Details

Time bar (total: 6.0s)

analyze3.0ms (0.1%)

Algorithm
1×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)

sample1.6s (26.8%)

Results
682.0ms2068×body1024valid
584.0ms4884×body256valid
244.0ms1058×body512valid
93.0ms246×body2048valid
1.0ms11×body256invalid

preprocess28.0ms (0.5%)

Algorithm
2×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
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify10.0ms (0.2%)

Algorithm
1×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
1×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))

eval0.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
31.6b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶31.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
3.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.0b
(sqrt.f64 (+.f64 x 1))
✓3.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 19 to 12 computations (36.8% saved)

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

rewrite47.0ms (0.8%)

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

simplify66.0ms (1.1%)

Algorithm
1×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
1×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)

eval19.0ms (0.3%)

Compiler

Compiled 829 to 549 computations (33.8% saved)

prune24.0ms (0.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New481765
Fresh000
Picked011
Done000
Total481866
Error
30.1b
Counts
66 → 18
Alt Table
Click to see full alt table
StatusErrorProgram
31.5b
(-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3) (sqrt.f64 x))
31.4b
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
31.9b
(/.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))))
31.7b
(-.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
▶31.5b
(-.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
31.9b
(-.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x))
31.7b
(/.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))))
32.0b
(/.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))))))
▶31.7b
(+.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)))
31.6b
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
31.9b
(+.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)))
▶31.6b
(-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
31.5b
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
▶31.1b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓31.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
▶32.6b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
32.5b
1
31.7b
(-.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
Compiler

Compiled 496 to 358 computations (27.8% saved)

localize17.0ms (0.3%)

Local error

Found 8 expressions with local error:

NewErrorProgram
3.4b
(+.f64 x (-.f64 1 x))
0.1b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓3.4b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 40 to 25 computations (37.5% saved)

series8.0ms (0.1%)

Counts
3 → 14
Calls

9 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
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
@-inf
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
1.0ms
x
@inf
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite91.0ms (1.5%)

Algorithm
1×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
1×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
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 x (-.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 x 1) x)) (/.f64 (pow.f64 (-.f64 1 x) 2) (+.f64 (-.f64 x 1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) (cbrt.f64 (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) 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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))))))))

simplify12.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0114
1414
Stop Event
1×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

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiled 22 to 15 computations (31.8% saved)

series2.0ms (0%)

Counts
1 → 3
Calls

3 calls:

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

rewrite49.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
931×pow1_binary64
870×log1p-expm1-u_binary64
870×expm1-log1p-u_binary64
869×add-log-exp_binary64
852×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
117710
2235810
Stop Event
1×node limit
Counts
1 → 47
Calls
Call 1
Inputs
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (*.f64 (-.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/2 x 1) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/2 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (fma.f64 1/2 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 (fma.f64 1/2 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 (fma.f64 1/2 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)) (fma.f64 1/2 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))) (sqrt.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 x 3/2)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (+.f64 x (*.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) x) (/.f64 1 (+.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (pow.f64 x 1/4)) (-.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (+.f64 x (*.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)))) (-.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)) (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 x 3/2)) (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (+.f64 x (*.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) x) (+.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 x 3/2))) (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (+.f64 x (*.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) x)) (neg.f64 (+.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 1/8 (pow.f64 x 3)) (pow.f64 (-.f64 1 (sqrt.f64 x)) 3)) (+.f64 (pow.f64 (*.f64 1/2 x) 2) (-.f64 (*.f64 (-.f64 1 (sqrt.f64 x)) (-.f64 1 (sqrt.f64 x))) (*.f64 (*.f64 1/2 x) (-.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (fma.f64 1/2 x 1) (neg.f64 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 1/2 x) 2) (*.f64 (-.f64 1 (sqrt.f64 x)) (-.f64 1 (sqrt.f64 x)))) (-.f64 (*.f64 1/2 x) (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (fma.f64 1/2 x 1) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 x) (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/2 x 1) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2) (cbrt.f64 (fma.f64 1/2 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) (cbrt.f64 (*.f64 1/2 x)) (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (sqrt.f64 (fma.f64 1/2 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 x)) (sqrt.f64 (*.f64 1/2 x)) (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))))

simplify7.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
059
189
Stop Event
1×saturated
Counts
50 → 49
Calls
Call 1
Inputs
1
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
1
(*.f64 1/2 x)
(*.f64 1/2 x)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
17.0b
(-.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)
✓0.3b
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
✓17.0b
(-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
Compiler

Compiled 32 to 24 computations (25% saved)

series5.0ms (0.1%)

Counts
2 → 13
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
1.0ms
x
@inf
(-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
1.0ms
x
@0
(-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
1.0ms
x
@-inf
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
0.0ms
x
@inf
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)

rewrite53.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
989×pow1_binary64
928×add-log-exp_binary64
928×log1p-expm1-u_binary64
928×expm1-log1p-u_binary64
106×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01019
122617
2273817
Stop Event
1×node limit
Counts
2 → 60
Calls
Call 1
Inputs
(-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
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) (pow.f64 (*.f64 (+.f64 x 1) x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (+.f64 x 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) (pow.f64 (*.f64 (+.f64 x 1) x) 1/2)) (-.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 (+.f64 x 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) (pow.f64 (*.f64 (+.f64 x 1) x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 x 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) (pow.f64 (*.f64 (+.f64 x 1) x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (+.f64 x 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 log.f64 (+.f64 1 (expm1.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 (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 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 log1p.f64 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))
((#(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 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/4)) (pow.f64 (+.f64 x 1) 1/4)))))) (#(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) 1/8) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/8)) (pow.f64 (+.f64 x 1) 1/8))))) (#(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 (*.f64 (pow.f64 (+.f64 x 1) 1/4) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(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 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 exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))

simplify39.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
742×associate-/l*_binary64
690×associate-*l*_binary64
618×associate-*r*_binary64
421×associate-/r*_binary64
351×associate-*l/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
070409
1185382
2537305
32022208
Stop Event
1×node limit
Counts
73 → 82
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)))))
(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)))))))
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 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 (*.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)))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)
(pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)
(sqrt.f64 (exp.f64 (log.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 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))
(*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 (exp.f64 (log.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 -1/8 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (*.f64 x x)) (fma.f64 1/2 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 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 (*.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 (-.f64 (*.f64 -1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x))) (/.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 (*.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (*.f64 x x)) (-.f64 -1/8 (/.f64 -1/16 x))) (fma.f64 1/2 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)))
(+.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 -1/8 (/.f64 1/16 x))) (*.f64 x x)))

localize22.0ms (0.4%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.3b
(cbrt.f64 (+.f64 x 1))
0.2b
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
0.2b
(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.2b
(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))
✓0.2b
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
✓0.3b
(cbrt.f64 (+.f64 x 1))
✓11.2b
(-.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
Compiler

