Details

Time bar (total: 12.0s)

analyze1.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
100%50%0%0%0%50%0%2
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.7s (14.1%)

Results
760.0ms2304×body1024valid
678.0ms4922×body256valid
230.0ms1030×body512valid
Bogosity

preprocess47.0ms (0.4%)

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
0917
11417
22017
32817
43817
55617
69317
712717
817117
920717
1023317
1123517
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Outputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify24.0ms (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
0917
11417
22017
32817
43817
55617
69317
712717
817117
920717
1023317
1123517
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Outputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

eval1.0ms (0%)

Compiler

Compiled 23 to 18 computations (21.7% saved)

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
19.8b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶19.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 12 to 10 computations (16.7% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x 1))
✓0.2b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.3b
(/.f64 1 (sqrt.f64 x))
✓4.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 33 to 23 computations (30.3% saved)

series19.0ms (0.2%)

Counts
4 → 8
Calls

12 calls:

TimeVariablePointExpression
8.0ms
x
@0
(/.f64 1 (sqrt.f64 x))
3.0ms
x
@inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms
x
@-inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms
x
@0
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@-inf
(/.f64 1 (sqrt.f64 x))

rewrite112.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
776×prod-diff_binary64
445×log-prod_binary64
351×fma-def_binary64
252×pow2_binary64
205×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0938
120730
2297930
Stop Event
1×node limit
Counts
4 → 229
Calls
Call 1
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 1 (sqrt.f64 x))
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
(sqrt.f64 (+.f64 x 1))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 x) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/6) (cbrt.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (+.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 -1 (/.f64 -1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/6))))) (#(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 (pow.f64 (+.f64 1 x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 x)) 1/2)))) (#(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) 3/2) -1/3)))) (#(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 (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) 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 (neg.f64 (neg.f64 (sqrt.f64 (+.f64 1 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2))))))) (#(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 (pow.f64 (+.f64 1 x) -1/2)))))) (#(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 1/2 (log1p.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2)))))))
((#(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 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 x)) 1)))) (#(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 (neg.f64 (sqrt.f64 (+.f64 1 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 (+.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 (pow.f64 (+.f64 1 x) -1/2) -1)))) (#(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) 3/2) 1/3)))) (#(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 (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) 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 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 hypot.f64 1 (sqrt.f64 x))))) (#(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 log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))

simplify161.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
1216×fma-def_binary64
750×sqr-pow_binary64
605×cube-prod_binary64
427×fabs-mul_binary64
370×pow-sqr_binary64
Iterations

Useful iterations: 10 (0.0ms)

IterNodesCost
03080
17576
218074
354662
4139558
5242358
6294558
7307858
8323258
9341958
10367256
11432356
12473056
13525856
14592656
15675456
16715756
17752356
18786756
Stop Event
1×node limit
Counts
237 → 242
Calls
Call 1
Inputs
1
(+.f64 (*.f64 -1/2 x) 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(+.f64 (*.f64 -1/2 x) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3)))))
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
(+.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/2 x 1) (*.f64 3/8 (*.f64 x x)))
(fma.f64 -1/2 x (fma.f64 3/8 (*.f64 x x) 1))
(fma.f64 x (*.f64 x 3/8) (fma.f64 -1/2 x 1))
(fma.f64 x (fma.f64 x 3/8 -1/2) 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3)))))
(+.f64 (fma.f64 -1/2 x 1) (fma.f64 3/8 (*.f64 x x) (*.f64 -5/16 (pow.f64 x 3))))
(fma.f64 -1/2 x (fma.f64 x (*.f64 x 3/8) (fma.f64 -5/16 (pow.f64 x 3) 1)))
(fma.f64 -1/2 x (fma.f64 x (*.f64 x (fma.f64 x -5/16 3/8)) 1))
(fma.f64 x (fma.f64 x (fma.f64 x -5/16 3/8) -1/2) 1)
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 (*.f64 x -1/8) (fma.f64 (pow.f64 x 3) 1/16 (fma.f64 x 1/2 1)))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 1))
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))) 1)
(fma.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2) 1)

eval166.0ms (1.4%)

Compiler

Compiled 4484 to 3575 computations (20.3% saved)

prune76.0ms (0.6%)

Pruning

34 alts after pruning (33 fresh and 1 done)

PrunedKeptTotal
New20933242
Fresh000
Picked011
Done000
Total20934243
Error
19.1b
Counts
243 → 34
Alt Table
Click to see full alt table
StatusErrorProgram
▶20.2b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
24.7b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) 1/4) 2)))
29.1b
(fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) 2) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1/2))
29.3b
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
▶19.8b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
31.7b
(-.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.3b
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
25.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
20.2b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
29.3b
(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
25.6b
(/.f64 (-.f64 (/.f64 1 x) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2)) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
22.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
30.5b
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
25.4b
(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
31.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
30.6b
(/.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 3)) (+.f64 (/.f64 1 x) (-.f64 (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2) (*.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))))
29.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))
✓19.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
40.3b
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
19.8b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
25.3b
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶31.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
22.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
20.2b
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
22.4b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
30.3b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
25.9b
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶32.1b
(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
22.9b
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
27.7b
(+.f64 (fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (neg.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x)))))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (/.f64 1 (cbrt.f64 (+.f64 1 x))) (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x))))))
29.6b
(+.f64 (fma.f64 (pow.f64 x -1/2) 1 (neg.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x)))))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (/.f64 1 (cbrt.f64 (+.f64 1 x))) (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x))))))
29.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
▶25.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
30.5b
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
Compiler

Compiled 1190 to 980 computations (17.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 1 x))
✓0.0b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
✓0.2b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x))
✓4.2b
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
Compiler

Compiled 44 to 26 computations (40.9% saved)

series17.0ms (0.1%)

Counts
4 → 5
Calls

12 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
3.0ms
x
@inf
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x))
2.0ms
x
@-inf
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x))
2.0ms
x
@-inf
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
2.0ms
x
@inf
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite96.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
522×log-prod_binary64
473×fma-def_binary64
371×pow-prod-down_binary64
266×pow2_binary64
237×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0957
120749
2324549
Stop Event
1×node limit
Counts
4 → 225
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(sqrt.f64 (+.f64 1 x))
Outputs
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(#(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 (+.f64 1 x)))) (exp.f64 (neg.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 (exp.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 (sqrt.f64 x))) (exp.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.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 (exp.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 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(sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (+.f64 1 x) 1/4)) (/.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) 2) (pow.f64 (+.f64 1 x) 1/4)) (/.f64 (cbrt.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) (pow.f64 (+.f64 1 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (sqrt.f64 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) 2) (+.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (sqrt.f64 (+.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (sqrt.f64 (+.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (sqrt.f64 (+.f64 1 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) 3) (pow.f64 (+.f64 1 x) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) (sqrt.f64 (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) 2) (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (sqrt.f64 (+.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) 3) (pow.f64 (+.f64 1 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) (*.f64 -1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 (log.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) (*.f64 -1/2 (log1p.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (sqrt.f64 (+.f64 1 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 (pow.f64 1 1/2) (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 /.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 (-.f64 1 x)))))) (#(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 (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 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 hypot.f64 1 (sqrt.f64 x))))) (#(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 log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))

simplify90.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
660×distribute-rgt-in_binary64
606×distribute-lft-in_binary64
536×unswap-sqr_binary64
516×associate-*l*_binary64
445×*-commutative_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01840
14738
210538
330032
474431
5241431
6405931
7428731
8458631
9512531
10612231
Stop Event
1×node limit
Counts
230 → 232
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 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 x (*.f64 x -1/8) (fma.f64 1/2 x (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 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))) 1)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
0.3b
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 15 to 9 computations (40% saved)

series1.0ms (0%)

Counts
1 → 2
Calls

3 calls:

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

rewrite47.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
588×pow1_binary64
551×add-log-exp_binary64
550×log1p-expm1-u_binary64
550×expm1-log1p-u_binary64
538×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
069
11297
216237
Stop Event
1×node limit
Counts
1 → 31
Calls
Call 1
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (pow.f64 x -1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -1/2) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (pow.f64 x -1/2) -1)) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 x -1/2) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 x -1/2) -1)) 2) (cbrt.f64 (+.f64 (pow.f64 x -1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (pow.f64 x -1/2) -1)) (sqrt.f64 (+.f64 (pow.f64 x -1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) -1) (/.f64 1 (+.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (sqrt.f64 x) -1/2) 1) (-.f64 (pow.f64 (sqrt.f64 x) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2))) (+.f64 (pow.f64 (sqrt.f64 x) -3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (/.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) -1) (+.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) -1) (+.f64 (/.f64 1 x) (-.f64 1 (*.f64 (pow.f64 x -1/2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 1 x) -1) (+.f64 1 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 1 x) -1) (-.f64 (pow.f64 x -1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) -1)) (neg.f64 (+.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (/.f64 1 x) -1)) (neg.f64 (+.f64 1 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (pow.f64 x -1/2) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (pow.f64 x -1/2) -1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (pow.f64 x -1/2) -1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (pow.f64 x -1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (pow.f64 x -1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (pow.f64 x -1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) -1)))))

simplify38.0ms (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
012
Stop Event
1×saturated
Counts
33 → 32
Calls
Call 1
Inputs
-1
-1
Outputs
-1
-1

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (+.f64 1 x))
✓0.3b
(/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓0.5b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
✓4.2b
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
Compiler

Compiled 73 to 57 computations (21.9% saved)

series11.0ms (0.1%)

Counts
4 → 48
Calls

12 calls:

