Details

Time bar (total: 10.3s)

analyze1.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%0%50%2
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.7s (16.8%)

Results
798.0ms2287×body1024valid
649.0ms4922×body256valid
239.0ms1047×body512valid

preprocess23.0ms (0.2%)

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)

simplify13.0ms (0.1%)

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)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
23.1b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶23.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 12 to 10 computations (16.7% saved)

localize50.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.2b
(/.f64 1 (sqrt.f64 x))
✓3.7b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 33 to 23 computations (30.3% saved)

series9.0ms (0.1%)

Counts
4 → 8
Calls

12 calls:

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

rewrite99.0ms (1%)

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 log1p.f64 (expm1.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 +.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 log1p.f64 (expm1.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))))))

simplify163.0ms (1.6%)

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)

eval136.0ms (1.3%)

Compiler

Compiled 4484 to 3575 computations (20.3% saved)

prune133.0ms (1.3%)

Pruning

40 alts after pruning (39 fresh and 1 done)

PrunedKeptTotal
New20339242
Fresh000
Picked011
Done000
Total20340243
Error
22.4b
Counts
243 → 40
Alt Table
Click to see full alt table
StatusErrorProgram
28.3b
(/.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)))))
32.8b
(*.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 (*.f64 x (+.f64 1 x)) -1/2)))))
29.3b
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
41.8b
(fma.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 (*.f64 x (+.f64 1 x)) -1/2)))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
33.1b
(/.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)))))))
31.7b
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
44.4b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
31.9b
(fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x)))) (pow.f64 (+.f64 1 x) -1/6) (pow.f64 x -1/2))
33.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
25.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
33.0b
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
25.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
25.1b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
32.8b
(/.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 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
32.1b
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (sqrt.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 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
23.1b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
26.9b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
23.2b
(/.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)))))
34.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
28.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
31.4b
(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))
32.8b
(/.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))))
▶34.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
✓23.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
28.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
33.0b
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶31.8b
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
30.6b
(+.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))))))
23.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (+.f64 1 x) 1/2)))
27.0b
(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
31.5b
(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
23.2b
(*.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)))
31.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))
▶28.3b
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
41.9b
(-.f64 (pow.f64 (pow.f64 x 3/2) -1/3) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
31.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
41.6b
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶23.2b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
▶23.1b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
Compiler

Compiled 1448 to 1184 computations (18.2% saved)

localize17.0ms (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)))
✓0.1b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x))
✓3.7b
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
Compiler

Compiled 44 to 26 computations (40.9% saved)

series19.0ms (0.2%)

Counts
4 → 5
Calls

12 calls:

TimeVariablePointExpression
5.0ms
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))

rewrite167.0ms (1.6%)

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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#<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (pow.f64 (+.f64 1 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (cbrt.f64 (+.f64 1 x))) (/.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) 2) (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) (cbrt.f64 (+.f64 1 x))) (/.f64 (sqrt.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1)) (pow.f64 (+.f64 1 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/4) (/.f64 (+.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) -1) (pow.f64 (+.f64 1 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (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 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 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 +.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 log1p.f64 (expm1.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))))))

simplify110.0ms (1.1%)

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)
0.2b
(/.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)

rewrite45.0ms (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 log1p.f64 (expm1.f64 (+.f64 (pow.f64 x -1/2) -1)))))) (#(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 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)))))

simplify6.0ms (0.1%)

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

localize140.0ms (1.4%)

Local error

Found 4 expressions with local error:

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

Compiled 60 to 46 computations (23.3% saved)

series11.0ms (0.1%)

Counts
4 → 48
Calls

12 calls:

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

rewrite148.0ms (1.4%)

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
01261
129646
2466346
Stop Event
1×node limit
Counts
4 → 363
Calls
Call 1
Inputs
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
(/.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))
(/.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 (cbrt.f64 (pow.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 log1p.f64 (expm1.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))))))

simplify115.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
635×fma-def_binary64
625×fma-neg_binary64
446×associate-+l+_binary64
321×associate-+r+_binary64
300×+-commutative_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01891796
15981716
217831560
368031493
Stop Event
1×node limit
Counts
411 → 436
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 (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)))))
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 (/.f64 1 x) (fma.f64 (-.f64 1 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 (/.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 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 5)))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (/.f64 -1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3)))))
(/.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 (/.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))))
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(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
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(-.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 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 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x 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 1/2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (*.f64 (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 1/2 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (*.f64 x x)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2))))
(-.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 (*.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 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 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x 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 1/2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (*.f64 (pow.f64 -1 -1/2) (*.f64 x x)))) (+.f64 (/.f64 5/16 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (*.f64 (pow.f64 -1 -1/2) (pow.f64 x 4)))) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))))))
(fma.f64 1/2 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (*.f64 x x)) (fma.f64 5/16 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (pow.f64 x 4)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2)))))
(-.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 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x 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 1/2 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (*.f64 (pow.f64 -1 -1/2) (*.f64 x x)))) (+.f64 (+.f64 (/.f64 5/16 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (*.f64 (pow.f64 -1 -1/2) (pow.f64 x 4)))) (/.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 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (*.f64 x x)) (fma.f64 5/16 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (pow.f64 x 4)) (fma.f64 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (pow.f64 x 5)) -35/128 (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2))))))
(+.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)))
(fma.f64 x -1/2 (+.f64 1 (pow.f64 x -1/2)))
(+.f64 (pow.f64 x -1/2) (fma.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)))))
(fma.f64 -1/2 x (+.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 (*.f64 x x) 3/8))))
(+.f64 (fma.f64 (*.f64 x x) 3/8 1) (fma.f64 x -1/2 (pow.f64 x -1/2)))
(+.f64 (pow.f64 x -1/2) (fma.f64 x -1/2 (fma.f64 x (*.f64 x 3/8) 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 (fma.f64 (*.f64 x x) 3/8 1) (*.f64 (pow.f64 x 3) -5/16)) (fma.f64 x -1/2 (pow.f64 x -1/2)))
(+.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 (*.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 2 (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 -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 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(+.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 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16 (*.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 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 (/.f64 -1 (/.f64 -1 x)) -1/2))
(+.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 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 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 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 (/.f64 -1 (/.f64 -1 x)) -1/2) (*.f64 (/.f64 -1/2 x) (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2)))
(+.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 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 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 (/.f64 -1 (/.f64 -1 x)) -1/2) (*.f64 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2) 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 2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 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 (/.f64 -1 (/.f64 -1 x)) -1/2) (pow.f64 x 3)) (fma.f64 2 (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2) (*.f64 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2) x) (+.f64 -1/2 (/.f64 3/8 x)))))
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 (pow.f64 x 3)) (+.f64 (/.f64 1 x) (/.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 1 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4)))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x)))) (/.f64 1 (pow.f64 x 4)))
(+.f64 (/.f64 1 x) (+.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.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 (pow.f64 x 3)) (+.f64 (/.f64 1 x) (/.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 1 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4)))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x)))) (/.f64 1 (pow.f64 x 4)))
(+.f64 (/.f64 1 x) (+.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 -1 (*.f64 x x))) (/.f64 -1 (pow.f64 x 4))))