Compiled 44 to 32 computations (27.3% saved)

series7.0ms (0.1%)

Counts
4 → 21
Calls

12 calls:

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

rewrite64.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
915×pow1_binary64
856×log1p-expm1-u_binary64
856×expm1-log1p-u_binary64
855×add-log-exp_binary64
832×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01031
121530
2249230
Stop Event
1×node limit
Counts
4 → 97
Calls
Call 1
Inputs
(-.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
(cbrt.f64 (+.f64 x 1))
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (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))) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.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 x (+.f64 1 (+.f64 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 x (+.f64 1 (+.f64 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 x (+.f64 1 (+.f64 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 x (+.f64 1 (+.f64 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)) (pow.f64 (+.f64 x 1) 1/6) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.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 (cbrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 1 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (+.f64 x 1))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2)) (sqrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 1/3) (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1/2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 x 1) 1/6)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 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 /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(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 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 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 exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))

simplify60.0ms (1%)

Algorithm
1×egg-herbie
Rules
903×fma-def_binary64
374×distribute-rgt-out_binary64
354×associate-*l*_binary64
309×times-frac_binary64
293×associate-*r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
077434
1206409
2538340
31574276
45247256
57602256
Stop Event
1×node limit
Counts
118 → 130
Calls
Call 1
Inputs
1
1
(+.f64 1 (*.f64 1/3 x))
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (*.f64 1/3 x)))
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x))))
1
(+.f64 1 (*.f64 1/6 x))
(+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2))))
(+.f64 (*.f64 55/1296 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2)))))
(pow.f64 x 1/6)
(+.f64 (pow.f64 x 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))
(+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))))
(+.f64 (*.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 55/1296 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
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 1 (*.f64 1/3 x))
(fma.f64 1/3 x 1)
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (*.f64 1/3 x)))
(fma.f64 -1/9 (*.f64 x x) (+.f64 1 (*.f64 1/3 x)))
(fma.f64 -1/9 (*.f64 x x) (fma.f64 1/3 x 1))
(fma.f64 x (*.f64 x -1/9) (fma.f64 1/3 x 1))
(fma.f64 x (fma.f64 x -1/9 1/3) 1)
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x))))
(fma.f64 -1/9 (*.f64 x x) (+.f64 1 (fma.f64 5/81 (pow.f64 x 3) (*.f64 1/3 x))))
(+.f64 (fma.f64 1/3 x (*.f64 5/81 (pow.f64 x 3))) (fma.f64 -1/9 (*.f64 x x) 1))
(fma.f64 x (*.f64 x -1/9) (fma.f64 1/3 x (fma.f64 5/81 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x -1/9 1/3) (fma.f64 5/81 (pow.f64 x 3) 1))
1
(+.f64 1 (*.f64 1/6 x))
(+.f64 1 (*.f64 x 1/6))
(fma.f64 x 1/6 1)
(+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2))))
(+.f64 1 (fma.f64 1/6 x (*.f64 (*.f64 x x) -5/72)))
(+.f64 1 (fma.f64 x 1/6 (*.f64 (*.f64 x x) -5/72)))
(fma.f64 x 1/6 (fma.f64 (*.f64 x x) -5/72 1))
(fma.f64 x (fma.f64 x -5/72 1/6) 1)
(+.f64 (*.f64 55/1296 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2)))))
(fma.f64 55/1296 (pow.f64 x 3) (+.f64 1 (fma.f64 1/6 x (*.f64 (*.f64 x x) -5/72))))
(fma.f64 (pow.f64 x 3) 55/1296 (+.f64 1 (fma.f64 x 1/6 (*.f64 (*.f64 x x) -5/72))))
(fma.f64 (pow.f64 x 3) 55/1296 (fma.f64 x 1/6 (fma.f64 (*.f64 x x) -5/72 1)))
(fma.f64 x (fma.f64 x -5/72 1/6) (fma.f64 (pow.f64 x 3) 55/1296 1))
(pow.f64 x 1/6)
(+.f64 (pow.f64 x 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6))
(+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))))
(+.f64 (pow.f64 x 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))))
(+.f64 (pow.f64 x 1/6) (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (pow.f64 x 1/6)))
(+.f64 (*.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))))
(fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (+.f64 (pow.f64 x 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))))
(+.f64 (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))) (fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 x 1/6)))
(fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (pow.f64 x 1/6))))
(fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 x 1/6))))
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 x 1/6))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 x 1/6)
(+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (*.f64 1/6 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x))
(fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 1/6 (/.f64 (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)) x) (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)))
(*.f64 (+.f64 (/.f64 1/6 x) 1) (pow.f64 (exp.f64 1/6) (log.f64 x)))
(*.f64 (+.f64 1 (/.f64 1/6 x)) (pow.f64 x 1/6))
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (*.f64 1/6 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x)))
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(fma.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6) (*.f64 (/.f64 (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)) x) (+.f64 1/6 (/.f64 -5/72 x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) x) (+.f64 1/6 (/.f64 -5/72 x)) (pow.f64 (exp.f64 1/6) (log.f64 x)))
(fma.f64 (/.f64 (pow.f64 x 1/6) x) (+.f64 1/6 (/.f64 -5/72 x)) (pow.f64 x 1/6))
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 55/1296 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (fma.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (+.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (*.f64 1/6 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x))))
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(fma.f64 55/1296 (/.f64 (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)) (pow.f64 x 3)) (fma.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6) (*.f64 (/.f64 (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)) x) (+.f64 1/6 (/.f64 -5/72 x)))))
(+.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) x) (+.f64 (+.f64 1/6 (/.f64 -5/72 x)) (/.f64 55/1296 (*.f64 x x)))))
(+.f64 (pow.f64 x 1/6) (*.f64 (/.f64 (pow.f64 x 1/6) x) (+.f64 1/6 (+.f64 (/.f64 55/1296 (*.f64 x x)) (/.f64 -5/72 x)))))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(fma.f64 x 1/2 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 (*.f64 x x) -1/8 (fma.f64 x 1/2 1))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x -1/8) 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 (pow.f64 x 3) 1/16)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 x 1/2 (fma.f64 (pow.f64 x 3) 1/16 1)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 3) 1/16 1)))
(fma.f64 x (fma.f64 x -1/8 1/2) (fma.f64 (pow.f64 x 3) 1/16 1))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 1))