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

rewrite149.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
688×log-prod_binary64
675×fma-def_binary64
323×fma-neg_binary64
251×expm1-udef_binary64
251×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01364
131449
2475449
Stop Event
1×node limit
Counts
4 → 371
Calls
Call 1
Inputs
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 1 (+.f64 1 x))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 x)))) (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 x)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 1 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -2)) (/.f64 1 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 -1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/4) (*.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 (+.f64 1 x) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 x)) -1) (pow.f64 (hypot.f64 1 (sqrt.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3))) (fma.f64 x (-.f64 x 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1 (*.f64 x x))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/2) (/.f64 1 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 x) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 x))))))))

simplify74.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
741×fma-def_binary64
430×associate-/r*_binary64
412×associate-+l+_binary64
327×associate-+r+_binary64
252×associate--r+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02191950
17211782
221811697
Stop Event
1×node limit
Counts
419 → 445
Calls
Call 1
Inputs
(/.f64 1 x)
(-.f64 (/.f64 1 x) 1)
(-.f64 (+.f64 (/.f64 1 x) x) 1)
(-.f64 (+.f64 (*.f64 -1 (pow.f64 x 2)) (+.f64 (/.f64 1 x) x)) 1)
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
(/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x))
(-.f64 (+.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(-.f64 (+.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(-.f64 (+.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (*.f64 (-.f64 (*.f64 5/16 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))) (+.f64 1 (pow.f64 x -1/2)))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (+.f64 (pow.f64 x -1/2) 1))) (+.f64 (*.f64 3/8 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 2)) (+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) (+.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/4 (/.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))))
(-.f64 (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))) (+.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 3/16 (/.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 5))) (+.f64 (*.f64 -1/4 (/.f64 (-.f64 (*.f64 1/2 (sqrt.f64 x)) (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/4 (-.f64 (*.f64 -1/2 (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 x)))))) (pow.f64 x 5))) (+.f64 (*.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (*.f64 -1/4 (/.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))))
(/.f64 1/2 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))
(-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 5/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 5/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (*.f64 35/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 5))))))
(/.f64 1 (+.f64 (pow.f64 x -1/2) 1))
(+.f64 (*.f64 1/2 (/.f64 x (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(+.f64 (*.f64 1/2 (/.f64 x (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (*.f64 (-.f64 (*.f64 1/4 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 (+.f64 (pow.f64 x -1/2) 1) 2)))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 2))))
(+.f64 (*.f64 1/2 (/.f64 x (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (*.f64 (-.f64 (*.f64 5/16 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 (+.f64 (pow.f64 x -1/2) 1) 2)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/4 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2) (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (+.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 3)) (+.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (*.f64 (-.f64 (*.f64 1/4 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 (+.f64 (pow.f64 x -1/2) 1) 2)))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 2)))))
(*.f64 1/2 (sqrt.f64 x))
(+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 1/2 (sqrt.f64 x)) (*.f64 -1 (/.f64 (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/32 (sqrt.f64 x))) (pow.f64 x 2)))))
(+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 1/2 (sqrt.f64 x)) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -5/64 (sqrt.f64 x)) (+.f64 (*.f64 1/4 (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/32 (sqrt.f64 x)))) (*.f64 3/128 (sqrt.f64 x)))) (pow.f64 x 3))) (*.f64 -1 (/.f64 (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/32 (sqrt.f64 x))) (pow.f64 x 2))))))
(/.f64 1/2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(+.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))) (*.f64 1/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) (*.f64 5/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))) (*.f64 1/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (+.f64 (*.f64 -1 x) (pow.f64 x 2)))
(+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 -1 x) (pow.f64 x 2))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
Outputs
(/.f64 1 x)
(-.f64 (/.f64 1 x) 1)
(+.f64 (/.f64 1 x) -1)
(-.f64 (+.f64 (/.f64 1 x) x) 1)
(+.f64 (/.f64 1 x) (-.f64 x 1))
(+.f64 x (+.f64 (/.f64 1 x) -1))
(-.f64 (+.f64 (*.f64 -1 (pow.f64 x 2)) (+.f64 (/.f64 1 x) x)) 1)
(+.f64 (fma.f64 -1 (*.f64 x x) (+.f64 x (/.f64 1 x))) -1)
(+.f64 -1 (-.f64 (+.f64 x (/.f64 1 x)) (*.f64 x x)))
(-.f64 (+.f64 x (/.f64 1 x)) (fma.f64 x x 1))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4)))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 5))))
(+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 5))))
(+.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 5))))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4)))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 5))))
(+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 5))))
(+.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 5))))
(/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x))
(/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2))))
(/.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (+.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (-.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (/.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2))) (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))))
(-.f64 (+.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (-.f64 (fma.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) x (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (fma.f64 x (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (-.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (-.f64 (/.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (fma.f64 x (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))))
(-.f64 (+.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (*.f64 (-.f64 (*.f64 5/16 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))) (+.f64 1 (pow.f64 x -1/2)))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (+.f64 (pow.f64 x -1/2) 1))) (+.f64 (*.f64 3/8 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 2)) (+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (-.f64 (fma.f64 (-.f64 (/.f64 5/16 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (+.f64 1 (pow.f64 x -1/2))) (fma.f64 3/8 (/.f64 (-.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))) (*.f64 x x) (fma.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) x (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (fma.f64 (*.f64 x x) (-.f64 (/.f64 5/16 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (-.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (+.f64 1 (pow.f64 x -1/2))) (fma.f64 3/8 (-.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))) (fma.f64 x (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (-.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (-.f64 (/.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))
(+.f64 (fma.f64 x (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (-.f64 (fma.f64 (*.f64 x x) (-.f64 (/.f64 5/16 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (fma.f64 -1/2 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (+.f64 1 (pow.f64 x -1/2))) (fma.f64 3/8 (+.f64 (/.f64 1/2 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -1 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))) (/.f64 1 (+.f64 x (sqrt.f64 x)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/8 (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 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) (+.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/4 (/.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))))
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(/.f64 1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))
(+.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (/.f64 1/8 (*.f64 x (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(fma.f64 1/2 (exp.f64 (*.f64 1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (/.f64 1/8 (*.f64 x (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (/.f64 1/8 (*.f64 x (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))) (*.f64 1/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (-.f64 (/.f64 1/8 (*.f64 x (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 1/16 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))))
(fma.f64 1/2 (exp.f64 (*.f64 1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (fma.f64 1/8 (/.f64 (exp.f64 (*.f64 1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x) (*.f64 (/.f64 (exp.f64 (*.f64 1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x x)) -1/16)))
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (+.f64 (/.f64 1/8 (*.f64 x (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))) (/.f64 (/.f64 -1/16 x) (*.f64 x (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) (*.f64 5/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))) (*.f64 1/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (+.f64 (/.f64 1/8 (*.f64 x (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 5/128 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))) (/.f64 1/16 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(+.f64 (fma.f64 1/2 (exp.f64 (*.f64 1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (fma.f64 (/.f64 (exp.f64 (*.f64 1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)) 5/128 (/.f64 1/8 (*.f64 x (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))) (*.f64 (/.f64 (exp.f64 (*.f64 1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x x)) -1/16))
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (+.f64 (/.f64 1/8 (*.f64 x (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))) (+.f64 (/.f64 5/128 (*.f64 (pow.f64 x 3) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))) (/.f64 (/.f64 -1/16 x) (*.f64 x (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))))))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (neg.f64 x))
(-.f64 1 x)
(+.f64 1 (+.f64 (*.f64 -1 x) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -1 x (*.f64 x x)))
(+.f64 1 (-.f64 (*.f64 x x) x))
(-.f64 (fma.f64 x x 1) x)
(+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 -1 x) (pow.f64 x 2))))
(fma.f64 -1 (pow.f64 x 3) (+.f64 1 (fma.f64 -1 x (*.f64 x x))))
(-.f64 (+.f64 1 (-.f64 (*.f64 x x) x)) (pow.f64 x 3))
(-.f64 (-.f64 (fma.f64 x x 1) x) (pow.f64 x 3))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x)))
(+.f64 (/.f64 1 x) (/.f64 -1 (*.f64 x x)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 -1 (*.f64 x x))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 1 x) (/.f64 -1 (*.f64 x x))) (/.f64 1 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 4))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x)))
(+.f64 (/.f64 1 x) (/.f64 -1 (*.f64 x x)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 -1 (*.f64 x x))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 1 x) (/.f64 -1 (*.f64 x x))) (/.f64 1 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 4))))

localize24.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2)
0.3b
(/.f64 1 (sqrt.f64 x))
✓20.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
Compiler

Compiled 38 to 28 computations (26.3% saved)

series9.0ms (0.1%)

Counts
2 → 14
Calls

6 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
2.0ms
x
@inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
1.0ms
x
@0
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
1.0ms
x
@-inf
(pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2)
1.0ms
x
@inf
(pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2)

rewrite96.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
605×prod-diff_binary64
478×log-prod_binary64
309×fma-def_binary64
296×pow2_binary64
208×pow-pow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01122
125420
2318220
Stop Event
1×node limit
Counts
2 → 138
Calls
Call 1
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
(pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2)
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 x) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/6) (cbrt.f64 (pow.f64 (+.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1)) (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 (pow.f64 1 -1/2) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (pow.f64 (+.f64 1 x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 1 x) 1/12) -4) (pow.f64 (+.f64 1 x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2))))))) (#(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 (pow.f64 (+.f64 1 x) -1/2)))))) (#(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 log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2)))))))

