Details

Time bar (total: 5.7s)

analyze3.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%50%25%3
37.5%25%37.5%4
43.7%12.5%43.8%5
46.9%6.2%46.9%6
48.4%3.1%48.5%7
49.2%1.6%49.2%8
49.6%0.8%49.6%9
49.8%0.4%49.8%10
49.9%0.2%49.9%11
49.9%0.1%50%12
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.3s (39.8%)

Results
837.0ms992×body512valid
764.0ms2010×body1024valid
373.0ms4235×body64valid
130.0ms245×body2048valid
110.0ms518×body256valid
37.0ms256×body128valid
1.0ms14×body64invalid

preprocess16.0ms (0.3%)

Algorithm
egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
15×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32311
43211
54911
68611
712311
816611
920211
1022811
1123011
011
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify11.0ms (0.2%)

Algorithm
egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
15×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32311
43211
54911
68611
712311
816611
920211
1022811
1123011
Stop Event
saturated
Counts
1 → 1
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
28.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
28.8b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
2.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series5.0ms (0.1%)

Counts
2 → 5
Calls

6 calls:

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

rewrite48.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
794×pow1_binary64
742×log1p-expm1-u_binary64
742×expm1-log1p-u_binary64
741×add-log-exp_binary64
723×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0717
115317
2208617
Stop Event
node limit
Counts
2 → 58
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (/.f64 1 (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)) (-.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x))) (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (neg.f64 (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 x (-.f64 1 x))) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))

simplify67.0ms (1.2%)

Algorithm
egg-herbie
Rules
664×distribute-rgt-in_binary64
610×distribute-lft-in_binary64
536×unswap-sqr_binary64
516×associate-*l*_binary64
442×fma-def_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01840
14738
210538
330232
472931
5230331
6394131
7416931
8446931
9500831
10600531
Stop Event
node limit
Counts
63 → 65
Calls
Call 1
Inputs
1
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
Outputs
1
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 -1/8 (*.f64 x x) 1))
(fma.f64 x (fma.f64 x -1/8 1/2) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 1) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 -1/8 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) (fma.f64 1/2 x 1))
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))) 1)

prune93.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New58765
Fresh000
Picked101
Done000
Total59766
Error
27.3b
Counts
66 → 7
Alt Table
StatusErrorProgram
29.3b
(/.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))
28.9b
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
30.7b
1
28.2b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
29.0b
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
28.7b
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
28.8b
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
Compiler

Compiled 1043 to 701 computations (32.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
2.2b
(+.f64 x (-.f64 1 x))

series7.0ms (0.1%)

Counts
3 → 14
Calls

9 calls:

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

rewrite91.0ms (1.6%)

Algorithm
batch-egg-rewrite
Rules
689×fma-def_binary64
545×log-prod_binary64
347×fma-neg_binary64
300×pow2_binary64
206×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01038
123629
2359729
Stop Event
node limit
Counts
3 → 303
Calls
Call 1
Inputs
(+.f64 x (-.f64 1 x))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
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(#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (exp.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 x)) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))

simplify15.0ms (0.3%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0114
1414
Stop Event
saturated
Counts
317 → 304
Calls
Call 1
Inputs
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Outputs
1
1
1
1
1
1
1
1
1
1
1
1
1
1

prune1.8s (31.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New3285333
Fresh606
Picked101
Done000
Total3355340
Error
0.1b
Counts
340 → 5
Alt Table
StatusErrorProgram
28.2b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
28.1b
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
28.8b
(log.f64 (+.f64 1 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))
28.2b
(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.1b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Compiler

Compiled 7140 to 4548 computations (36.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series2.0ms (0%)

Counts
1 → 1
Calls

3 calls:

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

rewrite45.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
905×pow1_binary64
845×log1p-expm1-u_binary64
845×expm1-log1p-u_binary64
844×add-log-exp_binary64
823×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
117814
2244214
Stop Event
node limit
Counts
1 → 22
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (-.f64 x x))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011
141
Stop Event
saturated
Counts
23 → 23
Calls
Call 1
Inputs
1
Outputs
1

prune271.0ms (4.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1017108
Fresh404
Picked011
Done000
Total1058113
Error
0.0b
Counts
113 → 8
Alt Table
StatusErrorProgram
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
15.3b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))
0.5b
(*.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.3b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1)))) (sqrt.f64 x)))
0.3b
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
0.1b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.2b
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
0.4b
(*.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))
Compiler