localize35.0ms (0.6%)

Local error

Found 6 expressions with local error:

NewErrorProgram
61.2b
(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))
3.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(sqrt.f64 (+.f64 x 1))
3.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓61.2b
(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))
Compiler

Compiled 55 to 35 computations (36.4% saved)

series2.0ms (0%)

Counts
1 → 1
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))
1.0ms
x
@0
(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))
1.0ms
x
@inf
(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))

rewrite41.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
522×pow1_binary64
507×add-sqr-sqrt_binary64
488×add-log-exp_binary64
487×log1p-expm1-u_binary64
487×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0715
11508
217438
Stop Event
1×node limit
Counts
1 → 19
Calls
Call 1
Inputs
(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) 2) (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)) (+.f64 x (-.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x x) (-.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 x))))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
3×sub-neg_binary64
2×+-commutative_binary64
2×fma-def_binary64
1×*-commutative_binary64
1×associate-+l-_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055
175
295
3105
4125
5165
6205
7255
Stop Event
1×saturated
Counts
20 → 21
Calls
Call 1
Inputs
(*.f64 -1 (sqrt.f64 x))
Outputs
(*.f64 -1 (sqrt.f64 x))
(neg.f64 (sqrt.f64 x))

eval321.0ms (5.3%)

Compiler

Compiled 13137 to 8577 computations (34.7% saved)

prune90.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New6728680
Fresh12012
Picked101
Done325
Total68810698
Error
0.2b
Counts
698 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
31.0b
(*.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))))
✓31.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
▶32.6b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
✓32.6b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
31.1b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (/.f64 (+.f64 x (-.f64 1 x)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))
▶31.1b
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (+.f64 x 1) x)))
▶32.6b
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
▶0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
▶60.8b
(*.f64 1/2 x)
32.5b
1
Compiler

Compiled 233 to 173 computations (25.8% saved)

localize12.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

Compiled 28 to 18 computations (35.7% saved)

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)))

rewrite48.0ms (0.8%)

Algorithm
1×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
1×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)))))))))

simplify7.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

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

localize4.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiled 23 to 14 computations (39.1% saved)

series1.0ms (0%)

Counts
1 → 2
Calls

3 calls:

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

rewrite44.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
676×pow1_binary64
631×add-log-exp_binary64
631×log1p-expm1-u_binary64
631×expm1-log1p-u_binary64
617×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
11329
217359
Stop Event
1×node limit
Counts
1 → 37
Calls
Call 1
Inputs
(-.f64 (*.f64 1/2 x) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 1/2 x) (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 (*.f64 1/2 x) (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)) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 x 3/2)) (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 1/4) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) x) (/.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (*.f64 1/2 x)) (pow.f64 x 1/4)) (-.f64 (sqrt.f64 (*.f64 1/2 x)) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (*.f64 x x) 1/4) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2)))) (-.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 1/2 x (sqrt.f64 x)) (-.f64 (*.f64 (*.f64 x x) 1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 x 3/2)) (+.f64 (*.f64 (*.f64 x x) 1/4) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) x) (fma.f64 1/2 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 x 3/2))) (neg.f64 (+.f64 (*.f64 (*.f64 x x) 1/4) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) x)) (neg.f64 (fma.f64 1/2 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (*.f64 (*.f64 x x) 1/4) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) (cbrt.f64 (*.f64 1/2 x)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 x)) (sqrt.f64 (*.f64 1/2 x)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048
158
Stop Event
1×saturated
Counts
39 → 38
Calls
Call 1
Inputs
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
(*.f64 1/2 x)
(*.f64 1/2 x)

localize18.0ms (0.3%)

Local error

Found 6 expressions with local error:

NewErrorProgram
3.4b
(+.f64 x (-.f64 1 x))
0.0b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
0.0b
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
✓0.0b
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
✓0.0b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
3.4b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 44 to 29 computations (34.1% saved)

series5.0ms (0.1%)

Counts
2 → 6
Calls

6 calls:

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

rewrite66.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
715×fma-def_binary64
609×log-prod_binary64
404×fma-neg_binary64
229×expm1-udef_binary64
229×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01129
126229
2396129
Stop Event
1×node limit
Counts
2 → 126
Calls
Call 1
Inputs
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))) (cbrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 x 1) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) (/.f64 x (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) 2) (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) (*.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (/.f64 1 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 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(hypot.f64 1 (pow.f64 x 1/4)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (cbrt.f64 x)) (fma.f64 x 1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 x) (fma.f64 x 1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 1/2) (pow.f64 (cbrt.f64 x) 1/2) (fma.f64 x 1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))))

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0718
11018
Stop Event
1×saturated
Counts
132 → 130
Calls
Call 1
Inputs
1
(/.f64 2 x)
(/.f64 2 x)
1
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
1
(/.f64 2 x)
(/.f64 2 x)
1
(*.f64 1/2 x)
(*.f64 x 1/2)
(*.f64 1/2 x)
(*.f64 x 1/2)

localize21.0ms (0.4%)

Local error

Found 8 expressions with local error:

NewErrorProgram
3.4b
(-.f64 (+.f64 x 1) x)
0.1b
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (+.f64 x 1) x)))
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (+.f64 x 1) x)))
✓3.4b
(-.f64 (+.f64 x 1) x)
Compiler

