3))))
(fma.f64 2 (fma.f64 x x x) (*.f64 4/3 (pow.f64 x 3)))
(+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 4/3 (pow.f64 x 3)) (*.f64 2 x))))
(fma.f64 2/3 (pow.f64 x 4) (fma.f64 2 (*.f64 x x) (fma.f64 2 x (*.f64 4/3 (pow.f64 x 3)))))
(fma.f64 2/3 (pow.f64 x 4) (fma.f64 2 (fma.f64 x x x) (*.f64 4/3 (pow.f64 x 3))))
(fma.f64 2 (fma.f64 x x x) (fma.f64 4/3 (pow.f64 x 3) (*.f64 2/3 (pow.f64 x 4))))
(fma.f64 2 (fma.f64 x x x) (*.f64 (pow.f64 x 3) (+.f64 4/3 (*.f64 x 2/3))))
1
(+.f64 1 (*.f64 2 x))
(+.f64 (*.f64 2 x) 1)
(fma.f64 2 x 1)
(+.f64 1 (+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 2 x)))
(+.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) 1)
(fma.f64 2 (fma.f64 x x x) 1)
(+.f64 1 (+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2 x) (*.f64 4/3 (pow.f64 x 3)))))
(+.f64 (fma.f64 2 (*.f64 x x) (fma.f64 2 x (*.f64 4/3 (pow.f64 x 3)))) 1)
(+.f64 (fma.f64 2 (fma.f64 x x x) (*.f64 4/3 (pow.f64 x 3))) 1)
(fma.f64 2 (fma.f64 x x x) (fma.f64 4/3 (pow.f64 x 3) 1))
(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 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
(+.f64 (fma.f64 1/4 (/.f64 (*.f64 x x) (sqrt.f64 2)) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))) (*.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3))))
(-.f64 (fma.f64 1/4 (/.f64 x (/.f64 (sqrt.f64 2) x)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))) (*.f64 1/16 (/.f64 x (/.f64 (sqrt.f64 2) x))))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
(-.f64 (+.f64 (*.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
(-.f64 (fma.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 1/4 (/.f64 (*.f64 x x) (sqrt.f64 2)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (*.f64 1/8 (+.f64 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3)) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)))))
(-.f64 (fma.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 1/4 (/.f64 x (/.f64 (sqrt.f64 2) x)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))))) (+.f64 (*.f64 1/16 (/.f64 x (/.f64 (sqrt.f64 2) x))) (*.f64 1/16 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))))
(+.f64 (fma.f64 1/4 (*.f64 (/.f64 x (sqrt.f64 2)) x) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))) (-.f64 (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) 1/48) (/.f64 (/.f64 (*.f64 x x) 16) (sqrt.f64 2))))
(-.f64 (+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (sqrt.f64 2))) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/48))
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (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 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (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 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (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 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (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 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (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 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (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 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (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 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
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 (*.f64 x x) 1/2 x))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) x))
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 x (*.f64 1/6 (pow.f64 x 3)))))
(+.f64 2 (+.f64 (fma.f64 1/2 (*.f64 x x) x) (*.f64 (pow.f64 x 3) 1/6)))
(+.f64 2 (fma.f64 (*.f64 x x) 1/2 (fma.f64 (pow.f64 x 3) 1/6 x)))
(+.f64 (fma.f64 x (*.f64 x 1/2) x) (fma.f64 (pow.f64 x 3) 1/6 2))
(+.f64 2 (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 3) 1/6 x)))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (expm1.f64 x))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 1 (exp.f64 x)) 1)
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (expm1.f64 x))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 1 (exp.f64 x)) 1)
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (expm1.f64 x))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 1 (exp.f64 x)) 1)
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (expm1.f64 x))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 1 (exp.f64 x)) 1)
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (expm1.f64 x))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 1 (exp.f64 x)) 1)
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (expm1.f64 x))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 1 (exp.f64 x)) 1)
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (expm1.f64 x))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 1 (exp.f64 x)) 1)
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (expm1.f64 x))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 1 (exp.f64 x)) 1)

prune157.0ms (3.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2200220
Fresh000
Picked011
Done022
Total2203223
Error
0b
Counts
223 → 3
Alt Table
StatusErrorProgram
✓0.0b
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
✓43.2b
(sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x)))
✓17.3b
(sqrt.f64 (+.f64 2 (fma.f64 x (*.f64 x 1/2) x)))
Compiler

Compiled 4264 to 2218 computations (48% saved)

regimes56.0ms (1.4%)

Accuracy

Total 0.0b remaining (32.8%)

Threshold costs 0.0b (32.8%)

Counts
48 → 1
Compiler

Compiled 406 to 283 computations (30.3% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
Stop Event
1×saturated
Calls
Call 1
Inputs
(fabs.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
Outputs
(fabs.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))

end60.0ms (1.5%)

Stop Event
1×done
Compiler

Compiled 47 to 35 computations (25.5% saved)

Profiling

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