Compiled 1848 to 1347 computations (27.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (+.f64 x 1) 1/4)
0.0b
(+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
0.1b
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
0.3b
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)

series17.0ms (0.3%)

Counts
4 → 26
Calls

12 calls:

TimeVariablePointExpression
6.0ms
x
@-inf
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
3.0ms
x
@inf
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
2.0ms
x
@-inf
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
1.0ms
x
@0
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
1.0ms
x
@inf
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)

rewrite77.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
444×log-prod_binary64
406×fma-def_binary64
328×exp-prod_binary64
304×pow-prod-down_binary64
271×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01141
125138
2309638
Stop Event
node limit
Counts
4 → 171
Calls
Call 1
Inputs
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
(+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
(pow.f64 (+.f64 x 1) 1/4)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 3/8) (pow.f64 (+.f64 x 1) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 5/6) (pow.f64 (+.f64 x 1) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (-.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 1 (pow.f64 x 3/2)) (hypot.f64 x (sqrt.f64 (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log1p.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (*.f64 1/2 (log1p.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log1p.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/4 (log1p.f64 x)) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))
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(sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (exp.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 x)) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 x 1/6) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/6) (cbrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (+.f64 x 1) 1/6) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 3/8) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 3/8) (pow.f64 (+.f64 x 1) 1/8) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 5/6) (pow.f64 (+.f64 x 1) 1/12) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 x 1) 1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/12) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/4 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/4 (log1p.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log1p.f64 x)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (*.f64 1/4 (log1p.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/8 (log1p.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/4 (log1p.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1/2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1/8) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 x 1) 1/4)))))))

simplify59.0ms (1%)