Compiled 52 to 33 computations (36.5% saved)

series3.0ms (0%)

Counts
2 → 13
Calls

6 calls:

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

rewrite92.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
625×fma-def_binary64
555×log-prod_binary64
303×fma-neg_binary64
292×pow2_binary64
202×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01030
123718
2361018
Stop Event
1×node limit
Counts
2 → 308
Calls
Call 1
Inputs
(-.f64 (+.f64 x 1) x)
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (+.f64 x 1) x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (-.f64 1 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x 1) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x 1) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (-.f64 1 x)) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (-.f64 1 x)) (+.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (-.f64 1 x)) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 x) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x (-.f64 1 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 x (-.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 x (-.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 x (-.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) (cbrt.f64 (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (sqrt.f64 (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3)) (/.f64 1 (fma.f64 x (+.f64 x (+.f64 x 1)) (pow.f64 (+.f64 x 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x)) (/.f64 1 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x (+.f64 x (+.f64 x 1)) (pow.f64 (+.f64 x 1) 2)) (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x (+.f64 x 1)) (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3)) (fma.f64 x (+.f64 x (+.f64 x 1)) (pow.f64 (+.f64 x 1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x)) (+.f64 x (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3))) (neg.f64 (fma.f64 x (+.f64 x (+.f64 x 1)) (pow.f64 (+.f64 x 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x))) (neg.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (-.f64 1 x) 3)) (fma.f64 x x (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 (neg.f64 x) 3)) (+.f64 (pow.f64 (+.f64 x 1) 2) (-.f64 (pow.f64 (neg.f64 x) 2) (*.f64 (+.f64 x 1) (neg.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 1 x) 2)) (-.f64 x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 2) (pow.f64 (neg.f64 x) 2)) (-.f64 (+.f64 x 1) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x (+.f64 x (+.f64 x 1)) (pow.f64 (+.f64 x 1) 2)) (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x (+.f64 x 1)) (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 x (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 x 1))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (+.f64 x 1)) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 x 1))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (exp.f64 (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x 1))) (exp.f64 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 x 1)) (/.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x 1))) (/.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 x)) (exp.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (exp.f64 x)) (exp.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 x)) (+.f64 1 (expm1.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (exp.f64 x)) (+.f64 1 (expm1.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (-.f64 1 x)) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (-.f64 1 x)) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (-.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (-.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (*.f64 (-.f64 1 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 (-.f64 1 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x 1) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x 1) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x (-.f64 1 x)) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x (-.f64 1 x)) (+.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x (-.f64 1 x)) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 x) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x 1) 1 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x 1) 1 (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (-.f64 1 x)) 1 (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (-.f64 1 x)) 1 (+.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (-.f64 1 x)) 1 (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)) (neg.f64 x))))) (#(struct:change #<rule 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simplify25.0ms (0.4%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0113
1413
Stop Event
1×saturated
Counts
321 → 309
Calls
Call 1
Inputs
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

eval664.0ms (11%)

Compiler

Compiled 16021 to 10600 computations (33.8% saved)

prune243.0ms (4%)

Pruning

17 alts after pruning (12 fresh and 5 done)

PrunedKeptTotal
New76411775
Fresh213
Picked101
Done156
Total76817785
Error
0.0b
Counts
785 → 17
Alt Table
Click to see full alt table
StatusErrorProgram
0.3b
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
0.7b
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
▶32.6b
(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
✓31.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
9.3b
(/.f64 1 (/.f64 1 (/.f64 (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))
✓32.6b
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
▶0.2b
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
✓60.8b
(*.f64 1/2 x)
0.3b
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
32.5b
1
31.7b
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
0.2b
(/.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
▶9.1b
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
▶17.4b
(*.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)))))
✓32.6b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
▶60.0b
(/.f64 2 x)
✓0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Compiler

Compiled 352 to 281 computations (20.2% saved)

localize34.0ms (0.6%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
0.1b
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓0.0b
(sqrt.f64 (+.f64 1 x))
✓0.1b
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
✓0.3b
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
Compiler

Compiled 39 to 26 computations (33.3% saved)

series20.0ms (0.3%)

Counts
4 → 7
Calls

12 calls:

TimeVariablePointExpression
6.0ms
x
@-inf
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
4.0ms
x
@inf
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
2.0ms
x
@0
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
2.0ms
x
@-inf
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
1.0ms
x
@inf
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))

rewrite127.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
439×fma-def_binary64
434×prod-exp_binary64
414×log-prod_binary64
298×exp-prod_binary64
294×pow-prod-down_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01045
121645
2272145
Stop Event
1×node limit
Counts
4 → 190
Calls
Call 1
Inputs
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
(sqrt.f64 (+.f64 1 x))
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
Outputs
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(sqrt.f64 x)))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -3 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 -2 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 -2 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (+.f64 1 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (fma.f64 x (-.f64 x 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 x)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log1p.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (log1p.f64 x))) 2)) (cbrt.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 1/2 (log1p.f64 x)))) (sqrt.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 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 1/3 (*.f64 1/2 (log1p.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log1p.f64 x)) 2))))) (#(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 (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 hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 1 x) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 x (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (sqrt.f64 x) (pow.f64 (+.f64 1 x) 3/2)) (/.f64 1 (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (-.f64 x x)) (/.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 x (+.f64 1 x)))) (fma.f64 x (sqrt.f64 x) (pow.f64 (+.f64 1 x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 1 (-.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x (sqrt.f64 x) (pow.f64 (+.f64 1 x) 3/2)) (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 x (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x (sqrt.f64 x) (pow.f64 (+.f64 1 x) 3/2)) (+.f64 x (-.f64 (+.f64 1 x) (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (-.f64 x x)) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) (pow.f64 (+.f64 1 x) 3/2))) (neg.f64 (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (-.f64 x x))) (neg.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x (+.f64 1 x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 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 (E.f64) (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 x (+.f64 1 x)))) (fma.f64 x (sqrt.f64 x) (pow.f64 (+.f64 1 x) 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 1 (-.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2)) (cbrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x)))) (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x)))) (+.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 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 x)) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) 1 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/6) (cbrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 x 1/6) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (+.f64 1 x) 1/6) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4) (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 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))

simplify69.0ms (1.1%)