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
0.1b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.5b
(pow.f64 (pow.f64 x -1/4) 2)
✓16.3b
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 38 to 30 computations (21.1% saved)

series71.0ms (0.7%)

Counts
2 → 18
Calls

6 calls:

TimeVariablePointExpression
34.0ms
x
@-inf
(pow.f64 (pow.f64 x -1/4) 2)
27.0ms
x
@0
(pow.f64 (pow.f64 x -1/4) 2)
7.0ms
x
@inf
(pow.f64 (pow.f64 x -1/4) 2)
1.0ms
x
@-inf
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@0
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite159.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
568×prod-diff_binary64
469×log-prod_binary64
302×pow-prod-down_binary64
300×fma-def_binary64
286×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01119
125317
2315417
Stop Event
1×node limit
Counts
2 → 145
Calls
Call 1
Inputs
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(pow.f64 (pow.f64 x -1/4) 2)
Outputs
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simplify123.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
796×times-frac_binary64
376×fma-def_binary64
370×div-sub_binary64
313×unswap-sqr_binary64
288×sub-neg_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
034157
192153
2228153
3714147
42130146
54966110
Stop Event
1×node limit
Counts
163 → 156
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (/.f64 1 x)) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/8 (pow.f64 x 2)))) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 5/16 (pow.f64 x 3)) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/8 (pow.f64 x 2))))) 1)
(sqrt.f64 (/.f64 1 x))
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(sqrt.f64 (/.f64 1 x))
(sqrt.f64 (/.f64 1 x))
(sqrt.f64 (/.f64 1 x))
(sqrt.f64 (/.f64 1 x))
(sqrt.f64 (/.f64 1 x))
(sqrt.f64 (/.f64 1 x))
(sqrt.f64 (/.f64 1 x))
(sqrt.f64 (/.f64 1 x))
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
Outputs
(-.f64 (sqrt.f64 (/.f64 1 x)) 1)
(+.f64 (sqrt.f64 (/.f64 1 x)) -1)
(+.f64 (pow.f64 x -1/2) -1)
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(+.f64 (fma.f64 1/2 x (sqrt.f64 (/.f64 1 x))) -1)
(+.f64 (fma.f64 x 1/2 (sqrt.f64 (/.f64 1 x))) -1)
(+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 x 1/2 -1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x 1/2 -1))
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/8 (pow.f64 x 2)))) 1)
(+.f64 (+.f64 (fma.f64 1/2 x (sqrt.f64 (/.f64 1 x))) (*.f64 -3/8 (*.f64 x x))) -1)
(+.f64 (fma.f64 x 1/2 (fma.f64 -3/8 (*.f64 x x) (sqrt.f64 (/.f64 1 x)))) -1)
(+.f64 (fma.f64 x 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 -3/8 (*.f64 x x) -1))
(+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 x (fma.f64 x -3/8 1/2) -1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x (fma.f64 x -3/8 1/2) -1))
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 5/16 (pow.f64 x 3)) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/8 (pow.f64 x 2))))) 1)
(+.f64 (fma.f64 1/2 x (fma.f64 5/16 (pow.f64 x 3) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/8 (*.f64 x x))))) -1)
(+.f64 (fma.f64 x 1/2 (fma.f64 5/16 (pow.f64 x 3) (fma.f64 -3/8 (*.f64 x x) (sqrt.f64 (/.f64 1 x))))) -1)
(+.f64 (fma.f64 x (*.f64 x -3/8) (fma.f64 x 1/2 (sqrt.f64 (/.f64 1 x)))) (fma.f64 5/16 (pow.f64 x 3) -1))
(fma.f64 x (*.f64 x (fma.f64 x 5/16 -3/8)) (+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 x 1/2 -1)))
(+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 5/16 -3/8))) -1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 5/16 -3/8))) -1))
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)

localize26.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 1 x))
✓0.1b
(/.f64 -1 (sqrt.f64 (+.f64 1 x)))
✓31.7b
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
Compiler

Compiled 34 to 26 computations (23.5% saved)

series3.0ms (0%)

Counts
2 → 10
Calls

6 calls:

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

rewrite84.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
950×pow1_binary64
889×add-log-exp_binary64
887×log1p-expm1-u_binary64
887×expm1-log1p-u_binary64
101×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01028
121024
2245524
Stop Event
1×node limit
Counts
2 → 44
Calls
Call 1
Inputs
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(/.f64 -1 (sqrt.f64 (+.f64 1 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))))) (#(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 (*.f64 (pow.f64 x -1/2) 1) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))) (pow.f64 (cbrt.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))) 2) (cbrt.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))) (sqrt.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (pow.f64 x -1/2) 3) (pow.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 3)) (+.f64 (*.f64 (pow.f64 x -1/2) (pow.f64 x -1/2)) (-.f64 (/.f64 1 (+.f64 x 1)) (*.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x -1/2) (pow.f64 x -1/2)) (/.f64 1 (+.f64 x 1))) (-.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))) (cbrt.f64 (/.f64 1 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1))) (cbrt.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))) (sqrt.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) -1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (+.f64 x 1)) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))))