simplify52.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
418×unswap-sqr_binary64
408×fma-def_binary64
384×associate-*l*_binary64
351×distribute-rgt-out_binary64
345×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
096544
1279524
2939464
34206329
Stop Event
1×node limit
Counts
152 → 164
Calls
Call 1
Inputs
(*.f64 -1 (sqrt.f64 (/.f64 1 x)))
(/.f64 -1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
1
(+.f64 (*.f64 -1/2 x) 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(+.f64 (*.f64 -1/2 x) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3)))))
(sqrt.f64 (/.f64 1 x))
(+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (+.f64 (*.f64 -3/32 (pow.f64 (/.f64 1 x) 1/4)) (*.f64 -1/16 (pow.f64 (/.f64 1 x) 1/4))))) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (*.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (+.f64 (*.f64 -1/4 (+.f64 (*.f64 -3/32 (pow.f64 (/.f64 1 x) 1/4)) (*.f64 -1/16 (pow.f64 (/.f64 1 x) 1/4)))) (+.f64 (*.f64 3/128 (pow.f64 (/.f64 1 x) 1/4)) (*.f64 7/128 (pow.f64 (/.f64 1 x) 1/4)))))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (+.f64 (*.f64 -3/32 (pow.f64 (/.f64 1 x) 1/4)) (*.f64 -1/16 (pow.f64 (/.f64 1 x) 1/4))))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (*.f64 1/2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (+.f64 (*.f64 -3/32 (pow.f64 (/.f64 1 x) 1/4)) (*.f64 -1/16 (pow.f64 (/.f64 1 x) 1/4))))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))
(/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(-.f64 (/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 3/8 (/.f64 1 (*.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 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 3/8 (/.f64 1 (*.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 5/16 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)))))
Outputs
(*.f64 -1 (sqrt.f64 (/.f64 1 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(/.f64 -1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(/.f64 -1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(/.f64 -1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(/.f64 -1 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))
(neg.f64 (exp.f64 (*.f64 (log.f64 x) -1/2)))
1
(+.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x 1)
(fma.f64 x -1/2 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/2 x 1) (*.f64 3/8 (*.f64 x x)))
(fma.f64 x -1/2 (fma.f64 3/8 (*.f64 x x) 1))
(fma.f64 x -1/2 (fma.f64 x (*.f64 x 3/8) 1))
(fma.f64 x (*.f64 x 3/8) (fma.f64 x -1/2 1))
(+.f64 (*.f64 -1/2 x) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3)))))
(+.f64 (fma.f64 -1/2 x 1) (fma.f64 3/8 (*.f64 x x) (*.f64 -5/16 (pow.f64 x 3))))
(+.f64 (fma.f64 x -1/2 1) (fma.f64 3/8 (*.f64 x x) (*.f64 -5/16 (pow.f64 x 3))))
(fma.f64 x -1/2 (fma.f64 x (*.f64 x 3/8) (fma.f64 -5/16 (pow.f64 x 3) 1)))
(+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8)))))
(sqrt.f64 (/.f64 1 x))
(+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))
(+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (+.f64 (*.f64 -3/32 (pow.f64 (/.f64 1 x) 1/4)) (*.f64 -1/16 (pow.f64 (/.f64 1 x) 1/4))))) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (*.f64 (pow.f64 (/.f64 1 x) 1/4) -5/32)) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (*.f64 (pow.f64 (/.f64 1 x) 1/4) -5/32)) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (*.f64 (pow.f64 (/.f64 1 x) 1/4) 5/16) (sqrt.f64 (/.f64 1 x)))))
(+.f64 (*.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (+.f64 (*.f64 -1/4 (+.f64 (*.f64 -3/32 (pow.f64 (/.f64 1 x) 1/4)) (*.f64 -1/16 (pow.f64 (/.f64 1 x) 1/4)))) (+.f64 (*.f64 3/128 (pow.f64 (/.f64 1 x) 1/4)) (*.f64 7/128 (pow.f64 (/.f64 1 x) 1/4)))))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (+.f64 (*.f64 -3/32 (pow.f64 (/.f64 1 x) 1/4)) (*.f64 -1/16 (pow.f64 (/.f64 1 x) 1/4))))) (+.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (*.f64 1/2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (+.f64 (*.f64 -3/32 (pow.f64 (/.f64 1 x) 1/4)) (*.f64 -1/16 (pow.f64 (/.f64 1 x) 1/4))))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))
(fma.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (fma.f64 -1/4 (*.f64 (pow.f64 (/.f64 1 x) 1/4) -5/32) (*.f64 (pow.f64 (/.f64 1 x) 1/4) 5/64))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (*.f64 (pow.f64 (/.f64 1 x) 1/4) -5/32)) (+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 1/2 (*.f64 (*.f64 (pow.f64 (/.f64 1 x) 1/4) -5/32) (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))
(fma.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (fma.f64 (pow.f64 (/.f64 1 x) 1/4) 5/64 (*.f64 (pow.f64 (/.f64 1 x) 1/4) 5/128))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 (fma.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (*.f64 (pow.f64 (/.f64 1 x) 1/4) -5/32)) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))) (*.f64 (*.f64 (pow.f64 (/.f64 1 x) 1/4) -5/32) (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) 1/2)))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (*.f64 (pow.f64 (/.f64 1 x) 1/4) 15/128)) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (*.f64 (pow.f64 (/.f64 1 x) 1/4) 5/16) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (*.f64 (pow.f64 (/.f64 1 x) 1/4) -5/64) (sqrt.f64 (/.f64 1 x)))))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4) (*.f64 (pow.f64 (/.f64 1 x) 1/4) 5/16) (sqrt.f64 (/.f64 1 x)))) (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/4) (+.f64 (*.f64 (pow.f64 (/.f64 1 x) 1/4) -5/64) (*.f64 -2 (*.f64 (pow.f64 (/.f64 1 x) 1/4) 15/128))))))
(/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(/.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(/.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(exp.f64 (neg.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 1/2)))
(exp.f64 (*.f64 (log.f64 x) -1/2))
(-.f64 (/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))))
(-.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) (/.f64 1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))))
(-.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (/.f64 (/.f64 1/2 x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))
(+.f64 (exp.f64 (neg.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 1/2))) (/.f64 (/.f64 -1/2 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) x))
(fma.f64 -1/2 (/.f64 (exp.f64 (*.f64 (log.f64 x) -1/2)) x) (exp.f64 (*.f64 (log.f64 x) -1/2)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 3/8 (/.f64 1 (*.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 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))))
(+.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) (-.f64 (/.f64 3/8 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x))) (/.f64 1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)))))
(+.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (-.f64 (/.f64 3/8 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x))) (/.f64 (/.f64 1/2 x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))))
(+.f64 (exp.f64 (neg.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 1/2))) (+.f64 (/.f64 3/8 (*.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (*.f64 x x))) (/.f64 (/.f64 -1/2 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) x)))
(+.f64 (exp.f64 (*.f64 (log.f64 x) -1/2)) (*.f64 (/.f64 (exp.f64 (*.f64 (log.f64 x) -1/2)) x) (-.f64 (/.f64 3/8 x) 1/2)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 3/8 (/.f64 1 (*.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 5/16 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) (/.f64 3/8 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)))) (+.f64 (/.f64 1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))) (/.f64 5/16 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (pow.f64 x 3)))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (/.f64 3/8 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x)))) (+.f64 (/.f64 (/.f64 1/2 x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (/.f64 (/.f64 5/16 (pow.f64 x 3)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))))
(+.f64 (exp.f64 (neg.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 1/2))) (+.f64 (/.f64 3/8 (*.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (*.f64 x x))) (+.f64 (/.f64 (/.f64 -1/2 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) x) (/.f64 -5/16 (*.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (pow.f64 x 3))))))
(+.f64 (*.f64 (/.f64 (exp.f64 (*.f64 (log.f64 x) -1/2)) (*.f64 x x)) (-.f64 3/8 (/.f64 5/16 x))) (fma.f64 -1/2 (/.f64 (exp.f64 (*.f64 (log.f64 x) -1/2)) x) (exp.f64 (*.f64 (log.f64 x) -1/2))))

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (+.f64 1 x) -1/2)
✓0.3b
(pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3)
✓4.2b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
✓12.3b
(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
Compiler

Compiled 50 to 40 computations (20% saved)

series24.0ms (0.2%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
8.0ms
x
@-inf
(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
5.0ms
x
@inf
(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
4.0ms
x
@0
(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
3.0ms
x
@inf
(pow.f64 (+.f64 1 x) -1/2)
1.0ms
x
@-inf
(pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3)

rewrite108.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
553×prod-diff_binary64
467×log-prod_binary64
319×fma-def_binary64
309×pow-prod-down_binary64
296×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01249
127949
2311649
Stop Event
1×node limit
Counts
4 → 280
Calls
Call 1
Inputs
(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
(pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3)
(pow.f64 (+.f64 1 x) -1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/6)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 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simplify119.0ms (1%)

Algorithm
1×egg-herbie
Rules
429×fma-def_binary64
361×cancel-sign-sub-inv_binary64
284×associate-*l/_binary64
229×associate-+r+_binary64
223×+-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03824073
112263621
247553071
Stop Event
1×node limit
Counts
328 → 262
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (+.f64 (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x))) (pow.f64 x -1/2)) 1)
(-.f64 (+.f64 (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x))) (+.f64 (pow.f64 x -1/2) (*.f64 1/3 (/.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (*.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (*.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1)) 1/3) (pow.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 2)))) (pow.f64 x 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))))) 1)
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(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))
(+.f64 (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (*.f64 -35/128 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))) (+.f64 (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
(pow.f64 (-.f64 (pow.f64 x -1/2) 1) 3)
(+.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 3))
(+.f64 (*.f64 (+.f64 (*.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (*.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (*.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (pow.f64 x 2)) (+.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 3)))
(+.f64 (*.f64 (+.f64 (*.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (*.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (*.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (pow.f64 x 2)) (+.f64 (*.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x) (+.f64 (*.f64 (+.f64 (*.f64 5/16 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (+.f64 (*.f64 1/2 (+.f64 1/4 (*.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (+.f64 (*.f64 (-.f64 (pow.f64 x -1/2) 1) (-.f64 (*.f64 5/8 (-.f64 (pow.f64 x -1/2) 1)) 3/8)) (*.f64 -3/8 (-.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 3)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 3))))
(*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9))))
(+.f64 (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9))))))
(+.f64 (*.f64 5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (+.f64 (*.f64 29/128 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (+.f64 (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (*.f64 9/64 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))))))))
(+.f64 (*.f64 -87/512 (sqrt.f64 (/.f64 1 (pow.f64 x 15)))) (+.f64 (*.f64 5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (+.f64 (*.f64 29/128 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (*.f64 -65/256 (sqrt.f64 (/.f64 1 (pow.f64 x 15)))) (+.f64 (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 11)))) (+.f64 (*.f64 9/64 (sqrt.f64 (/.f64 1 (pow.f64 x 13)))) (+.f64 (*.f64 -15/128 (sqrt.f64 (/.f64 1 (pow.f64 x 15)))) (*.f64 -35/512 (sqrt.f64 (/.f64 1 (pow.f64 x 15)))))))))))))
(*.f64 1/8 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 3)))
(+.f64 (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 4))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 3))) (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 4)))))
(+.f64 (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 4))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 5/16 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 9/64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))) (+.f64 (*.f64 -9/64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (*.f64 -5/64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)))) (pow.f64 x 5))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 3))) (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 4))))))
(+.f64 (*.f64 -1/2 (/.f64 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 35/128 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 15/64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (pow.f64 x 6))) (+.f64 (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 4))) (+.f64 (*.f64 -15/128 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 6))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -1/2 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 5/16 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 9/64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))))) (+.f64 (*.f64 -9/64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)) (*.f64 -5/64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3)))) (pow.f64 x 5))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 3))) (+.f64 (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 4))) (+.f64 (*.f64 -3/8 (/.f64 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 5/16 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 9/64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (pow.f64 x 6))) (*.f64 -35/512 (/.f64 (pow.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 3) (pow.f64 x 6))))))))))
1
(+.f64 (*.f64 -1/2 x) 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(+.f64 (*.f64 -1/2 x) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3)))))
(sqrt.f64 (/.f64 1 x))
(+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 -5/16 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
Outputs
(-.f64 (pow.f64 x -1/2) 1)
(+.f64 (pow.f64 x -1/2) -1)
(-.f64 (+.f64 (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x))) (pow.f64 x -1/2)) 1)
(+.f64 (fma.f64 1/3 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2))) (*.f64 x (*.f64 3/2 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2)))) (pow.f64 x -1/2)) -1)
(+.f64 (fma.f64 1/3 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2))) (*.f64 x (*.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2) 3/2))) (pow.f64 x -1/2)) -1)
(+.f64 (pow.f64 x -1/2) (fma.f64 1/3 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2))) (*.f64 x (*.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2) 3/2))) -1))
(-.f64 (+.f64 (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x))) (+.f64 (pow.f64 x -1/2) (*.f64 1/3 (/.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (*.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (*.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1)) 1/3) (pow.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 2)))) (pow.f64 x 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))))) 1)
(+.f64 (+.f64 (fma.f64 1/3 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2))) (*.f64 x (*.f64 3/2 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2)))) (pow.f64 x -1/2)) (/.f64 (*.f64 1/3 (*.f64 (+.f64 (fma.f64 1/2 (+.f64 (pow.f64 x -1/2) -1) (fma.f64 (+.f64 (pow.f64 x -1/2) -1) (+.f64 1/4 (*.f64 (+.f64 (pow.f64 x -1/2) -1) -3/4)) (*.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2) -3/8))) (*.f64 -1/3 (*.f64 (cbrt.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) -1))) (pow.f64 (*.f64 3/2 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2)) 2)))) (*.f64 x x))) (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2))) -1)
(fma.f64 1/3 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2))) (*.f64 x (*.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2) 3/2))) (+.f64 (fma.f64 1/3 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2) -3/8) (*.f64 (+.f64 (pow.f64 x -1/2) -1) (+.f64 1/2 (fma.f64 (+.f64 (pow.f64 x -1/2) -1) -3/4 1/4)))) (*.f64 (*.f64 -1/3 (cbrt.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) -1)))) (pow.f64 (*.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2) 3/2) 2))) (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2)) (*.f64 x x)) (pow.f64 x -1/2)) -1))
(+.f64 (fma.f64 1/3 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2))) (*.f64 x (*.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2) 3/2))) (pow.f64 x -1/2)) (fma.f64 1/3 (*.f64 (/.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 x -1/2) 1/4) -1/4) (*.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2) -9/8)) (fma.f64 (+.f64 (pow.f64 x -1/2) -1) 1/2 (*.f64 (*.f64 9/4 (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 4)) (*.f64 (cbrt.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) -1))) -1/3)))) (pow.f64 (+.f64 (pow.f64 x -1/2) -1) 2)) (*.f64 x x)) -1))
(-.f64 (+.f64 (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) x))) (+.f64 (*.f64 1/3 (/.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/2 (+.f64 1/4 (*.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (+.f64 (*.f64 5/16 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (+.f64 (*.f64 -3/8 (-.f64 (pow.f64 x -1/2) 1)) (*.f64 (-.f64 (pow.f64 x -1/2) 1) (-.f64 (*.f64 5/8 (-.f64 (pow.f64 x -1/2) 1)) 3/8))))) (+.f64 (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 5)) 1/3) (*.f64 (-.f64 (+.f64 (*.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (*.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (*.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1)) 1/3) (pow.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 2)))) (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))))) (+.f64 (*.f64 1/27 (/.f64 (pow.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 3) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 5)) 1/3) (*.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (-.f64 (+.f64 (*.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (*.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (*.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1)) 1/3) (pow.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 2)))))))))) (pow.f64 x 3)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))) (+.f64 (pow.f64 x -1/2) (*.f64 1/3 (/.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/2 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 (-.f64 (pow.f64 x -1/2) 1) (+.f64 1/4 (*.f64 -3/4 (-.f64 (pow.f64 x -1/2) 1)))) (*.f64 -3/8 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))) (*.f64 1/3 (*.f64 (pow.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1)) 1/3) (pow.f64 (+.f64 (*.f64 1/2 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 2)))) (pow.f64 x 2)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))))) 1)
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(+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 -5/16 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(+.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (fma.f64 -5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))))
(+.f64 (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (/.f64 -5/16 (/.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))) (fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (*.f64 x x)) (+.f64 3/8 (/.f64 -5/16 x))) (fma.f64 -1/2 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))))