Algorithm
1×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
01842
14740
210540
330234
472933
5230333
6394133
7416933
8446933
9500833
10600533
Stop Event
1×node limit
Counts
197 → 197
Calls
Call 1
Inputs
1
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)))))
1
Outputs
1
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)
1

localize2.0ms (0%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize17.0ms (0.3%)

Local error

Found 6 expressions with local error:

NewErrorProgram
3.4b
(-.f64 (+.f64 x 1) x)
0.0b
(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
0.0b
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
0.0b
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
✓0.0b
(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
3.4b
(-.f64 (+.f64 x 1) x)
Compiler

Compiled 44 to 29 computations (34.1% saved)

series1.0ms (0%)

Counts
1 → 3
Calls

3 calls:

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

rewrite63.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
747×fma-def_binary64
636×log-prod_binary64
458×fma-neg_binary64
232×log1p-udef_binary64
230×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
126619
2411219
Stop Event
1×node limit
Counts
1 → 54
Calls
Call 1
Inputs
(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (+.f64 x 1) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))) (cbrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 x 1) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) 2) (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) (*.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (/.f64 1 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (sqrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (*.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (/.f64 1 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (+.f64 x (-.f64 1 x))) (/.f64 1 (neg.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) (+.f64 x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) 1) (/.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 2)) (/.f64 (+.f64 x (-.f64 1 x)) (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) (pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 2)) (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 2)) (/.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (/.f64 (+.f64 x (-.f64 1 x)) (sqrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) (sqrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (/.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (sqrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (fma.f64 x 1/2 1) 3) (pow.f64 x 3/2))) (fma.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 x) (fma.f64 x 1/2 1)) (pow.f64 (fma.f64 x 1/2 1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (-.f64 1 x)) (-.f64 (pow.f64 (fma.f64 x 1/2 1) 2) x)) (-.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)) (+.f64 x (-.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 x (-.f64 1 x)) (neg.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 3) (pow.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log1p.f64 (-.f64 x x)) (log1p.f64 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log1p.f64 (-.f64 x x)) (log1p.f64 (fma.f64 x 1/2 (sqrt.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (+.f64 x 1) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x 1) (/.f64 1 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))) (cbrt.f64 (/.f64 (+.f64 x 1) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 2)) (/.f64 (+.f64 x 1) (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (/.f64 (+.f64 x 1) (sqrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1) (/.f64 (cbrt.f64 (+.f64 x 1)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) 1) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 2)) (/.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) 2)) (/.f64 (sqrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (sqrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (/.f64 (cbrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (/.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 x 1) (+.f64 (pow.f64 (fma.f64 x 1/2 1) 3) (pow.f64 x 3/2))) (fma.f64 (sqrt.f64 x) (-.f64 (sqrt.f64 x) (fma.f64 x 1/2 1)) (pow.f64 (fma.f64 x 1/2 1) 2)) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 x 1) (-.f64 (pow.f64 (fma.f64 x 1/2 1) 2) x)) (-.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)) (neg.f64 (/.f64 x (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))))

simplify13.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
059
179
Stop Event
1×saturated
Counts
57 → 56
Calls
Call 1
Inputs
1
(/.f64 2 x)
(/.f64 2 x)
Outputs
1
(/.f64 2 x)
(/.f64 2 x)

localize64.0ms (1.1%)

Local error

Found 8 expressions with local error:

NewErrorProgram
9.1b
(cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))
0.2b
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
0.0b
(pow.f64 (+.f64 x 1) 3/2)
0.0b
(+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x))
✓0.0b
(+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x))
✓0.0b
(pow.f64 (+.f64 x 1) 3/2)
✓0.2b
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
✓9.1b
(cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))
Compiler

Compiled 40 to 29 computations (27.5% saved)

series9.0ms (0.2%)

Counts
4 → 18
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(pow.f64 (+.f64 x 1) 3/2)
1.0ms
x
@inf
(pow.f64 (+.f64 x 1) 3/2)
1.0ms
x
@0
(pow.f64 (+.f64 x 1) 3/2)
1.0ms
x
@-inf
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
1.0ms
x
@-inf
(+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x))

rewrite68.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
974×prod-diff_binary64
418×log-prod_binary64
392×fma-def_binary64
254×pow2_binary64
231×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01047
122438
2293138
Stop Event
1×node limit
Counts
4 → 147
Calls
Call 1
Inputs
(cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
(pow.f64 (+.f64 x 1) 3/2)
(+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x))
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 (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) 1/4) (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 1/3) (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 /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (+.f64 x -1)))))) (#(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 pow.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 9/2) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 3/4)))) (#(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) 3/4) 2/3)))) (#(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 expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(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 (*.f64 3/2 (log1p.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))
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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 (pow.f64 x 1/6) (cbrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(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 (+.f64 x 1) 1/6) (cbrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(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) 1/4) (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 (+.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 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/3) (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))