simplify60.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
801×times-frac_binary64
410×fma-def_binary64
373×div-sub_binary64
320×fma-neg_binary64
313×unswap-sqr_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
040126
1113120
2263118
3740106
42154104
5512092
Stop Event
1×node limit
Counts
54 → 62
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (/.f64 1 x)) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/8 (pow.f64 x 2)))) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 5/16 (pow.f64 x 3)) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/8 (pow.f64 x 2))))) 1)
(sqrt.f64 (/.f64 1 x))
(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 (*.f64 1/2 x) (*.f64 -3/8 (pow.f64 x 2))) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 5/16 (pow.f64 x 3)) (*.f64 -3/8 (pow.f64 x 2)))) 1)
Outputs
(-.f64 (sqrt.f64 (/.f64 1 x)) 1)
(+.f64 (sqrt.f64 (/.f64 1 x)) -1)
(+.f64 (pow.f64 x -1/2) -1)
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(+.f64 (fma.f64 1/2 x (sqrt.f64 (/.f64 1 x))) -1)
(+.f64 (fma.f64 x 1/2 (sqrt.f64 (/.f64 1 x))) -1)
(+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 x 1/2 -1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x 1/2 -1))
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/8 (pow.f64 x 2)))) 1)
(+.f64 (+.f64 (fma.f64 1/2 x (sqrt.f64 (/.f64 1 x))) (*.f64 -3/8 (*.f64 x x))) -1)
(+.f64 (fma.f64 x 1/2 (sqrt.f64 (/.f64 1 x))) (fma.f64 -3/8 (*.f64 x x) -1))
(+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 x 1/2 (fma.f64 x (*.f64 x -3/8) -1)))
(+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 x (fma.f64 x -3/8 1/2) -1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x (fma.f64 x -3/8 1/2) -1))
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 5/16 (pow.f64 x 3)) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/8 (pow.f64 x 2))))) 1)
(+.f64 (fma.f64 1/2 x (fma.f64 5/16 (pow.f64 x 3) (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/8 (*.f64 x x))))) -1)
(+.f64 (fma.f64 5/16 (pow.f64 x 3) (fma.f64 -3/8 (*.f64 x x) (sqrt.f64 (/.f64 1 x)))) (fma.f64 x 1/2 -1))
(+.f64 (fma.f64 x (*.f64 x -3/8) (fma.f64 x 1/2 (sqrt.f64 (/.f64 1 x)))) (fma.f64 5/16 (pow.f64 x 3) -1))
(+.f64 (fma.f64 x (fma.f64 x -3/8 1/2) -1) (fma.f64 5/16 (pow.f64 x 3) (sqrt.f64 (/.f64 1 x))))
(+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 5/16 -3/8))) -1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 5/16 -3/8))) -1))
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(sqrt.f64 (/.f64 1 x))
(pow.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 (*.f64 1/2 x) (*.f64 -3/8 (pow.f64 x 2))) 1)
(+.f64 (fma.f64 1/2 x (*.f64 -3/8 (*.f64 x x))) -1)
(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 (fma.f64 x -3/8 1/2) -1)
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 5/16 (pow.f64 x 3)) (*.f64 -3/8 (pow.f64 x 2)))) 1)
(+.f64 (fma.f64 1/2 x (fma.f64 5/16 (pow.f64 x 3) (*.f64 -3/8 (*.f64 x x)))) -1)
(+.f64 -1 (fma.f64 x 1/2 (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)))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) (fma.f64 x 5/16 -3/8) -1))
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 5/16 -3/8))) -1)

eval1.1s (10.8%)

Compiler

Compiled 25757 to 20074 computations (22.1% saved)

prune384.0ms (3.7%)

Pruning

25 alts after pruning (23 fresh and 2 done)

PrunedKeptTotal
New1092181110
Fresh29534
Picked101
Done325
Total1125251150
Error
0.1b
Counts
1150 → 25
Alt Table
Click to see full alt table
StatusErrorProgram
▶34.4b
(pow.f64 x -1/2)
47.5b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
34.4b
(sqrt.f64 (/.f64 1 x))
34.0b
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
44.4b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
37.0b
(/.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)))
6.5b
(/.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)))
23.1b
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
33.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
25.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
36.4b
(/.f64 (/.f64 1 (*.f64 x x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
▶0.4b
(/.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)))
36.4b
(fma.f64 1/2 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (*.f64 x x)) (fma.f64 5/16 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (pow.f64 x 4)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2)))))
▶23.2b
(/.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)))))
▶34.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
✓34.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
37.0b
(fma.f64 1/2 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (*.f64 x x)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2))))
▶23.0b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
36.6b
(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
62.8b
-1
7.3b
(/.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)))
41.1b
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
✓23.2b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
34.6b
(-.f64 (pow.f64 x -1/2) 1)
33.0b
(/.f64 1 (+.f64 x (sqrt.f64 x)))
Compiler

Compiled 703 to 552 computations (21.5% saved)

localize89.0ms (0.9%)

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)))
✓0.1b
(/.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)

series42.0ms (0.4%)

Counts
4 → 3
Calls

12 calls:

TimeVariablePointExpression
16.0ms
x
@0
(/.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)))
6.0ms
x
@-inf
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x))
5.0ms
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)))
4.0ms
x
@inf
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x))
3.0ms
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)))

rewrite143.0ms (1.4%)

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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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))))))

simplify12.0ms (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

localize6.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
0.2b
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 28 to 19 computations (32.1% saved)

series1.0ms (0%)

Counts
1 → 4
Calls

3 calls:

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

rewrite73.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
437×fma-def_binary64
427×log-prod_binary64
318×exp-prod_binary64
282×pow-prod-down_binary64
248×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0913
120411
2283211
Stop Event
1×node limit
Counts
1 → 110
Calls
Call 1
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (neg.f64 (fma.f64 x -1/2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (neg.f64 (fma.f64 x -1/2 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (fma.f64 x -1/2 1)) (fma.f64 (neg.f64 (fma.f64 x -1/2 1)) 1 (fma.f64 x -1/2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (fma.f64 x -1/2 1)) (fma.f64 (neg.f64 (cbrt.f64 (fma.f64 x -1/2 1))) (pow.f64 (cbrt.f64 (fma.f64 x -1/2 1)) 2) (fma.f64 x -1/2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (fma.f64 x -1/2 1)) (+.f64 (neg.f64 (fma.f64 x -1/2 1)) (fma.f64 x -1/2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (pow.f64 x -1/2) (fma.f64 x -1/2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (fma.f64 x -1/2 1)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (*.f64 x -1/2)) -1)))) 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-1/2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x -1/4) (sqrt.f64 (fma.f64 x -1/2 1))) (-.f64 (pow.f64 x -1/4) (sqrt.f64 (fma.f64 x -1/2 1))) (fma.f64 (neg.f64 (cbrt.f64 (fma.f64 x -1/2 1))) (pow.f64 (cbrt.f64 (fma.f64 x -1/2 1)) 2) (fma.f64 x -1/2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x -1/4) (sqrt.f64 (fma.f64 x -1/2 1))) (-.f64 (pow.f64 x -1/4) (sqrt.f64 (fma.f64 x -1/2 1))) (+.f64 (neg.f64 (fma.f64 x -1/2 1)) (fma.f64 x -1/2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x -1/4) (sqrt.f64 (*.f64 x -1/2))) (-.f64 (pow.f64 x -1/4) (sqrt.f64 (*.f64 x -1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/2 1)) 2)) (cbrt.f64 (fma.f64 x -1/2 1)) (pow.f64 x -1/2))))))

simplify10.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×fma-neg_binary64
1×+-commutative_binary64
1×*-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
11318
21518
Stop Event
1×saturated
Counts
114 → 113
Calls
Call 1
Inputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
Outputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x -1)
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x -1)

localize45.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (+.f64 1 x) -1/2)
✓3.7b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
Compiler

Compiled 24 to 18 computations (25% saved)

series4.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite98.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
943×pow1_binary64
884×add-log-exp_binary64
883×log1p-expm1-u_binary64
883×expm1-log1p-u_binary64
93×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0820
118320
2241220
Stop Event
1×node limit
Counts
2 → 52
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
(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 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2))) (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)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (pow.f64 x -1/2) 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(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4)) (-.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x -1) (+.f64 (pow.f64 (+.f64 x 1) -1) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2)) (+.f64 (pow.f64 x -1) (+.f64 (pow.f64 (+.f64 x 1) -1) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2))) (neg.f64 (+.f64 (pow.f64 x -1) (+.f64 (pow.f64 (+.f64 x 1) -1) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))) (neg.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 3)) (+.f64 (pow.f64 x -1) (-.f64 (*.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))) (*.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -1) (*.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))) (-.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -1)) (cbrt.f64 (pow.f64 x -1/2)) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 x 1) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/2) (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) -1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) -1/2) (pow.f64 (sqrt.f64 (+.f64 x 1)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log1p.f64 x)))))))

simplify89.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
738×times-frac_binary64
478×associate-/l*_binary64
416×associate-/r*_binary64
375×unswap-sqr_binary64
362×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
099797
1268765
2687609
31971514
47380469
Stop Event
1×node limit
Counts
76 → 97
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (*.f64 -3/8 (pow.f64 x 2)))) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 (*.f64 5/16 (pow.f64 x 3)) (*.f64 -3/8 (pow.f64 x 2))))) 1)
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))
(+.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))))))
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 -1 (pow.f64 x -1/2))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(+.f64 (fma.f64 1/2 x (pow.f64 x -1/2)) -1)
(+.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) -1)
(+.f64 (pow.f64 x -1/2) (fma.f64 x 1/2 -1))
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (*.f64 -3/8 (pow.f64 x 2)))) 1)
(+.f64 (+.f64 (fma.f64 1/2 x (pow.f64 x -1/2)) (*.f64 -3/8 (*.f64 x x))) -1)
(+.f64 (fma.f64 x 1/2 (fma.f64 -3/8 (*.f64 x x) (pow.f64 x -1/2))) -1)
(+.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) (fma.f64 -3/8 (*.f64 x x) -1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x (+.f64 1/2 (*.f64 x -3/8)) -1))
(-.f64 (+.f64 (*.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 (*.f64 5/16 (pow.f64 x 3)) (*.f64 -3/8 (pow.f64 x 2))))) 1)
(+.f64 (+.f64 (fma.f64 1/2 x (pow.f64 x -1/2)) (fma.f64 5/16 (pow.f64 x 3) (*.f64 -3/8 (*.f64 x x)))) -1)
(+.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) (-.f64 (fma.f64 -3/8 (*.f64 x x) (*.f64 5/16 (pow.f64 x 3))) 1))
(+.f64 (fma.f64 x (*.f64 x -3/8) (fma.f64 5/16 (pow.f64 x 3) (pow.f64 x -1/2))) (fma.f64 x 1/2 -1))
(+.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) (fma.f64 (*.f64 x x) (+.f64 -3/8 (*.f64 x 5/16)) -1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x (+.f64 1/2 (*.f64 x (+.f64 -3/8 (*.f64 x 5/16)))) -1))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -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 -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 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.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 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))
(+.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 (*.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (*.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))) (fma.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (*.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))) (fma.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (*.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 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))))))
(*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))
(*.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))
(*.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x))
(*.f64 (/.f64 1/2 x) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))
(*.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (/.f64 1/2 x))
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
(+.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))))
(fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (*.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 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 -3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))))
(*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (+.f64 1/2 (/.f64 -3/8 x)))
(*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) x) (+.f64 1/2 (/.f64 -3/8 x)))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
(+.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)))))
(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 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (*.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) (-.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 -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 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) 1/2) (/.f64 (*.f64 x x) (pow.f64 -1 -1/2))) (+.f64 -3/8 (/.f64 5/16 x))))
(*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
(+.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))))))
(fma.f64 -35/128 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 4)) (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 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (*.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 -35/128 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 4)) (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 -3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))))))
(+.f64 (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (+.f64 1/2 (/.f64 -3/8 x))) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) 1/2) (/.f64 (*.f64 x x) (pow.f64 -1 -1/2))) (+.f64 (/.f64 5/16 x) (/.f64 -35/128 (*.f64 x x)))))
(+.f64 (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) x) (+.f64 1/2 (/.f64 -3/8 x))) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (log.f64 x)) (pow.f64 x 3)) (+.f64 5/16 (/.f64 -35/128 x))))
(+.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1/2 x)) (*.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 (/.f64 5/16 x) (+.f64 -3/8 (/.f64 -35/128 (*.f64 x x))))))
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 (*.f64 x x) 3/8))
(fma.f64 x -1/2 (fma.f64 (*.f64 x x) 3/8 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 (pow.f64 x 3) -5/16)))
(+.f64 (fma.f64 x -1/2 1) (fma.f64 (*.f64 x x) 3/8 (*.f64 (pow.f64 x 3) -5/16)))
(fma.f64 x -1/2 (fma.f64 x (*.f64 x 3/8) (fma.f64 (pow.f64 x 3) -5/16 1)))
(+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16))))))
(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 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))))))
(fma.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))))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/8 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/8 (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 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.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)))))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/8 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/8 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16 (sqrt.f64 (/.f64 1 x)))))
(exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))
(pow.f64 (exp.f64 -1/2) (log.f64 x))
(pow.f64 x -1/2)
(+.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 (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) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 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)))
(*.f64 (+.f64 (/.f64 -1/2 x) 1) (pow.f64 (exp.f64 -1/2) (log.f64 x)))
(*.f64 (+.f64 (/.f64 -1/2 x) 1) (pow.f64 x -1/2))
(+.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 (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)) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))
(+.f64 (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) (*.f64 (/.f64 3/8 x) (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x))))
(fma.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))))
(+.f64 (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 (pow.f64 x -1/2) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 -1/2 (/.f64 3/8 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)))))
(+.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 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) 3/8 (fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (/.f64 (*.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) -5/16) (pow.f64 x 3)))))
(fma.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2) (fma.f64 -1/2 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) x) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) 1/2) (/.f64 (*.f64 x x) (pow.f64 -1 -1/2))) (+.f64 3/8 (/.f64 -5/16 x)))))
(+.f64 (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 (/.f64 -5/16 (*.f64 x x)) (/.f64 3/8 x)))))
(+.f64 (*.f64 (+.f64 (/.f64 -1/2 x) 1) (pow.f64 x -1/2)) (*.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 3/8 (/.f64 -5/16 x))))