Algorithm
egg-herbie
Rules
582×associate-/r*_binary64
524×associate-*l/_binary64
430×fma-def_binary64
378×*-commutative_binary64
338×+-commutative_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0108744
1290703
2820558
32942426
47880386
Stop Event
node limit
Counts
197 → 212
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (*.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))))))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -7/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 3/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))))
1
1
1
(+.f64 1 (*.f64 1/4 x))
(+.f64 1 (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x)))
(+.f64 1 (+.f64 (*.f64 7/128 (pow.f64 x 3)) (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x))))
(pow.f64 x 1/4)
(+.f64 (pow.f64 x 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))
(+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(+.f64 (*.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 7/128 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 1) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) 1)))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))
(+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x)))
(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8))
(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (*.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))
(fma.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16))))))
(+.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(sqrt.f64 x)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(fma.f64 1/2 (/.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 2) x) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 2))
(*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 (exp.f64 (log.f64 x))))
(*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 x))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) (*.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)) -1/8))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (fma.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x)) -1/8 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))
(fma.f64 1/2 (/.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 2) x) (fma.f64 -1/8 (/.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 2) (*.f64 x x)) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 2)))
(+.f64 (sqrt.f64 (exp.f64 (log.f64 x))) (*.f64 (/.f64 (sqrt.f64 (exp.f64 (log.f64 x))) x) (+.f64 1/2 (/.f64 -1/8 x))))
(+.f64 (sqrt.f64 x) (*.f64 (/.f64 (sqrt.f64 x) x) (+.f64 1/2 (/.f64 -1/8 x))))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -7/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 3/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) (fma.f64 -1 (/.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) -1/16) (pow.f64 x 3)) (*.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)) -1/8)))
(+.f64 (fma.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x)) -1/8 (neg.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (/.f64 (pow.f64 x 3) -1/16)))) (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))
(+.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 2) (fma.f64 1/2 (/.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 2) x) (*.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 2) (*.f64 x x)) (-.f64 -1/8 (/.f64 -1/16 x)))))
(-.f64 (*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 (exp.f64 (log.f64 x)))) (*.f64 (/.f64 (sqrt.f64 (exp.f64 (log.f64 x))) (*.f64 x x)) (-.f64 (/.f64 -1/16 x) -1/8)))
(-.f64 (*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 x)) (*.f64 (/.f64 (sqrt.f64 x) (*.f64 x x)) (-.f64 (/.f64 -1/16 x) -1/8)))
1
1
1
(+.f64 1 (*.f64 1/4 x))
(+.f64 1 (*.f64 x 1/4))
(fma.f64 x 1/4 1)
(+.f64 1 (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x)))
(+.f64 1 (fma.f64 -3/32 (*.f64 x x) (*.f64 x 1/4)))
(+.f64 1 (fma.f64 (*.f64 x x) -3/32 (*.f64 x 1/4)))
(fma.f64 x 1/4 (fma.f64 x (*.f64 x -3/32) 1))
(+.f64 1 (+.f64 (*.f64 7/128 (pow.f64 x 3)) (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x))))
(+.f64 1 (fma.f64 7/128 (pow.f64 x 3) (fma.f64 -3/32 (*.f64 x x) (*.f64 x 1/4))))
(+.f64 (fma.f64 (pow.f64 x 3) 7/128 (*.f64 x (*.f64 x -3/32))) (fma.f64 x 1/4 1))
(fma.f64 (pow.f64 x 3) 7/128 (fma.f64 x 1/4 (fma.f64 x (*.f64 x -3/32) 1)))
(pow.f64 x 1/4)
(+.f64 (pow.f64 x 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))
(fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (pow.f64 x 1/4))
(+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(+.f64 (pow.f64 x 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (fma.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (pow.f64 x 1/4)))
(+.f64 (*.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (+.f64 (pow.f64 x 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(+.f64 (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))) (fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (pow.f64 x 1/4)))
(fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (fma.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (pow.f64 x 1/4))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 x 1/4)
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (*.f64 1/4 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x))
(fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 1/4 (/.f64 (pow.f64 (/.f64 -1 x) -1/4) (/.f64 x (pow.f64 -1 1/4))) (*.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 x) -1/4)))
(*.f64 (+.f64 (/.f64 1/4 x) 1) (pow.f64 (exp.f64 (log.f64 x)) 1/4))
(*.f64 (+.f64 (/.f64 1/4 x) 1) (pow.f64 x 1/4))
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)))))
(fma.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -1/4) (/.f64 x (pow.f64 -1 1/4))) (+.f64 1/4 (/.f64 -3/32 x))))
(+.f64 (pow.f64 (exp.f64 (log.f64 x)) 1/4) (*.f64 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 1/4) x) (+.f64 1/4 (/.f64 -3/32 x))))
(+.f64 (pow.f64 x 1/4) (*.f64 (/.f64 (pow.f64 x 1/4) x) (+.f64 1/4 (/.f64 -3/32 x))))
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 7/128 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x))))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))))))
(fma.f64 7/128 (/.f64 (pow.f64 (/.f64 -1 x) -1/4) (/.f64 (pow.f64 x 3) (pow.f64 -1 1/4))) (fma.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -1/4) (/.f64 x (pow.f64 -1 1/4))) (+.f64 1/4 (/.f64 -3/32 x)))))
(+.f64 (pow.f64 (exp.f64 (log.f64 x)) 1/4) (*.f64 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 1/4) x) (+.f64 (/.f64 -3/32 x) (+.f64 1/4 (/.f64 7/128 (*.f64 x x))))))
(+.f64 (pow.f64 x 1/4) (*.f64 (/.f64 (pow.f64 x 1/4) x) (+.f64 (/.f64 -3/32 x) (+.f64 1/4 (/.f64 7/128 (*.f64 x x))))))

prune716.0ms (12.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2102212
Fresh336
Picked101
Done011
Total2146220
Error
0.0b
Counts
220 → 6
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -2)))
0.3b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1)))) (sqrt.f64 x)))
0.3b
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
0.3b
(/.f64 1 (+.f64 (pow.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 2) (sqrt.f64 x)))
0.1b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
15.3b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))
Compiler

Compiled 3715 to 2826 computations (23.9% saved)

regimes29.0ms (0.5%)

Accuracy

Total -32.3b remaining (-22348.5%)

Threshold costs -32.3b (-22348.5%)

Counts
22 → 1
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -2)))
(/.f64 1 (+.f64 (pow.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 2) (sqrt.f64 x)))
(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1)))) (sqrt.f64 x)))
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
(log.f64 (+.f64 1 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))
(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
1
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Results
13.0ms0.1bx
4.0ms0.1b(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms0.1b(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 364 to 251 computations (31% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
11214
Stop Event
saturated
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Outputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

end16.0ms (0.3%)

Stop Event
fuel
Compiler

Compiled 20 to 16 computations (20% saved)

Profiling

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