simplify54.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
632×fma-def_binary64
338×distribute-rgt-out_binary64
309×times-frac_binary64
233×associate-/l*_binary64
215×distribute-lft-out_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
061372
1154353
2393274
31194216
44145193
56478189
Stop Event
1×node limit
Counts
165 → 175
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)))))
1
1
(+.f64 1 (*.f64 3/2 x))
(+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 3/2 x)))
(+.f64 (*.f64 -1/16 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 3/2 x))))
(sqrt.f64 (pow.f64 x 3))
(+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 x)))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 x))))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (sqrt.f64 (pow.f64 x 3)) (+.f64 (*.f64 3/2 (sqrt.f64 x)) (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 -1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
1
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))
(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 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x -1/8 1/2) (fma.f64 1/16 (pow.f64 x 3) 1))
(fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) (fma.f64 1/2 x 1))
1
1
(+.f64 1 (*.f64 3/2 x))
(+.f64 1 (*.f64 x 3/2))
(fma.f64 x 3/2 1)
(+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 3/2 x)))
(+.f64 1 (fma.f64 3/8 (*.f64 x x) (*.f64 x 3/2)))
(+.f64 (*.f64 x (*.f64 x 3/8)) (fma.f64 x 3/2 1))
(fma.f64 x (*.f64 x 3/8) (fma.f64 x 3/2 1))
(fma.f64 x (fma.f64 x 3/8 3/2) 1)
(+.f64 (*.f64 -1/16 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 3/2 x))))
(fma.f64 -1/16 (pow.f64 x 3) (+.f64 1 (fma.f64 3/8 (*.f64 x x) (*.f64 x 3/2))))
(+.f64 (fma.f64 x 3/2 (*.f64 x (*.f64 x 3/8))) (fma.f64 (pow.f64 x 3) -1/16 1))
(fma.f64 (pow.f64 x 3) -1/16 (fma.f64 x (*.f64 x 3/8) (fma.f64 x 3/2 1)))
(fma.f64 x (fma.f64 x 3/8 3/2) (fma.f64 (pow.f64 x 3) -1/16 1))
(sqrt.f64 (pow.f64 x 3))
(pow.f64 x 3/2)
(+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 x)))
(fma.f64 3/2 (sqrt.f64 x) (sqrt.f64 (pow.f64 x 3)))
(fma.f64 3/2 (sqrt.f64 x) (pow.f64 x 3/2))
(*.f64 (sqrt.f64 x) (+.f64 3/2 x))
(*.f64 (sqrt.f64 x) (+.f64 x 3/2))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 x))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 x))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 3/2 (sqrt.f64 x) (sqrt.f64 (pow.f64 x 3))))
(fma.f64 3/2 (sqrt.f64 x) (fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (pow.f64 x 3/2)))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 x) (+.f64 3/2 x)))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 x) (+.f64 x 3/2)))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (sqrt.f64 (pow.f64 x 3)) (+.f64 (*.f64 3/2 (sqrt.f64 x)) (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (+.f64 (sqrt.f64 (pow.f64 x 3)) (fma.f64 3/2 (sqrt.f64 x) (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (fma.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 3/2 (sqrt.f64 x))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (pow.f64 x 3))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 3/2 (sqrt.f64 x) (fma.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 x 3/2))))
(fma.f64 3/2 (sqrt.f64 x) (fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 x 3/2))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 x) (+.f64 3/2 x))))
(fma.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 x) (+.f64 x 3/2))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(sqrt.f64 (pow.f64 x 3))
(pow.f64 x 3/2)
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 3/2 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))
(*.f64 (+.f64 (/.f64 3/2 x) 1) (pow.f64 (exp.f64 3/2) (log.f64 x)))
(*.f64 (+.f64 1 (/.f64 3/2 x)) (pow.f64 x 3/2))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))
(+.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) x) (+.f64 3/2 (/.f64 3/8 x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) x) (+.f64 3/2 (/.f64 3/8 x)) (pow.f64 (exp.f64 3/2) (log.f64 x)))
(fma.f64 (/.f64 (pow.f64 x 3/2) x) (+.f64 3/2 (/.f64 3/8 x)) (pow.f64 x 3/2))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 -1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(+.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))))
(+.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))))))
(fma.f64 -1/16 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) (pow.f64 x 3)) (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) x) (+.f64 3/2 (/.f64 3/8 x)))))
(+.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) x) (+.f64 (/.f64 3/8 x) (+.f64 3/2 (/.f64 -1/16 (*.f64 x x))))))
(+.f64 (*.f64 (/.f64 (pow.f64 x 3/2) x) (+.f64 (/.f64 -1/16 (*.f64 x x)) (+.f64 3/2 (/.f64 3/8 x)))) (pow.f64 x 3/2))
(fma.f64 (/.f64 (pow.f64 x 3/2) x) (+.f64 3/2 (/.f64 3/8 x)) (fma.f64 -1/16 (pow.f64 x -3/2) (pow.f64 x 3/2)))
1

localize94.0ms (1.6%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (+.f64 1 x) (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))
0.0b
(pow.f64 (+.f64 1 x) 3/2)
0.0b
(+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))
0.0b
(*.f64 (+.f64 1 x) x)
✓0.6b
(/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))
✓3.6b
(-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))
✓8.6b
(*.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)))))
✓16.1b
(sqrt.f64 (*.f64 (+.f64 1 x) x))
Compiler

Compiled 90 to 65 computations (27.8% saved)

series26.0ms (0.4%)

Counts
4 → 37
Calls

12 calls:

TimeVariablePointExpression
5.0ms
x
@0
(*.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)))))
5.0ms
x
@-inf
(sqrt.f64 (*.f64 (+.f64 1 x) x))
4.0ms
x
@-inf
(*.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)))))
3.0ms
x
@inf
(*.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)))))
1.0ms
x
@-inf
(/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))

rewrite142.0ms (2.4%)