eval1.2s (9.9%)

Compiler

Compiled 35521 to 28715 computations (19.2% saved)

prune655.0ms (5.5%)

Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New1222171239
Fresh23528
Picked101
Done415
Total1250231273
Error
0.1b
Counts
1273 → 23
Alt Table
Click to see full alt table
StatusErrorProgram
3.7b
(/.f64 (*.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (+.f64 1 (-.f64 x x))) (fma.f64 x x x))
▶62.7b
(neg.f64 (sqrt.f64 (/.f64 1 x)))
▶20.2b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓31.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
▶0.5b
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
3.7b
(/.f64 (+.f64 1 (-.f64 x x)) (*.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 x x x)))
20.2b
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
30.3b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
19.9b
(*.f64 (neg.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))
22.4b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
35.3b
(*.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
19.9b
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
62.8b
-1
31.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
30.6b
(/.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
▶46.3b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
29.9b
(/.f64 1 (+.f64 x (sqrt.f64 x)))
3.6b
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
▶22.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
31.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
40.6b
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
19.7b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
31.4b
(-.f64 (pow.f64 x -1/2) 1)
Compiler

Compiled 629 to 490 computations (22.1% saved)

localize87.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓0.1b
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
✓0.2b
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓0.3b
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x))
Compiler

Compiled 77 to 42 computations (45.5% saved)

series45.0ms (0.4%)

Counts
4 → 3
Calls

12 calls:

TimeVariablePointExpression
10.0ms
x
@-inf
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x))
7.0ms
x
@inf
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x))
6.0ms
x
@-inf
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
5.0ms
x
@-inf
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
4.0ms
x
@0
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x))

rewrite186.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
917×prod-diff_binary64
588×log-prod_binary64
470×fma-def_binary64
230×log-div_binary64
220×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01271
130058
2378258
Stop Event
1×node limit
Counts
4 → 229
Calls
Call 1
Inputs
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 (sqrt.f64 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 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (fma.f64 -1 (sqrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) 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(sqrt.f64 x)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 x)))) (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 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 (hypot.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 x)) (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (sqrt.f64 x)) 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) 1 (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (cbrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (hypot.f64 1 (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 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (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)) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 x) (hypot.f64 1 (sqrt.f64 x)))))) (#(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) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 1/2) (sqrt.f64 x))))))

simplify14.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
056
176
Stop Event
1×saturated
Counts
232 → 231
Calls
Call 1
Inputs
(/.f64 1/2 x)
1
1
Outputs
(/.f64 1/2 x)
1
1

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.4b
(sqrt.f64 (/.f64 1 x))
Compiler

Compiled 15 to 11 computations (26.7% saved)

series1.0ms (0%)

Counts
1 → 0
Calls

3 calls:

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

rewrite43.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
399×pow1_binary64
386×add-sqr-sqrt_binary64
376×*-un-lft-identity_binary64
371×add-log-exp_binary64
371×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
056
1994
211014
Stop Event
1×node limit
Counts
1 → 46
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (pow.f64 1 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x -1/2)) (sqrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x -2))) (pow.f64 (*.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 -1) (pow.f64 (/.f64 1 (neg.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -1/2)) (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -1/2)) (pow.f64 (*.f64 (cbrt.f64 (pow.f64 x -1/2)) (pow.f64 x -1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (pow.f64 x -1/2))) (pow.f64 (*.f64 (sqrt.f64 (pow.f64 x -1/2)) (pow.f64 x -1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -1/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1/2) (pow.f64 (cbrt.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (sqrt.f64 (pow.f64 x -1/2)) 3) 1/2) (sqrt.f64 (sqrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1 (cbrt.f64 x))) 1/2) (sqrt.f64 (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (/.f64 1 x) 3/2)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (/.f64 1 x) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 x) (/.f64 1 (cbrt.f64 x))) 1/3) (cbrt.f64 (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (pow.f64 x -1/2))) 1/3) (sqrt.f64 (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x -1/2))) 2) 3) (cbrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) -1) (pow.f64 (sqrt.f64 (cbrt.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 1)))) (#(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 (sqrt.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 x -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -1/2)))))) (#(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 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/2)))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
46 → 46
Calls
Call 1
Inputs
Outputs

localize21.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (+.f64 1 x))
✓0.5b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
4.2b
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
Compiler

Compiled 44 to 31 computations (29.5% saved)

series3.0ms (0%)

Counts
1 → 0
Calls

3 calls:

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

rewrite71.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
907×prod-diff_binary64
575×log-prod_binary64
387×fma-def_binary64
211×expm1-udef_binary64
211×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01121
124921
2350021
Stop Event
1×node limit
Counts
1 → 28
Calls
Call 1
Inputs
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (*.f64 x 1/4))) (*.f64 (/.f64 -1 (+.f64 1 x)) (sqrt.f64 (*.f64 x 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 x 1/4)) (/.f64 1 x)) (*.f64 (sqrt.f64 (*.f64 x 1/4)) (/.f64 -1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 x 1/4))) (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))))) (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 x 1/4))) (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 x 1/4))) (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 x 1/4))) (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 x 1/4))) (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (*.f64 x 1/4))) (fma.f64 x x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 x -3) (pow.f64 (+.f64 1 x) -3)) (sqrt.f64 (*.f64 x 1/4))) (+.f64 (pow.f64 x -2) (+.f64 (pow.f64 (+.f64 1 x) -2) (/.f64 1 (fma.f64 x x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 x -2) (pow.f64 (+.f64 1 x) -2)) (sqrt.f64 (*.f64 x 1/4))) (+.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x 1/4)) (+.f64 1 (-.f64 x x))) (fma.f64 x x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x 1/4)) (-.f64 (pow.f64 x -3) (pow.f64 (+.f64 1 x) -3))) (+.f64 (pow.f64 x -2) (+.f64 (pow.f64 (+.f64 1 x) -2) (/.f64 1 (fma.f64 x x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 x 1/4)) (-.f64 (pow.f64 x -2) (pow.f64 (+.f64 1 x) -2))) (+.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x 1/4) (pow.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 x 1/4))) (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) 3) (pow.f64 (sqrt.f64 (*.f64 x 1/4)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 x 1/4)) 3) (pow.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 (/.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))) (sqrt.f64 (*.f64 x 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (sqrt.f64 (*.f64 x 1/4)) (*.f64 (/.f64 -1 (+.f64 1 x)) (sqrt.f64 (*.f64 x 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/4)) (/.f64 1 x) (*.f64 (sqrt.f64 (*.f64 x 1/4)) (/.f64 -1 (+.f64 1 x))))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
28 → 28
Calls
Call 1
Inputs
Outputs

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (+.f64 1 x) -1/2)
0.3b
(/.f64 1 (sqrt.f64 x))
✓12.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
Compiler