localize46.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
✓0.1b
(/.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)))))
✓0.2b
(/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))))
3.6b
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
Compiler

Compiled 81 to 63 computations (22.2% saved)

series5.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite236.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
723×log-prod_binary64
662×fma-def_binary64
326×fma-neg_binary64
281×log-div_binary64
259×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01359
131929
2492829
Stop Event
1×node limit
Counts
2 → 215
Calls
Call 1
Inputs
(/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 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)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))) (cbrt.f64 (exp.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -1/2) 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simplify92.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
887×fma-def_binary64
445×associate--r+_binary64
336×distribute-rgt-in_binary64
327×associate--l+_binary64
318×associate-/r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02011705
16911594
222571304
Stop Event
1×node limit
Counts
239 → 262
Calls
Call 1
Inputs
(*.f64 (+.f64 (pow.f64 x -1/2) 1) x)
(+.f64 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x) (*.f64 -1 (*.f64 (+.f64 1/2 (*.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (pow.f64 x 2))))
(+.f64 (*.f64 -1 (*.f64 (+.f64 9/8 (+.f64 (pow.f64 x -1/2) (*.f64 -1 (+.f64 (pow.f64 x -1/2) 1)))) (pow.f64 x 3))) (+.f64 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x) (*.f64 -1 (*.f64 (+.f64 1/2 (*.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (pow.f64 x 2)))))
(+.f64 (*.f64 -1 (*.f64 (+.f64 (pow.f64 x -1/2) (+.f64 23/16 (+.f64 (*.f64 -1 (+.f64 1/2 (*.f64 -1 (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 -2 (+.f64 1 (pow.f64 x -1/2)))))) (pow.f64 x 4))) (+.f64 (*.f64 -1 (*.f64 (+.f64 9/8 (+.f64 (pow.f64 x -1/2) (*.f64 -1 (+.f64 (pow.f64 x -1/2) 1)))) (pow.f64 x 3))) (+.f64 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x) (*.f64 -1 (*.f64 (+.f64 1/2 (*.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (pow.f64 x 2))))))
(*.f64 2 (sqrt.f64 (pow.f64 x 3)))
(+.f64 (*.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x)))) x) (*.f64 2 (sqrt.f64 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x)))) x) (*.f64 2 (sqrt.f64 (pow.f64 x 3))))) (+.f64 (*.f64 -1 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x))))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))
(-.f64 (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x)))) x) (+.f64 (*.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (pow.f64 x 3)))))) (+.f64 (*.f64 -1 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x))))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 -1 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x))))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))) x)) (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))))
(*.f64 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 (*.f64 (-.f64 (*.f64 1/2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) x)) (*.f64 2 (*.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 (*.f64 (-.f64 (*.f64 1/2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) x)) (+.f64 (*.f64 3/8 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 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 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 5/16 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 3/8 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) x)) (+.f64 (*.f64 -1 (*.f64 (-.f64 (*.f64 1/2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) x)) (+.f64 (*.f64 3/8 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 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 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(/.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))))))
Outputs
(*.f64 (+.f64 (pow.f64 x -1/2) 1) x)
(*.f64 x (+.f64 (pow.f64 x -1/2) 1))
(+.f64 x (sqrt.f64 x))
(+.f64 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x) (*.f64 -1 (*.f64 (+.f64 1/2 (*.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (pow.f64 x 2))))
(fma.f64 (+.f64 (pow.f64 x -1/2) 1) x (*.f64 (neg.f64 (+.f64 1/2 (neg.f64 (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 x x)))
(fma.f64 (+.f64 -1/2 (+.f64 (pow.f64 x -1/2) 1)) (*.f64 x x) (*.f64 x (+.f64 (pow.f64 x -1/2) 1)))
(fma.f64 (*.f64 x x) (+.f64 (pow.f64 x -1/2) 1/2) (+.f64 x (sqrt.f64 x)))
(+.f64 (*.f64 -1 (*.f64 (+.f64 9/8 (+.f64 (pow.f64 x -1/2) (*.f64 -1 (+.f64 (pow.f64 x -1/2) 1)))) (pow.f64 x 3))) (+.f64 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x) (*.f64 -1 (*.f64 (+.f64 1/2 (*.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (pow.f64 x 2)))))
(fma.f64 -1 (*.f64 (+.f64 9/8 (+.f64 (pow.f64 x -1/2) (neg.f64 (+.f64 (pow.f64 x -1/2) 1)))) (pow.f64 x 3)) (fma.f64 (+.f64 (pow.f64 x -1/2) 1) x (*.f64 (neg.f64 (+.f64 1/2 (neg.f64 (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 x x))))
(-.f64 (fma.f64 (+.f64 -1/2 (+.f64 (pow.f64 x -1/2) 1)) (*.f64 x x) (*.f64 x (+.f64 (pow.f64 x -1/2) 1))) (*.f64 (+.f64 9/8 (-.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 x -1/2) 1))) (pow.f64 x 3)))
(fma.f64 (*.f64 x x) (+.f64 (pow.f64 x -1/2) 1/2) (fma.f64 (pow.f64 x 3) (fma.f64 -1 (+.f64 -1 (*.f64 0 (pow.f64 x -1/2))) -9/8) (+.f64 x (sqrt.f64 x))))
(+.f64 (*.f64 -1 (*.f64 (+.f64 (pow.f64 x -1/2) (+.f64 23/16 (+.f64 (*.f64 -1 (+.f64 1/2 (*.f64 -1 (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 -2 (+.f64 1 (pow.f64 x -1/2)))))) (pow.f64 x 4))) (+.f64 (*.f64 -1 (*.f64 (+.f64 9/8 (+.f64 (pow.f64 x -1/2) (*.f64 -1 (+.f64 (pow.f64 x -1/2) 1)))) (pow.f64 x 3))) (+.f64 (*.f64 (+.f64 (pow.f64 x -1/2) 1) x) (*.f64 -1 (*.f64 (+.f64 1/2 (*.f64 -1 (+.f64 1 (pow.f64 x -1/2)))) (pow.f64 x 2))))))
(fma.f64 -1 (*.f64 (+.f64 (pow.f64 x -1/2) (+.f64 23/16 (fma.f64 -1 (+.f64 1/2 (neg.f64 (+.f64 (pow.f64 x -1/2) 1))) (+.f64 -2 (*.f64 -2 (pow.f64 x -1/2)))))) (pow.f64 x 4)) (fma.f64 -1 (*.f64 (+.f64 9/8 (+.f64 (pow.f64 x -1/2) (neg.f64 (+.f64 (pow.f64 x -1/2) 1)))) (pow.f64 x 3)) (fma.f64 (+.f64 (pow.f64 x -1/2) 1) x (*.f64 (neg.f64 (+.f64 1/2 (neg.f64 (+.f64 (pow.f64 x -1/2) 1)))) (*.f64 x x)))))
(-.f64 (-.f64 (fma.f64 (+.f64 -1/2 (+.f64 (pow.f64 x -1/2) 1)) (*.f64 x x) (*.f64 x (+.f64 (pow.f64 x -1/2) 1))) (*.f64 (+.f64 9/8 (-.f64 (pow.f64 x -1/2) (+.f64 (pow.f64 x -1/2) 1))) (pow.f64 x 3))) (*.f64 (+.f64 (+.f64 15/16 (+.f64 (pow.f64 x -1/2) 1)) (+.f64 (*.f64 (+.f64 (pow.f64 x -1/2) 1) -2) (pow.f64 x -1/2))) (pow.f64 x 4)))
(fma.f64 (pow.f64 x 4) (-.f64 (+.f64 (+.f64 1/2 (+.f64 (pow.f64 x -1/2) 1)) -23/16) (pow.f64 x -1/2)) (fma.f64 (*.f64 x x) (+.f64 (pow.f64 x -1/2) 1/2) (fma.f64 (pow.f64 x 3) (fma.f64 -1 (+.f64 -1 (*.f64 0 (pow.f64 x -1/2))) -9/8) (+.f64 x (sqrt.f64 x)))))
(*.f64 2 (sqrt.f64 (pow.f64 x 3)))
(*.f64 2 (pow.f64 x 3/2))
(+.f64 (*.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x)))) x) (*.f64 2 (sqrt.f64 (pow.f64 x 3))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 3/2) x (*.f64 2 (sqrt.f64 (pow.f64 x 3))))