Algorithm
1×batch-egg-rewrite
Rules
441×fma-neg_binary64
279×expm1-udef_binary64
278×log1p-udef_binary64
250×log-div_binary64
238×log-pow_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01470
134070
2537961
Stop Event
1×node limit
Counts
4 → 155
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (+.f64 1 x) 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 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))
(/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) (cbrt.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 x))) (cbrt.f64 (+.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 x))) (sqrt.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 2)) 1/2) (pow.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 (log.f64 x) (log1p.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 x (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (cbrt.f64 (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (cbrt.f64 (pow.f64 x 3/2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 x))))))))
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simplify86.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
778×fma-def_binary64
427×associate-+l+_binary64
339×associate-+r+_binary64
310×associate-/r*_binary64
266×+-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02191886
16751579
222071295
Stop Event
1×node limit
Counts
192 → 215
Calls
Call 1
Inputs
x
(+.f64 1/2 x)
(-.f64 (+.f64 1/2 x) (*.f64 1/8 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) x)) (*.f64 1/8 (/.f64 1 x)))
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(+.f64 1/2 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))
(+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(-.f64 (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/4 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))) (pow.f64 x 2))) (*.f64 3/16 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2)))))))))
(*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 -1 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 -3/4 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (*.f64 -3/32 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) x)))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 3/16 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (+.f64 (*.f64 -1/64 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 -3/4 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 -3/4 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (*.f64 -3/32 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))))))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 -3/4 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (*.f64 -3/32 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) x))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
-1/2
(-.f64 (*.f64 1/8 (/.f64 1 x)) 1/2)
(-.f64 (*.f64 1/8 (/.f64 1 x)) (+.f64 1/2 (*.f64 1/16 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 5/128 (/.f64 1 (pow.f64 x 3))) (*.f64 1/8 (/.f64 1 x))) (+.f64 1/2 (*.f64 1/16 (/.f64 1 (pow.f64 x 2)))))
(*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x)
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) 1/2)
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) (+.f64 1/2 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 9/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 1/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (+.f64 1 (pow.f64 x 3/2))))) (pow.f64 x 3)) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2)))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -3/4 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -9/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(/.f64 1/2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(-.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) (*.f64 7/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))))))
Outputs
x
(+.f64 1/2 x)
(+.f64 x 1/2)
(-.f64 (+.f64 1/2 x) (*.f64 1/8 (/.f64 1 x)))
(+.f64 1/2 (-.f64 x (/.f64 1/8 x)))
(+.f64 x (-.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) x)) (*.f64 1/8 (/.f64 1 x)))
(+.f64 1/2 (-.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (+.f64 1/2 (/.f64 -1/8 x)))
(+.f64 (/.f64 1/16 (*.f64 x x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))
x
(+.f64 1/2 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(+.f64 x 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))
(+.f64 1/2 (-.f64 x (/.f64 1/8 x)))
(+.f64 x (-.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))
(+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))
(+.f64 1/2 (-.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (+.f64 1/2 (/.f64 -1/8 x)))
(+.f64 (/.f64 1/16 (*.f64 x x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8))
(-.f64 (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(-.f64 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (fma.f64 3/4 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) x) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32))))
(-.f64 (-.f64 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/32) x))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 x -3/32)))))
(-.f64 (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/4 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))) (pow.f64 x 2))) (*.f64 3/16 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2)))))))))
(-.f64 (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (fma.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 3/4 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) x) (fma.f64 3/4 (/.f64 (-.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 3/4 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)))) (*.f64 x x)) (*.f64 3/16 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) (*.f64 x x)))))))))
(-.f64 (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -1/64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/8 (+.f64 (fma.f64 3/4 (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/32) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/32)) (*.f64 x x)) (*.f64 (/.f64 3/16 x) (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 x -1/8)))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/32) x))))))
(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (fma.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -1/64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32 (+.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/64) (*.f64 x x)) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 x -1/8)) (+.f64 3/4 (/.f64 3/16 x))))))))
(*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(*.f64 1/2 (/.f64 (*.f64 x (+.f64 2 (pow.f64 (sqrt.f64 -1) 2))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(/.f64 (*.f64 1/2 x) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(*.f64 1/2 (/.f64 (/.f64 x (pow.f64 (/.f64 -1 x) -3/2)) (pow.f64 -1 3/2)))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(+.f64 (/.f64 1/4 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (-.f64 (*.f64 1/2 (/.f64 (*.f64 x (+.f64 2 (pow.f64 (sqrt.f64 -1) 2))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 (*.f64 3/8 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
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(fma.f64 (*.f64 x x) (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x 3/2)))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 9/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 1/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (+.f64 1 (pow.f64 x 3/2))))) (pow.f64 x 3)) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2)))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (fma.f64 (-.f64 (+.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 3/2 (/.f64 (-.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 1 (pow.f64 x 3/2))))) (pow.f64 x 3) (*.f64 (*.f64 x x) (-.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))))))
(+.f64 (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x 3/2)))) (fma.f64 (pow.f64 x 3) (+.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (+.f64 (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.f64 -3/2 (-.f64 (/.f64 9/4 (*.f64 (+.f64 1 (pow.f64 x 3/2)) (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)))))) (*.f64 x (*.f64 x (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))))))
(+.f64 (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x 3/2)))) (*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 x (+.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (-.f64 (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 (+.f64 (/.f64 27/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 1 (pow.f64 x 3/2)))))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(fma.f64 -1 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16) (*.f64 x x)) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)))
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) x) (/.f64 -3/16 x)))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/16) (*.f64 x x))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -3/4 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -9/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(fma.f64 -1 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16) (*.f64 x x)) (fma.f64 -1 (/.f64 (fma.f64 -3/4 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -11/128)) (pow.f64 x 3)) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8))))
(-.f64 (-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -11/128 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 9/64)) (pow.f64 x 3))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) x) (/.f64 -3/16 x)))
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (fma.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) x) (/.f64 -3/16 x) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 7/128) (pow.f64 x 3))))
(/.f64 1/2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(/.f64 1/2 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(-.f64 (/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(fma.f64 1/2 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (/.f64 -3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (/.f64 -3/8 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (*.f64 (pow.f64 -1 3/2) x))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (/.f64 3/16 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (-.f64 (/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))))
(fma.f64 3/16 (/.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (*.f64 x x)) (fma.f64 1/2 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (/.f64 -3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (+.f64 (/.f64 (/.f64 (/.f64 3/16 (*.f64 x x)) (pow.f64 (/.f64 -1 x) -3/2)) (pow.f64 -1 3/2)) (/.f64 -3/8 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (*.f64 (pow.f64 -1 3/2) x)))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) (*.f64 7/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))))))
(+.f64 (/.f64 3/16 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (-.f64 (/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (+.f64 (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 7/128 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))))
(+.f64 (fma.f64 3/16 (/.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (*.f64 x x)) (fma.f64 1/2 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (/.f64 -3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))) (*.f64 -7/128 (/.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (pow.f64 x 3))))
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (+.f64 (/.f64 (/.f64 (/.f64 3/16 (*.f64 x x)) (pow.f64 (/.f64 -1 x) -3/2)) (pow.f64 -1 3/2)) (+.f64 (/.f64 -3/8 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (*.f64 (pow.f64 -1 3/2) x))) (/.f64 -7/128 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (*.f64 (pow.f64 -1 3/2) (pow.f64 x 3)))))))

eval589.0ms (9.8%)

Compiler

Compiled 19604 to 13859 computations (29.3% saved)

prune145.0ms (2.4%)