Compiled 28 to 19 computations (32.1% saved)

series7.0ms (0.1%)

Counts
1 → 2
Calls

3 calls:

TimeVariablePointExpression
6.0ms
x
@inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
1.0ms
x
@-inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
0.0ms
x
@0
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))

rewrite69.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
595×prod-diff_binary64
409×log-prod_binary64
301×fma-def_binary64
266×pow-prod-down_binary64
250×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0915
120613
2270913
Stop Event
1×node limit
Counts
1 → 107
Calls
Call 1
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 1 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (cbrt.f64 (pow.f64 (+.f64 1 x) -1)) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (+.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)) (-.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)) (+.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1))) (pow.f64 (+.f64 1 x) -1/6) (pow.f64 x -1/2))))))

simplify56.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
379×times-frac_binary64
282×unswap-sqr_binary64
257×fma-def_binary64
147×div-sub_binary64
133×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01616
13716
27316
317416
448716
5144816
6652216
Stop Event
1×unsound
Counts
109 → 110
Calls
Call 1
Inputs
(*.f64 -1 (sqrt.f64 (/.f64 1 x)))
(*.f64 -1 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
Outputs
(*.f64 -1 (sqrt.f64 (/.f64 1 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(*.f64 -1 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(neg.f64 (sqrt.f64 (/.f64 1 x)))

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
0.0b
(/.f64 1 (+.f64 1 x))
✓0.6b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
4.2b
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
Compiler

Compiled 60 to 46 computations (23.3% saved)

series3.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite141.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
678×log-prod_binary64
654×fma-def_binary64
347×fma-neg_binary64
268×log-div_binary64
243×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01241
129626
2466326
Stop Event
1×node limit
Counts
2 → 216
Calls
Call 1
Inputs
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
Outputs
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2)) (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)) (hypot.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (/.f64 1 (+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (fma.f64 x x x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (fma.f64 x x x) -1/2))) (+.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (+.f64 (/.f64 1 x) (/.f64 -1 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 1 x) (/.f64 -1 (+.f64 1 x))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (/.f64 1 x) (/.f64 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(pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2))) (exp.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)) (+.f64 1 (expm1.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2))) (+.f64 1 (expm1.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) 1 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) -1/2) 1 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (/.f64 1 (cbrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)) (/.f64 1 (cbrt.f64 (+.f64 1 x))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -1/2)) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x -2))) (sqrt.f64 (/.f64 1 (cbrt.f64 x))) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -2))) (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x)))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 -1/2) (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 -1/2) (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))) (#(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) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) 2)) -1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 x)) -1/2) (pow.f64 (hypot.f64 1 (sqrt.f64 x)) -1/2) (pow.f64 x -1/2))))))

simplify117.0ms (1%)

Algorithm
1×egg-herbie
Rules
597×sub-neg_binary64
545×fma-def_binary64
491×fma-neg_binary64
406×associate-+l+_binary64
284×associate-+r+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01661418
15251344
215731194
361511081
Stop Event
1×node limit
Counts
240 → 262
Calls
Call 1
Inputs
(/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x))
(-.f64 (+.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(-.f64 (+.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(-.f64 (+.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (+.f64 (*.f64 (-.f64 (*.f64 5/16 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))) (+.f64 1 (pow.f64 x -1/2)))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))) (+.f64 (pow.f64 x -1/2) 1))) (+.f64 (*.f64 3/8 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 2)) (+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2)))) (+.f64 (pow.f64 x -1/2) 1))))) x) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) (+.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/4 (/.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))))))
(-.f64 (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))) (+.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 3/16 (/.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 5))) (+.f64 (*.f64 -1/4 (/.f64 (-.f64 (*.f64 1/2 (sqrt.f64 x)) (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/4 (-.f64 (*.f64 -1/2 (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 x)))))) (pow.f64 x 5))) (+.f64 (*.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (+.f64 (*.f64 -1/4 (/.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 x))) (pow.f64 x 4))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))))))
(/.f64 1/2 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))
(-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 5/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 5/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (*.f64 35/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 5))))))
(+.f64 1 (pow.f64 x -1/2))
(+.f64 (*.f64 -1/2 x) (+.f64 (pow.f64 x -1/2) 1))
(+.f64 (*.f64 -1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 3/8 (pow.f64 x 2)))))
(+.f64 (*.f64 -1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3))))))
(*.f64 2 (sqrt.f64 (/.f64 1 x)))
(+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))))
(*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(+.f64 (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 -5/16 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
Outputs
(/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x))
(/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2))))
(/.f64 (/.f64 1 x) (+.f64 1 (pow.f64 x -1/2)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (+.f64 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (/.f64 1 (+.f64 (pow.f64 x -1/2) 1)))
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(+.f64 (/.f64 (/.f64 (/.f64 1/2 (pow.f64 (/.f64 -1 x) 1/2)) (pow.f64 -1 -1/2)) (*.f64 x x)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))))
(fma.f64 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) x) (/.f64 1/2 x) (/.f64 (*.f64 -3/8 (exp.f64 (log.f64 (sqrt.f64 x)))) (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 5/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (-.f64 (/.f64 5/16 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 3/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))))
(+.f64 (/.f64 (/.f64 1/2 (*.f64 x x)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (+.f64 (/.f64 (/.f64 5/16 (pow.f64 x 4)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 (+.f64 (/.f64 (/.f64 (/.f64 1/2 (pow.f64 (/.f64 -1 x) 1/2)) (pow.f64 -1 -1/2)) (*.f64 x x)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))))) (/.f64 5/16 (*.f64 (pow.f64 x 4) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))))
(fma.f64 1/2 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (*.f64 x x)) (fma.f64 5/16 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (pow.f64 x 4)) (/.f64 (*.f64 -3/8 (exp.f64 (log.f64 (sqrt.f64 x)))) (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 5/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))))) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (*.f64 35/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 5))))))
(-.f64 (+.f64 (/.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 5/16 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))) (+.f64 (/.f64 3/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 35/128 (*.f64 (pow.f64 x 5) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))))
(+.f64 (/.f64 (/.f64 1/2 (*.f64 x x)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (-.f64 (+.f64 (/.f64 (/.f64 5/16 (pow.f64 x 4)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))) (/.f64 35/128 (*.f64 (pow.f64 x 5) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 (/.f64 (/.f64 (/.f64 1/2 (pow.f64 (/.f64 -1 x) 1/2)) (pow.f64 -1 -1/2)) (*.f64 x x)) (+.f64 (/.f64 5/16 (*.f64 (pow.f64 x 4) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))) (+.f64 (/.f64 -3/8 (*.f64 (pow.f64 x 3) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))) (/.f64 -35/128 (*.f64 (*.f64 (pow.f64 x 5) (pow.f64 (/.f64 -1 x) 1/2)) (pow.f64 -1 -1/2))))))
(fma.f64 1/2 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (*.f64 x x)) (fma.f64 5/16 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (pow.f64 x 4)) (fma.f64 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (pow.f64 x 3)) -3/8 (*.f64 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (pow.f64 x 5)) -35/128))))
(+.f64 1 (pow.f64 x -1/2))
(+.f64 (*.f64 -1/2 x) (+.f64 (pow.f64 x -1/2) 1))
(fma.f64 -1/2 x (+.f64 1 (pow.f64 x -1/2)))
(+.f64 1 (fma.f64 x -1/2 (pow.f64 x -1/2)))
(+.f64 (*.f64 -1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 3/8 (pow.f64 x 2)))))
(fma.f64 -1/2 x (+.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 3/8 (*.f64 x x)))))
(+.f64 (fma.f64 3/8 (*.f64 x x) 1) (fma.f64 x -1/2 (pow.f64 x -1/2)))
(+.f64 (pow.f64 x -1/2) (fma.f64 x -1/2 (fma.f64 3/8 (*.f64 x x) 1)))
(+.f64 (*.f64 -1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -5/16 (pow.f64 x 3))))))
(fma.f64 -1/2 x (+.f64 (pow.f64 x -1/2) (+.f64 1 (fma.f64 3/8 (*.f64 x x) (*.f64 (pow.f64 x 3) -5/16)))))
(+.f64 (+.f64 1 (fma.f64 x -1/2 (pow.f64 x -1/2))) (fma.f64 3/8 (*.f64 x x) (*.f64 (pow.f64 x 3) -5/16)))
(+.f64 (fma.f64 x (*.f64 x 3/8) (fma.f64 (pow.f64 x 3) -5/16 1)) (fma.f64 x -1/2 (pow.f64 x -1/2)))
(*.f64 2 (sqrt.f64 (/.f64 1 x)))
(*.f64 2 (sqrt.f64 (pow.f64 x -1)))
(+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (pow.f64 x -1))))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (pow.f64 x -1)))))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 2 (sqrt.f64 (pow.f64 x -1)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16))))
(*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(*.f64 2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(*.f64 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(*.f64 2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))
(*.f64 2 (pow.f64 (exp.f64 -1/2) (log.f64 x)))
(+.f64 (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(fma.f64 2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(fma.f64 2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (*.f64 (/.f64 -1/2 x) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))))
(fma.f64 2 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (*.f64 (/.f64 -1/2 x) (pow.f64 (exp.f64 -1/2) (log.f64 x))))
(+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (fma.f64 2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))
(fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(fma.f64 2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (+.f64 -1/2 (/.f64 3/8 x))))
(fma.f64 2 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) x) (+.f64 -1/2 (/.f64 3/8 x))))
(+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 -5/16 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (fma.f64 -5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))))
(fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 -5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(fma.f64 -5/16 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (pow.f64 x 3)) (fma.f64 2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (+.f64 -1/2 (/.f64 3/8 x)))))
(fma.f64 -5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) x) (+.f64 -1/2 (/.f64 3/8 x)))))

eval1.8s (15%)

Compiler

Compiled 28848 to 21592 computations (25.2% saved)

prune391.0ms (3.3%)

Pruning

32 alts after pruning (27 fresh and 5 done)