(fma.f64 x (*.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (*.f64 2 (sqrt.f64 (pow.f64 x 3))))
(fma.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 3/2 x) (*.f64 2 (pow.f64 x 3/2)))
(-.f64 (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x)))) x) (*.f64 2 (sqrt.f64 (pow.f64 x 3))))) (+.f64 (*.f64 -1 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x))))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))
(-.f64 (fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 3/2) x (*.f64 2 (sqrt.f64 (pow.f64 x 3))))) (fma.f64 -1 (*.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))
(-.f64 (fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 (fma.f64 x (*.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (*.f64 2 (sqrt.f64 (pow.f64 x 3))))) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 x)) -3/2)))
(-.f64 (fma.f64 2 (pow.f64 x 3/2) (*.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (*.f64 3/2 x) 3/8))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(-.f64 (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x)))) x) (+.f64 (*.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (pow.f64 x 3)))))) (+.f64 (*.f64 -1 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x))))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 -1 (-.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -2 (sqrt.f64 (/.f64 1 x))))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))) x)) (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))))
(-.f64 (fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 3/2) x (fma.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (pow.f64 x 3)))))) (fma.f64 -1 (*.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (fma.f64 -1 (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 3/8) (fma.f64 -1 (*.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (*.f64 2 (sqrt.f64 (/.f64 1 x))))) x) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))))))
(-.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 (fma.f64 x (*.f64 (sqrt.f64 (/.f64 1 x)) 3/2) (fma.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (pow.f64 x 3)))))) (*.f64 (sqrt.f64 (/.f64 1 x)) -3/2)) (-.f64 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (sqrt.f64 (/.f64 1 x)))) (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 3/8) (fma.f64 2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 x)) -3/2))) x)))
(+.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) (+.f64 (*.f64 3/2 x) 3/8)) (-.f64 (-.f64 (fma.f64 -5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (pow.f64 x 3/2))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 x)))) x))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))
(*.f64 2 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))
(*.f64 2 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(*.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 (*.f64 x x) 2))
(*.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (*.f64 x (*.f64 x 2)))
(+.f64 (*.f64 -1 (*.f64 (-.f64 (*.f64 1/2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) x)) (*.f64 2 (*.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))
(fma.f64 -1 (*.f64 x (*.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) -3/2)) (*.f64 2 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(-.f64 (*.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 (*.f64 x x) 2)) (*.f64 x (*.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) -3/2)))
(*.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (-.f64 (*.f64 x (*.f64 x 2)) (*.f64 -3/2 x)))
(-.f64 (+.f64 (*.f64 -1 (*.f64 (-.f64 (*.f64 1/2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 2 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) x)) (+.f64 (*.f64 3/8 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 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 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
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(-.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 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 -1/2 (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))) (fma.f64 3/16 (/.f64 (*.f64 (sqrt.f64 x) -3/8) (pow.f64 x 5)) (fma.f64 -1/4 (/.f64 (-.f64 (*.f64 1/2 (sqrt.f64 x)) (fma.f64 3/32 (sqrt.f64 x) (*.f64 -1/4 (*.f64 (sqrt.f64 x) -3/8)))) (pow.f64 x 5)) (fma.f64 -5/64 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (fma.f64 -1/4 (/.f64 (*.f64 (sqrt.f64 x) -3/8) (pow.f64 x 4)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) 3/32)))))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (-.f64 (+.f64 (*.f64 1/2 (+.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (fma.f64 3/16 (/.f64 (sqrt.f64 x) (/.f64 (pow.f64 x 5) -3/8)) (fma.f64 -1/4 (/.f64 (-.f64 (*.f64 (sqrt.f64 x) 13/32) (*.f64 (sqrt.f64 x) 3/32)) (pow.f64 x 5)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) -5/64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) 3/32 (/.f64 (*.f64 (sqrt.f64 x) 3/32) (pow.f64 x 4))))))))
(-.f64 (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (fma.f64 1/2 (+.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) 3/32 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) -5/64 (/.f64 (sqrt.f64 x) (/.f64 (pow.f64 x 4) 3/32)))) (fma.f64 -1/4 (/.f64 (*.f64 (sqrt.f64 x) 5/16) (pow.f64 x 5)) (/.f64 (*.f64 (sqrt.f64 x) -9/128) (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 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x x))
(/.f64 (/.f64 (/.f64 1/2 x) x) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))
(-.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 1/2 (*.f64 (*.f64 x x) (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 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x 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 1/2 x) x) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (/.f64 (/.f64 -3/8 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (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 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x x)) (+.f64 (/.f64 5/16 (*.f64 (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 5/16 (*.f64 (pow.f64 x 4) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))) (+.f64 (/.f64 (/.f64 (/.f64 1/2 x) x) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (/.f64 (/.f64 -3/8 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (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 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 5)))))
(+.f64 (/.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x x)) (-.f64 (/.f64 5/16 (*.f64 (pow.f64 x 4) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (+.f64 (/.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 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 5))))))
(+.f64 (/.f64 (/.f64 (/.f64 1/2 x) x) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (+.f64 (/.f64 5/16 (*.f64 (pow.f64 x 4) (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)))) (+.f64 (/.f64 (/.f64 -3/8 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2))) (pow.f64 x 3)) (/.f64 -35/128 (*.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/2) (pow.f64 -1 -1/2)) (pow.f64 x 5))))))