Pruning

16 alts after pruning (11 fresh and 5 done)

PrunedKeptTotal
New85810868
Fresh617
Picked101
Done459
Total86916885
Error
0b
Counts
885 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
31.7b
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
0.2b
(/.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
32.5b
1
0.3b
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -1/2) 2)
✓31.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.3b
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
38.1b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (+.f64 (/.f64 1/8 x) -1/2)))
✓60.8b
(*.f64 1/2 x)
34.2b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) -1/2))
28.8b
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
✓32.6b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
32.9b
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
28.0b
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
✓60.0b
(/.f64 2 x)
0.7b
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -3)
Compiler

Compiled 160 to 132 computations (17.5% saved)

regimes48.0ms (0.8%)

Counts
47 → 1
Calls
Call 1
Inputs
1
1
1
(/.f64 2 x)
(*.f64 1/2 x)
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
(/.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (+.f64 x 1) x)))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) -1/2))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (+.f64 (/.f64 1/8 x) -1/2)))
(-.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
(-.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x))
(-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 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))))
(*.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 (expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -3)
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
(-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3) (sqrt.f64 x))
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -1/2) 2)
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
(-.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.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)))
(/.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))))
(/.f64 1 (/.f64 1 (/.f64 (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))
(*.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))))
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.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)))
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (/.f64 (+.f64 x (-.f64 1 x)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 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)))
(/.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))))))
Outputs
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
Calls

3 calls:

20.0ms
x
5.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Results
ErrorSegmentsBranch
0.2b1x
0.2b1(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b1(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 600 to 408 computations (32% saved)

regimes36.0ms (0.6%)

Counts
32 → 1
Calls
Call 1
Inputs
1
1
1
(/.f64 2 x)
(*.f64 1/2 x)
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
(/.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (+.f64 x 1) x)))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) -1/2))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 1 x) (+.f64 (/.f64 1/8 x) -1/2)))
(-.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
(-.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x))
(-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 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))))
(*.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 (expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -3)
Outputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Calls

3 calls:

16.0ms
x
5.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Results
ErrorSegmentsBranch
0.2b1x
0.2b1(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b1(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 344 to 247 computations (28.2% saved)

regimes29.0ms (0.5%)

Counts
15 → 2
Calls
Call 1
Inputs
1
1
1
(/.f64 2 x)
(*.f64 1/2 x)
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Calls

3 calls:

15.0ms
x
5.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Results
ErrorSegmentsBranch
0.2b2x
0.2b2(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b2(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 118 to 83 computations (29.7% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
3.166496753692627e-8
0.00019311175447001006
Compiler

Compiled 12 to 9 computations (25% saved)

regimes18.0ms (0.3%)

Counts
14 → 2
Calls
Call 1
Inputs
1
1
1
(/.f64 2 x)
(*.f64 1/2 x)
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
Outputs
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
Calls

1 calls:

15.0ms
x
Results
ErrorSegmentsBranch
1.0b2x
Compiler

Compiled 95 to 67 computations (29.5% saved)

bsearch30.0ms (0.5%)

Algorithm
1×binary-search
Steps
TimeLeftRight
30.0ms
0.004028897698743788
1.3662673287561915
Compiler

Compiled 12 to 9 computations (25% saved)

regimes14.0ms (0.2%)

Counts
9 → 2
Calls
Call 1
Inputs
1
1
1
(/.f64 2 x)
(*.f64 1/2 x)
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
Outputs
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
Calls

1 calls:

11.0ms
x
Results
ErrorSegmentsBranch
1.0b2x
Compiler

Compiled 39 to 30 computations (23.1% saved)

bsearch21.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
21.0ms
0.004028897698743788
1.3662673287561915
Compiler

Compiled 12 to 9 computations (25% saved)

regimes12.0ms (0.2%)

Counts
8 → 2
Calls
Call 1
Inputs
1
1
1
(/.f64 2 x)
(*.f64 1/2 x)
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
Outputs
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
Calls

1 calls:

10.0ms
x
Results
ErrorSegmentsBranch
1.3b2x
Compiler

Compiled 31 to 25 computations (19.4% saved)

bsearch23.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
0.004028897698743788
1.3662673287561915
Compiler

Compiled 12 to 9 computations (25% saved)

regimes11.0ms (0.2%)

Counts
6 → 2
Calls
Call 1
Inputs
1
1
1
(/.f64 2 x)
(*.f64 1/2 x)
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
Outputs
1
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
Calls

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
1.8b2x
Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch18.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
18.0ms
0.004028897698743788
1.3662673287561915
Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (0.1%)

Accuracy

Total -28.3b remaining (-87.3%)

Threshold costs -28.3b (-87.3%)

Counts
5 → 1
Calls
Call 1
Inputs
1
1
1
(/.f64 2 x)
(*.f64 1/2 x)
Outputs
1
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
32.5b1x
Compiler

Compiled 12 to 9 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
10×+-commutative_binary64
4×sub-neg_binary64
3×*-commutative_binary64
1×neg-sub0_binary64
1×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036161
150161
256161
358161
459161
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 944473296573929/18889465931478580854784) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(if (<=.f64 x 74320044747884016/18446744073709551616) (-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 74320044747884016/18446744073709551616) (+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 74320044747884016/18446744073709551616) (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 74320044747884016/18446744073709551616) 1 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
1
Outputs
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))) -2))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 944473296573929/18889465931478580854784) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 944473296573929/18889465931478580854784) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(if (<=.f64 x 74320044747884016/18446744073709551616) (-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 4645002796742751/1152921504606846976) (-.f64 (+.f64 1 (*.f64 x 1/2)) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 74320044747884016/18446744073709551616) (+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 4645002796742751/1152921504606846976) (+.f64 1 (-.f64 (*.f64 x 1/2) (sqrt.f64 x))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 74320044747884016/18446744073709551616) (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 4645002796742751/1152921504606846976) (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 74320044747884016/18446744073709551616) 1 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 4645002796742751/1152921504606846976) 1 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
1

end72.0ms (1.2%)

Stop Event
1×fuel
Compiler

Compiled 221 to 170 computations (23.1% saved)

Profiling

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