PrunedKeptTotal
New1109151124
Fresh51217
Picked011
Done145
Total1115321147
Error
0b
Counts
1147 → 32
Alt Table
Click to see full alt table
StatusErrorProgram
56.1b
(*.f64 (/.f64 1 x) (*.f64 1/2 (sqrt.f64 x)))
✓46.3b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
29.9b
(/.f64 1 (+.f64 x (sqrt.f64 x)))
3.6b
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
▶0.3b
(+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)))
4.0b
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (fma.f64 x x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓62.7b
(neg.f64 (sqrt.f64 (/.f64 1 x)))
✓20.2b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
3.6b
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
30.4b
(/.f64 (*.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (*.f64 x 1/4))) (fma.f64 x x x))
▶35.3b
(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
62.7b
(neg.f64 (/.f64 1 (sqrt.f64 x)))
36.0b
(/.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
30.9b
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
▶40.6b
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
31.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
✓31.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
43.9b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (pow.f64 (+.f64 1 x) -1/2))
22.4b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
30.3b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
35.3b
(*.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
▶35.3b
(*.f64 (/.f64 1 (*.f64 x x)) (*.f64 1/2 (sqrt.f64 x)))
19.9b
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
62.8b
-1
19.7b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
30.1b
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 1/2 (sqrt.f64 x)))
▶62.7b
(neg.f64 (pow.f64 x -1/2))
✓22.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
3.7b
(/.f64 (+.f64 1 (-.f64 x x)) (*.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 x x x)))
56.0b
(*.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (*.f64 x x))) (-.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
31.4b
(-.f64 (pow.f64 x -1/2) 1)
31.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
Compiler

Compiled 795 to 602 computations (24.3% saved)

localize43.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (+.f64 1 x) -1/2)
✓0.0b
(hypot.f64 1 (sqrt.f64 x))
✓0.1b
(fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)
✓0.2b
(/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x))
Compiler

Compiled 57 to 34 computations (40.4% saved)

series171.0ms (1.4%)

Counts
3 → 3
Calls

9 calls:

TimeVariablePointExpression
145.0ms
x
@-inf
(hypot.f64 1 (sqrt.f64 x))
8.0ms
x
@-inf
(/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x))
6.0ms
x
@inf
(/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x))
6.0ms
x
@0
(hypot.f64 1 (sqrt.f64 x))
3.0ms
x
@0
(/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x))

rewrite86.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
446×log-prod_binary64
337×exp-prod_binary64
292×pow-prod-down_binary64
290×prod-diff_binary64
258×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01039
121639
2265639
Stop Event
1×node limit
Counts
3 → 130
Calls
Call 1
Inputs
(/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x))
(fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)
(hypot.f64 1 (sqrt.f64 x))
Outputs
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(log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 -1/2 (log1p.f64 x)) (*.f64 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (*.f64 -1/2 (log1p.f64 x)) 1) (*.f64 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))) (pow.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))) 2) (cbrt.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))) (sqrt.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) 3) (pow.f64 x 3)) (+.f64 (*.f64 x (+.f64 1 x)) (-.f64 (*.f64 x x) (*.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x (+.f64 1 x)) (*.f64 x x)) (-.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))) 2)) (cbrt.f64 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))) (sqrt.f64 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (exp.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 1 x)))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 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 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (+.f64 1 x) -1/2))))) (#(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 /.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -1/2) -1)))) (#(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) 3/2) 1/3)))) (#(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 (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 (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) -1/4) -2)))) (#(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 sqrt.f64 (+.f64 1 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 (*.f64 1/2 (log1p.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 exp.f64 (*.f64 (*.f64 3 (*.f64 1/2 (log1p.f64 x))) 1/3))))) (#(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 1/2 (*.f64 1/2 (log1p.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
023
153
Stop Event
1×saturated
Counts
133 → 132
Calls
Call 1
Inputs
x
x
1
Outputs
x
x
1

localize10.0ms (0.1%)

Compiler

Compiled 10 to 7 computations (30% saved)

localize130.0ms (1.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 1 (*.f64 x x))
✓7.0b
(*.f64 (/.f64 1 (*.f64 x x)) (*.f64 1/2 (sqrt.f64 x)))
Compiler

Compiled 28 to 14 computations (50% saved)

series3.0ms (0%)

Counts
2 → 12
Calls

6 calls:

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

rewrite55.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
792×pow1_binary64
736×add-log-exp_binary64
735×log1p-expm1-u_binary64
735×expm1-log1p-u_binary64
718×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0919
118316
2216016
Stop Event
1×node limit
Counts
2 → 48
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (*.f64 x x)) (*.f64 1/2 (sqrt.f64 x)))
(/.f64 1 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x x) (*.f64 1/2 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (*.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 (sqrt.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 x 1/4)) (/.f64 (*.f64 x x) (cbrt.f64 (*.f64 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 1/2 (sqrt.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (*.f64 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 1/2 (sqrt.f64 x))) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 (sqrt.f64 x)) x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 (sqrt.f64 x)) 1) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 (sqrt.f64 x)) (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (*.f64 1/2 (sqrt.f64 x))) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 x) (*.f64 1/2 (sqrt.f64 x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 1/2 (sqrt.f64 x)) -1) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 1/2 (sqrt.f64 x)) (/.f64 1 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 1/2 (sqrt.f64 x))) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 x 1/4) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (sqrt.f64 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 1/2 (sqrt.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -2) 3) (pow.f64 (*.f64 1/2 (sqrt.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 1/2 (sqrt.f64 x)) 3) (pow.f64 (pow.f64 x -2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (/.f64 1 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) (cbrt.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 x 4)) -1) (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 x -2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 x -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 x -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -2)))))))

simplify156.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
1118×associate-/r*_binary64
1082×sqr-pow_binary64
560×fabs-mul_binary64
560×cube-prod_binary64
523×pow-sqr_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
21984
33484
47484
522084
681984
7202884
8219484
9237884
10258684
11288584
12327884
13375984
14432784
15501784
16585684
17625284
18654284
19681684
20689084
21692484
Stop Event
1×node limit
Counts
60 → 50
Calls
Call 1
Inputs
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (pow.f64 x 2))
Outputs
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))

localize43.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
✓0.3b
(/.f64 1 (pow.f64 x 3))
✓16.9b
(sqrt.f64 (/.f64 1 (pow.f64 x 3)))
Compiler

Compiled 27 to 22 computations (18.5% saved)

series4.0ms (0%)

Counts
3 → 0
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 1 (pow.f64 x 3))
1.0ms
x
@-inf
(sqrt.f64 (/.f64 1 (pow.f64 x 3)))
0.0ms
x
@0
(sqrt.f64 (/.f64 1 (pow.f64 x 3)))
0.0ms
x
@inf
(sqrt.f64 (/.f64 1 (pow.f64 x 3)))
0.0ms
x
@-inf
(/.f64 1 (pow.f64 x 3))

rewrite129.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
725×pow1_binary64
682×add-log-exp_binary64
680×log1p-expm1-u_binary64
680×expm1-log1p-u_binary64
665×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0919
119115
2199715
Stop Event
1×node limit
Counts
3 → 67
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 1 (pow.f64 x 3)))
(/.f64 1 (pow.f64 x 3))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x -3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x -3/2)) (sqrt.f64 (pow.f64 x -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x -6))) (sqrt.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 x -6)) 1/2) (pow.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 x 3/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 x -3) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (sqrt.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 x -3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 x -3) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 x -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -3/2)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x -3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -3/2) (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 x -6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (*.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 x -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -6)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x -3/2)) (*.f64 (sqrt.f64 (pow.f64 x -3/2)) (pow.f64 x -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x -3/2) (sqrt.f64 (pow.f64 x -3/2))) (sqrt.f64 (pow.f64 x -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -3) (pow.f64 (cbrt.f64 x) -3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) -3) (pow.f64 (sqrt.f64 x) -3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1) (pow.f64 (*.f64 x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x x) -1) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x -3/2) (/.f64 1 x)) (/.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -6) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 x -3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 x -6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 x -3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 x) -3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -3)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (pow.f64 x -3/2) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -3/2) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x -3/2) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -3/2) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 x -3/2) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x -3) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) (pow.f64 x -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x -3/2) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x -3/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x -3/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x -3/2) 1/2)))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
67 → 67
Calls
Call 1
Inputs
Outputs

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (+.f64 1 x) -1/2)
0.0b
(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
0.4b
(/.f64 1 (*.f64 x x))
✓6.8b
(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
Compiler

Compiled 47 to 31 computations (34% saved)

series3.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite74.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
875×prod-diff_binary64
556×log-prod_binary64
360×fma-def_binary64
209×expm1-udef_binary64
209×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01122
125719
2363119
Stop Event
1×node limit
Counts
1 → 38
Calls
Call 1
Inputs
(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (*.f64 (/.f64 1 x) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))) 2) (cbrt.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 x -2)) 2) (*.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4))) (/.f64 (/.f64 1 x) (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 x -2)) (/.f64 1 (neg.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 x -2)) 2) 1) (/.f64 (cbrt.f64 (pow.f64 x -2)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) 1) (/.f64 (/.f64 1 x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 2)) (/.f64 (pow.f64 x -2) (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 x -2)) 2) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 2)) (cbrt.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 2)) (/.f64 (/.f64 1 x) (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4))) (/.f64 (pow.f64 x -2) (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 x -2)) 2) (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4))) (/.f64 (cbrt.f64 (pow.f64 x -2)) (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))) (-.f64 (+.f64 (/.f64 1 x) (pow.f64 (+.f64 1 x) -1)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -2) (-.f64 (/.f64 1 x) (pow.f64 (+.f64 1 x) -1))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 1 x) (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 x -2) (neg.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 x -2) 3) (pow.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 x -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))))))