eval944.0ms (9.2%)

Compiler

Compiled 25535 to 19552 computations (23.4% saved)

prune446.0ms (4.3%)

Pruning

28 alts after pruning (22 fresh and 6 done)

PrunedKeptTotal
New92912941
Fresh81018
Picked011
Done156
Total93828966
Error
0b
Counts
966 → 28
Alt Table
Click to see full alt table
StatusErrorProgram
▶29.4b
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
✓34.4b
(pow.f64 x -1/2)
29.6b
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
47.5b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
34.3b
(-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
▶0.5b
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x)))))
34.4b
(sqrt.f64 (/.f64 1 x))
6.5b
(/.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)))
23.1b
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
▶33.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
▶25.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
62.3b
(-.f64 (*.f64 1/2 x) 1)
✓23.2b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
28.4b
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
34.6b
(-.f64 (pow.f64 x -1/2) 1)
▶61.3b
(*.f64 1/2 x)
✓23.2b
(/.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)))))
✓34.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
29.4b
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
✓34.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
30.0b
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
✓23.0b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
36.6b
(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
44.4b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
33.9b
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
6.5b
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
33.0b
(/.f64 1 (+.f64 x (sqrt.f64 x)))
62.8b
-1
Compiler

Compiled 602 to 468 computations (22.3% saved)

localize160.0ms (1.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x)))))
✓0.2b
(/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))))
✓0.3b
(cbrt.f64 (hypot.f64 1 (sqrt.f64 x)))
✓0.3b
(cbrt.f64 (+.f64 1 x))
Compiler

Compiled 84 to 50 computations (40.5% saved)

series408.0ms (4%)

Counts
4 → 5
Calls

12 calls:

TimeVariablePointExpression
177.0ms
x
@inf
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x)))))
162.0ms
x
@-inf
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x)))))
34.0ms
x
@inf
(cbrt.f64 (hypot.f64 1 (sqrt.f64 x)))
14.0ms
x
@-inf
(/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))))
8.0ms
x
@inf
(/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))))