simplify81.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
548×associate-/l*_binary64
414×associate-/l/_binary64
387×distribute-rgt-in_binary64
359×distribute-lft-in_binary64
354×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0109700
1340649
2970592
33291458
Stop Event
1×node limit
Counts
50 → 61
Calls
Call 1
Inputs
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 x 2)))
(+.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 x 2))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 x 2))))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)))) (+.f64 (*.f64 (-.f64 (*.f64 5/16 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/4 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 (+.f64 (pow.f64 x -1/2) 1) 2)))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (+.f64 1 (pow.f64 x -1/2)))) (*.f64 3/16 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2) (+.f64 (pow.f64 x -1/2) 1)))))) x) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 x 2)))))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/32 (sqrt.f64 x))) (pow.f64 x 4))) (+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/32 (sqrt.f64 x))) (pow.f64 x 4))) (+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -1 (/.f64 (+.f64 (*.f64 -5/64 (sqrt.f64 x)) (+.f64 (*.f64 1/4 (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/32 (sqrt.f64 x)))) (*.f64 3/128 (sqrt.f64 x)))) (pow.f64 x 5))))))
(/.f64 1/2 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))
(+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))) (*.f64 1/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4)))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 5/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 5)))))) (*.f64 1/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4)))))
Outputs
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 x 2)))
(/.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (*.f64 x x))
(/.f64 1 (*.f64 x (*.f64 x (+.f64 1 (pow.f64 x -1/2)))))
(/.f64 (/.f64 1 x) (+.f64 x (sqrt.f64 x)))
(/.f64 1 (*.f64 x (+.f64 x (sqrt.f64 x))))
(+.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 x 2))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)))))
(+.f64 (/.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (*.f64 x x)) (/.f64 1/2 (*.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2) x)))
(+.f64 (/.f64 1 (*.f64 x (*.f64 x (+.f64 1 (pow.f64 x -1/2))))) (/.f64 1/2 (*.f64 x (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))))
(+.f64 (/.f64 (/.f64 1 x) (+.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1/2 x) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))
(+.f64 (/.f64 1 (*.f64 x (+.f64 x (sqrt.f64 x)))) (/.f64 (/.f64 1/2 x) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 x 2))))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2) x)) (-.f64 (+.f64 (/.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (*.f64 x x)) (/.f64 1/4 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))))
(+.f64 (/.f64 1/2 (*.f64 x (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (+.f64 (/.f64 1 (*.f64 x (*.f64 x (+.f64 1 (pow.f64 x -1/2))))) (+.f64 (/.f64 1/4 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))))
(+.f64 (/.f64 1/4 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (-.f64 (+.f64 (/.f64 (/.f64 1 x) (+.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1/2 x) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))))
(+.f64 (+.f64 (/.f64 1 (*.f64 x (+.f64 x (sqrt.f64 x)))) (/.f64 1/4 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) 6))) (*.f64 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (-.f64 (/.f64 1/2 x) 3/8)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (*.f64 (+.f64 (pow.f64 x -1/2) 1) x)))) (+.f64 (*.f64 (-.f64 (*.f64 5/16 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/4 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 (+.f64 (pow.f64 x -1/2) 1) 2)))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1))))) (+.f64 1 (pow.f64 x -1/2)))) (*.f64 3/16 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2) (+.f64 (pow.f64 x -1/2) 1)))))) x) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2) (+.f64 (pow.f64 x -1/2) 1)))) (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 x 2)))))) (*.f64 3/8 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (+.f64 (pow.f64 x -1/2) 1)))))
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2) x)) (-.f64 (fma.f64 (-.f64 (/.f64 5/16 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 1/4 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (+.f64 1 (pow.f64 x -1/2))) (/.f64 3/16 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))))) x (+.f64 (/.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (*.f64 x x)) (/.f64 1/4 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))))
(+.f64 (+.f64 (/.f64 1 (*.f64 x (*.f64 x (+.f64 1 (pow.f64 x -1/2))))) (fma.f64 x (-.f64 (/.f64 5/16 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (fma.f64 -1/2 (-.f64 (/.f64 1/4 (*.f64 (+.f64 1 (pow.f64 x -1/2)) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3))) (/.f64 3/16 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)))) (/.f64 1/4 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)))) (-.f64 (/.f64 1/2 (*.f64 x (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))))
(+.f64 (/.f64 (/.f64 1/2 x) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (fma.f64 x (+.f64 (/.f64 5/16 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (-.f64 (/.f64 -3/16 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 (+.f64 (/.f64 -1/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 3/16 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))) (+.f64 1 (pow.f64 x -1/2))))) (+.f64 (/.f64 (/.f64 1 x) (+.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1/4 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2))))))
(+.f64 (fma.f64 x (+.f64 (/.f64 5/16 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (fma.f64 -1/2 (+.f64 (/.f64 3/8 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) 6)) (/.f64 -1/4 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 4))) (/.f64 -3/16 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) 6)))) (/.f64 1 (*.f64 x (+.f64 x (sqrt.f64 x))))) (+.f64 (/.f64 1/4 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) 6)) (*.f64 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)) (-.f64 (/.f64 1/2 x) 3/8))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/32 (sqrt.f64 x))) (pow.f64 x 4))) (+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 -1 (/.f64 (*.f64 (sqrt.f64 x) 1/16) (pow.f64 x 4)) (fma.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (/.f64 (sqrt.f64 x) (/.f64 (pow.f64 x 4) 1/16)))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (/.f64 (*.f64 (sqrt.f64 x) -1/16) (pow.f64 x 4))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 (/.f64 (sqrt.f64 x) (pow.f64 x 4)) -1/16)))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/32 (sqrt.f64 x))) (pow.f64 x 4))) (+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -1 (/.f64 (+.f64 (*.f64 -5/64 (sqrt.f64 x)) (+.f64 (*.f64 1/4 (+.f64 (*.f64 3/32 (sqrt.f64 x)) (*.f64 -1/32 (sqrt.f64 x)))) (*.f64 3/128 (sqrt.f64 x)))) (pow.f64 x 5))))))
(fma.f64 -1 (/.f64 (*.f64 (sqrt.f64 x) 1/16) (pow.f64 x 4)) (fma.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (neg.f64 (/.f64 (fma.f64 -5/64 (sqrt.f64 x) (fma.f64 1/4 (*.f64 (sqrt.f64 x) 1/16) (*.f64 (sqrt.f64 x) 3/128))) (pow.f64 x 5))))))
(-.f64 (-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (/.f64 (fma.f64 (sqrt.f64 x) -5/64 (fma.f64 (sqrt.f64 x) 3/128 (*.f64 (sqrt.f64 x) 1/64))) (pow.f64 x 5))) (/.f64 (sqrt.f64 x) (/.f64 (pow.f64 x 4) 1/16)))
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (/.f64 (*.f64 (sqrt.f64 x) -1/16) (pow.f64 x 4)))) (/.f64 (fma.f64 (sqrt.f64 x) -5/64 (*.f64 (sqrt.f64 x) 5/128)) (pow.f64 x 5)))
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 (/.f64 (sqrt.f64 x) (pow.f64 x 4)) -1/16))) (/.f64 (*.f64 (sqrt.f64 x) -5/128) (pow.f64 x 5)))
(/.f64 1/2 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))
(/.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(/.f64 (/.f64 1/2 (*.f64 x x)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(/.f64 (/.f64 (/.f64 1/2 (pow.f64 (/.f64 -1 x) 1/2)) (pow.f64 -1 -1/2)) (*.f64 x x))
(*.f64 (/.f64 1/2 (*.f64 x x)) (exp.f64 (log.f64 (sqrt.f64 x))))
(+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (/.f64 1/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(+.f64 (/.f64 (/.f64 1/8 (pow.f64 x 3)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (/.f64 (/.f64 1/2 (*.f64 x x)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(+.f64 (/.f64 1/8 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (*.f64 (pow.f64 -1 -1/2) (pow.f64 x 3)))) (/.f64 (/.f64 (/.f64 1/2 (pow.f64 (/.f64 -1 x) 1/2)) (pow.f64 -1 -1/2)) (*.f64 x x)))
(*.f64 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (*.f64 x x)) (+.f64 (/.f64 1/8 x) 1/2))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))) (*.f64 1/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4)))))
(+.f64 (/.f64 1/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (-.f64 (/.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 1/16 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))))
(+.f64 (/.f64 (/.f64 1/8 (pow.f64 x 3)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (-.f64 (/.f64 (/.f64 1/2 (*.f64 x x)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (/.f64 (/.f64 1/16 (pow.f64 x 4)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(+.f64 (/.f64 1/8 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (*.f64 (pow.f64 -1 -1/2) (pow.f64 x 3)))) (+.f64 (/.f64 (/.f64 (/.f64 1/2 (pow.f64 (/.f64 -1 x) 1/2)) (pow.f64 -1 -1/2)) (*.f64 x x)) (/.f64 -1/16 (*.f64 (pow.f64 x 4) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))))))
(fma.f64 1/2 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (*.f64 x x)) (*.f64 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (pow.f64 x 3)) (-.f64 1/8 (/.f64 1/16 x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 5/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 5)))))) (*.f64 1/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4)))))
(+.f64 (/.f64 1/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (-.f64 (+.f64 (/.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 5/128 (*.f64 (pow.f64 x 5) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))) (/.f64 1/16 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))))
(+.f64 (/.f64 (/.f64 1/8 (pow.f64 x 3)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (+.f64 (/.f64 5/128 (*.f64 (pow.f64 x 5) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (-.f64 (/.f64 (/.f64 1/2 (*.f64 x x)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (/.f64 (/.f64 1/16 (pow.f64 x 4)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 (/.f64 1/8 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (*.f64 (pow.f64 -1 -1/2) (pow.f64 x 3)))) (+.f64 (/.f64 5/128 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (*.f64 (pow.f64 -1 -1/2) (pow.f64 x 5)))) (+.f64 (/.f64 (/.f64 (/.f64 1/2 (pow.f64 (/.f64 -1 x) 1/2)) (pow.f64 -1 -1/2)) (*.f64 x x)) (/.f64 -1/16 (*.f64 (pow.f64 x 4) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))))))
(fma.f64 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (pow.f64 x 4)) -1/16 (fma.f64 5/128 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (pow.f64 x 5)) (*.f64 (/.f64 (exp.f64 (log.f64 (sqrt.f64 x))) (*.f64 x x)) (+.f64 (/.f64 1/8 x) 1/2))))

eval555.0ms (4.6%)

Compiler

Compiled 9898 to 7434 computations (24.9% saved)

prune180.0ms (1.5%)

Pruning

26 alts after pruning (22 fresh and 4 done)

PrunedKeptTotal
New4846490
Fresh61622
Picked101
Done549
Total49626522
Error
0b
Counts
522 → 26
Alt Table
Click to see full alt table
StatusErrorProgram
56.1b
(*.f64 (/.f64 1 x) (*.f64 1/2 (sqrt.f64 x)))
✓46.3b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
35.3b
(/.f64 (*.f64 1/2 (sqrt.f64 x)) (*.f64 x x))
3.6b
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
30.4b
(/.f64 (*.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (*.f64 x 1/4))) (fma.f64 x x x))
31.7b
(*.f64 1/2 (pow.f64 x -3/2))
3.5b
(+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) x)))
✓22.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
✓31.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
43.9b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (pow.f64 (+.f64 1 x) -1/2))
22.4b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
51.1b
(-.f64 (+.f64 1 (*.f64 (pow.f64 x -3/2) 1/2)) 1)
30.3b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
19.9b
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
62.8b
-1
19.7b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
30.1b
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 1/2 (sqrt.f64 x)))
3.6b
(+.f64 0 (pow.f64 (*.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))) (sqrt.f64 (+.f64 1 x))) -1))
31.4b
(-.f64 (pow.f64 x -1/2) 1)
✓62.7b
(neg.f64 (pow.f64 x -1/2))
4.0b
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (fma.f64 x x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
30.9b
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
31.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
31.9b
(/.f64 1/2 (pow.f64 x 3/2))
56.0b
(*.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (*.f64 x x))) (-.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
31.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
Compiler

Compiled 319 to 246 computations (22.9% saved)

regimes392.0ms (3.3%)

Counts
72 → 1
Calls
Call 1
Inputs
-1
(neg.f64 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -3/2))
(/.f64 1/2 (pow.f64 x 3/2))
(neg.f64 (/.f64 1 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (*.f64 1/2 (sqrt.f64 x)) (*.f64 x x))
(*.f64 (/.f64 1 x) (*.f64 1/2 (sqrt.f64 x)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (+.f64 1 (*.f64 (pow.f64 x -3/2) 1/2)) 1)
(*.f64 (/.f64 1 (*.f64 x x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (*.f64 x x))) (-.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(/.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
(/.f64 (*.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (*.f64 x 1/4))) (fma.f64 x x x))
(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) x)))
(*.f64 (neg.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))
(*.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) 1/4) 2)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(+.f64 0 (pow.f64 (*.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))) (sqrt.f64 (+.f64 1 x))) -1))
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (fma.f64 x x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (+.f64 1 (-.f64 x x)) (*.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 x x x)))
(/.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (*.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (+.f64 1 (-.f64 x x))) (fma.f64 x x x))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(/.f64 (-.f64 (/.f64 1 x) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2)) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
(+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)))
(fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) 2) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1/2))
(/.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 3)) (+.f64 (/.f64 1 x) (-.f64 (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2) (*.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))))
(+.f64 (fma.f64 (pow.f64 x -1/2) 1 (neg.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x)))))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (/.f64 1 (cbrt.f64 (+.f64 1 x))) (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x))))))
(+.f64 (fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (neg.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x)))))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (/.f64 1 (cbrt.f64 (+.f64 1 x))) (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x))))))
Outputs
(+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)))
Calls

3 calls:

84.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
79.0ms
x
23.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.3b1x
0.3b1(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.3b1(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 1070 to 792 computations (26% saved)

regimes262.0ms (2.2%)

Counts
67 → 1
Calls
Call 1
Inputs
-1
(neg.f64 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -3/2))
(/.f64 1/2 (pow.f64 x 3/2))
(neg.f64 (/.f64 1 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (*.f64 1/2 (sqrt.f64 x)) (*.f64 x x))
(*.f64 (/.f64 1 x) (*.f64 1/2 (sqrt.f64 x)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (+.f64 1 (*.f64 (pow.f64 x -3/2) 1/2)) 1)
(*.f64 (/.f64 1 (*.f64 x x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (*.f64 x x))) (-.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(/.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
(/.f64 (*.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (*.f64 x 1/4))) (fma.f64 x x x))
(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) x)))
(*.f64 (neg.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))
(*.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) 1/4) 2)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(+.f64 0 (pow.f64 (*.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))) (sqrt.f64 (+.f64 1 x))) -1))
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (fma.f64 x x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (+.f64 1 (-.f64 x x)) (*.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 x x x)))
(/.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (*.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (+.f64 1 (-.f64 x x))) (fma.f64 x x x))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(/.f64 (-.f64 (/.f64 1 x) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2)) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
Outputs
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
Calls

3 calls:

56.0ms
x
20.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
16.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.5b1x
0.5b1(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.5b1(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 907 to 659 computations (27.3% saved)

regimes448.0ms (3.7%)

Counts
65 → 2
Calls
Call 1
Inputs
-1
(neg.f64 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -3/2))
(/.f64 1/2 (pow.f64 x 3/2))
(neg.f64 (/.f64 1 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (*.f64 1/2 (sqrt.f64 x)) (*.f64 x x))
(*.f64 (/.f64 1 x) (*.f64 1/2 (sqrt.f64 x)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (+.f64 1 (*.f64 (pow.f64 x -3/2) 1/2)) 1)
(*.f64 (/.f64 1 (*.f64 x x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (*.f64 x x))) (-.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(/.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
(/.f64 (*.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (*.f64 x 1/4))) (fma.f64 x x x))
(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) x)))
(*.f64 (neg.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))
(*.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) 1/4) 2)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(+.f64 0 (pow.f64 (*.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x)))) (sqrt.f64 (+.f64 1 x))) -1))
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (fma.f64 x x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (+.f64 1 (-.f64 x x)) (*.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 x x x)))
(/.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (*.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (+.f64 1 (-.f64 x x))) (fma.f64 x x x))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
Outputs
(*.f64 1/2 (pow.f64 x -3/2))
(+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) x)))
Calls

3 calls:

254.0ms
x
29.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
23.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.2b2x
0.2b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 863 to 628 computations (27.2% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0
1.0058516248644817e-21
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes130.0ms (1.1%)

Counts
34 → 2
Calls
Call 1
Inputs
-1
(neg.f64 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -3/2))
(/.f64 1/2 (pow.f64 x 3/2))
(neg.f64 (/.f64 1 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (*.f64 1/2 (sqrt.f64 x)) (*.f64 x x))
(*.f64 (/.f64 1 x) (*.f64 1/2 (sqrt.f64 x)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (+.f64 1 (*.f64 (pow.f64 x -3/2) 1/2)) 1)
(*.f64 (/.f64 1 (*.f64 x x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (*.f64 x x))) (-.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(/.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
(/.f64 (*.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (*.f64 x 1/4))) (fma.f64 x x x))
(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
Outputs
(*.f64 1/2 (pow.f64 x -3/2))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
Calls

3 calls:

72.0ms
x
25.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
20.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.4b2x
0.4b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.4b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 353 to 252 computations (28.6% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
5.3245338097352574e-17
1.0206701412870944e-10
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes76.0ms (0.6%)

Counts
24 → 2
Calls
Call 1
Inputs
-1
(neg.f64 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -3/2))
(/.f64 1/2 (pow.f64 x 3/2))
(neg.f64 (/.f64 1 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (*.f64 1/2 (sqrt.f64 x)) (*.f64 x x))
(*.f64 (/.f64 1 x) (*.f64 1/2 (sqrt.f64 x)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (+.f64 1 (*.f64 (pow.f64 x -3/2) 1/2)) 1)
(*.f64 (/.f64 1 (*.f64 x x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 1 (-.f64 1 (*.f64 x x))) (-.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(/.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
Outputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 1/2 (pow.f64 x -3/2))
Calls

1 calls:

61.0ms
x
Results
ErrorSegmentsBranch
1.2b2x
Compiler

Compiled 213 to 150 computations (29.6% saved)

bsearch160.0ms (1.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
159.0ms
0.30714854063448394
1.4386861012604875
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes26.0ms (0.2%)

Counts
19 → 2
Calls
Call 1
Inputs
-1
(neg.f64 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -3/2))
(/.f64 1/2 (pow.f64 x 3/2))
(neg.f64 (/.f64 1 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (*.f64 1/2 (sqrt.f64 x)) (*.f64 x x))
(*.f64 (/.f64 1 x) (*.f64 1/2 (sqrt.f64 x)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (+.f64 1 (*.f64 (pow.f64 x -3/2) 1/2)) 1)
(*.f64 (/.f64 1 (*.f64 x x)) (*.f64 1/2 (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 1/2 (sqrt.f64 x)))
(*.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x)) (*.f64 1/2 (sqrt.f64 x)))
Outputs
(-.f64 (pow.f64 x -1/2) 1)
(*.f64 1/2 (pow.f64 x -3/2))
Calls

1 calls:

21.0ms
x
Results
ErrorSegmentsBranch
1.3b2x
Compiler

Compiled 150 to 104 computations (30.7% saved)

bsearch79.0ms (0.7%)

Algorithm
1×binary-search
Steps
TimeLeftRight
79.0ms
0.30714854063448394
1.4386861012604875
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes7.0ms (0.1%)

Counts
6 → 1
Calls
Call 1
Inputs
-1
(neg.f64 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -3/2))
(/.f64 1/2 (pow.f64 x 3/2))
(neg.f64 (/.f64 1 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 (/.f64 1 x)))
Outputs
(*.f64 1/2 (pow.f64 x -3/2))
Calls

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
31.7b1x
Compiler

Compiled 28 to 22 computations (21.4% saved)

regimes4.0ms (0%)

Accuracy

Total -0.2b remaining (-0.3%)

Threshold costs -0.2b (-0.3%)

Counts
2 → 1
Calls
Call 1
Inputs
-1
(neg.f64 (pow.f64 x -1/2))
Outputs
(neg.f64 (pow.f64 x -1/2))
Calls

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
62.7b1x
Compiler

Compiled 8 to 6 computations (25% saved)

simplify22.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
058220
188220
2107220
3124220
4136220
5147220
6157220
7169220
8172220
9173220
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 0) (*.f64 1/2 (pow.f64 x -3/2)) (+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) x))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 2028240960365167/20282409603651670423947251286016) (*.f64 1/2 (pow.f64 x -3/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
(if (<=.f64 x 2766548106297707/9007199254740992) (-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8)))))) (*.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 2766548106297707/9007199254740992) (-.f64 (pow.f64 x -1/2) 1) (*.f64 1/2 (pow.f64 x -3/2)))
(*.f64 1/2 (pow.f64 x -3/2))
(neg.f64 (pow.f64 x -1/2))
-1
Outputs
(+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)))
(/.f64 (pow.f64 (+.f64 1 x) -1/2) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 0) (*.f64 1/2 (pow.f64 x -3/2)) (+.f64 0 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 (sqrt.f64 (*.f64 x (+.f64 1 x))) x))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 0) (*.f64 1/2 (pow.f64 x -3/2)) (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))
(if (<=.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) 0) (*.f64 1/2 (pow.f64 x -3/2)) (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 1 x))))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 2028240960365167/20282409603651670423947251286016) (*.f64 1/2 (pow.f64 x -3/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 2028240960365167/20282409603651670423947251286016) (*.f64 1/2 (pow.f64 x -3/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) 2028240960365167/20282409603651670423947251286016) (*.f64 1/2 (pow.f64 x -3/2)) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 x 2766548106297707/9007199254740992) (-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8)))))) (*.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 2766548106297707/9007199254740992) (-.f64 (pow.f64 x -1/2) 1) (*.f64 1/2 (pow.f64 x -3/2)))
(if (<=.f64 x 2766548106297707/9007199254740992) (+.f64 (pow.f64 x -1/2) -1) (*.f64 1/2 (pow.f64 x -3/2)))
(*.f64 1/2 (pow.f64 x -3/2))
(neg.f64 (pow.f64 x -1/2))
-1
Compiler

Compiled 156 to 121 computations (22.4% saved)

soundness0.0ms (0%)

end242.0ms (2%)

Compiler

Compiled 148 to 109 computations (26.4% saved)

Profiling

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