rewrite97.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
638×log-prod_binary64
323×pow2_binary64
316×prod-diff_binary64
233×fma-def_binary64
226×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01372
128159
2385359
Stop Event
1×node limit
Counts
4 → 167
Calls
Call 1
Inputs
(cbrt.f64 (+.f64 1 x))
(cbrt.f64 (hypot.f64 1 (sqrt.f64 x)))
(/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))))
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x)))))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (+.f64 1 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) 1/6))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) 1/6)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 x) 1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 1 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) 1/6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 1 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (+.f64 1 x) 1/6)) (sqrt.f64 (pow.f64 (+.f64 1 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (exp.f64 (*.f64 2/3 (log1p.f64 x))))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 (+.f64 1 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 x) 1/6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (+.f64 1 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 1 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 x) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/6 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/6 (log1p.f64 x)) 1))))))
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simplify95.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
640×distribute-rgt-in_binary64
584×distribute-lft-in_binary64
536×unswap-sqr_binary64
476×associate-*l*_binary64
432×fma-def_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01844
14740
210738
328132
472231
5231731
6391931
7415731
8445731
9499631
10599331
Stop Event
1×node limit
Counts
172 → 174
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/3 x))
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (*.f64 1/3 x)))
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x))))
1
Outputs
1
(+.f64 1 (*.f64 1/3 x))
(fma.f64 1/3 x 1)
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (*.f64 1/3 x)))
(fma.f64 -1/9 (*.f64 x x) (+.f64 1 (*.f64 1/3 x)))
(fma.f64 -1/9 (*.f64 x x) (fma.f64 1/3 x 1))
(fma.f64 x (*.f64 x -1/9) (fma.f64 1/3 x 1))
(fma.f64 x (fma.f64 x -1/9 1/3) 1)
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x))))
(fma.f64 -1/9 (*.f64 x x) (+.f64 1 (fma.f64 5/81 (pow.f64 x 3) (*.f64 1/3 x))))
(+.f64 (fma.f64 -1/9 (*.f64 x x) (fma.f64 1/3 x 1)) (*.f64 5/81 (pow.f64 x 3)))
(fma.f64 x (*.f64 x -1/9) (fma.f64 1/3 x (fma.f64 5/81 (pow.f64 x 3) 1)))
(fma.f64 5/81 (pow.f64 x 3) (fma.f64 x (fma.f64 x -1/9 1/3) 1))
(fma.f64 x (+.f64 1/3 (*.f64 x (fma.f64 x 5/81 -1/9))) 1)
1

localize8.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize25.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiled 17 to 12 computations (29.4% saved)

series3.0ms (0%)

Counts
1 → 0
Calls

3 calls:

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

rewrite72.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
675×pow1_binary64
629×add-log-exp_binary64
629×log1p-expm1-u_binary64
629×expm1-log1p-u_binary64
616×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
115410
2180510
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 x -1/2) (/.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (*.f64 (pow.f64 x -1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x -1/2) 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (pow.f64 x -1/2) 1/2)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 x -1/2) 1/2) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 x -1/2) 1/2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 x -1/2) 1/2) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1/2 (pow.f64 x -1/2)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x -1/2) -1/2) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1/2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (/.f64 1/2 x)) (pow.f64 x -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 1/2 x)) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1/2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -1/2) 3) (pow.f64 (/.f64 1/2 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1/2 x) 3) (pow.f64 (pow.f64 x -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))))))))

simplify12.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
22 → 22
Calls
Call 1
Inputs
Outputs

localize33.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
✓0.0b
(/.f64 1 (+.f64 (*.f64 1/2 x) 1))
0.2b
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 37 to 27 computations (27% saved)

series8.0ms (0.1%)

Counts
2 → 12
Calls

6 calls:

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

rewrite117.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
982×prod-diff_binary64
496×log-prod_binary64
404×fma-def_binary64
235×fma-neg_binary64
191×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01024
122922
2324322
Stop Event
1×node limit
Counts
2 → 165
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (*.f64 1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1)))) (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (fma.f64 1/2 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 1))) (cbrt.f64 (pow.f64 (fma.f64 1/2 x 1) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 x 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 1/2 x 1) -1/2) (pow.f64 (fma.f64 1/2 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 -1 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2)) (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/8 (pow.f64 x 3) 1)) (-.f64 (fma.f64 1/4 (*.f64 x x) 1) (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/4 (*.f64 x x) -1)) (fma.f64 1/2 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 1) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 1) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (fma.f64 1/2 x 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 x 1) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (fma.f64 1/2 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 x 1) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (*.f64 1/2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 (*.f64 1/2 x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (/.f64 -1 (fma.f64 1/2 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 1/2 x 1))) (fma.f64 (/.f64 -1 (fma.f64 1/2 x 1)) 1 (/.f64 1 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 1/2 x 1))) (fma.f64 (neg.f64 (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 1)))) (cbrt.f64 (pow.f64 (fma.f64 1/2 x 1) -2)) (/.f64 1 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 1/2 x 1))) (+.f64 (/.f64 -1 (fma.f64 1/2 x 1)) (/.f64 1 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -1/2) (/.f64 -1 (fma.f64 1/2 x 1))) (fma.f64 -1 (/.f64 1 (fma.f64 1/2 x 1)) (/.f64 1 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 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simplify69.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
775×distribute-neg-frac_binary64
729×fma-def_binary64
721×associate-*l*_binary64
494×associate-*r*_binary64
417×times-frac_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
035181
193177
2231177
3626171
41927170
57347170
Stop Event
1×node limit
Counts
177 → 179
Calls
Call 1
Inputs
1
(+.f64 (*.f64 -1/2 x) 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/4 (pow.f64 x 2))))
(+.f64 (*.f64 -1/8 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/4 (pow.f64 x 2)))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))
Outputs
1
(+.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/4 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/2 x 1) (*.f64 1/4 (*.f64 x x)))
(fma.f64 -1/2 x (fma.f64 1/4 (*.f64 x x) 1))
(fma.f64 x (*.f64 x 1/4) (fma.f64 -1/2 x 1))
(fma.f64 x (fma.f64 x 1/4 -1/2) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/4 (pow.f64 x 2)))))
(fma.f64 -1/8 (pow.f64 x 3) (+.f64 (fma.f64 -1/2 x 1) (*.f64 1/4 (*.f64 x x))))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 -1/2 x (fma.f64 1/4 (*.f64 x x) 1)))
(fma.f64 -1/2 x (fma.f64 -1/8 (pow.f64 x 3) (fma.f64 x (*.f64 x 1/4) 1)))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 x (fma.f64 x 1/4 -1/2) 1))
(fma.f64 x (+.f64 -1/2 (*.f64 x (fma.f64 x -1/8 1/4))) 1)
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 2 x) (/.f64 4 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -4 (*.f64 x x)))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 8 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 4 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 -4 (*.f64 x x))) (/.f64 8 (pow.f64 x 3)))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (pow.f64 x 3)) (/.f64 -4 (*.f64 x x))))
(+.f64 (/.f64 2 x) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 8 x) 4)))
(+.f64 (/.f64 2 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 8 x) -4)))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (pow.f64 x 3))) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 16 (pow.f64 x 4))))
(+.f64 (/.f64 8 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 2 x) (/.f64 -4 (*.f64 x x))) (/.f64 16 (pow.f64 x 4))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (pow.f64 x 3)) (-.f64 (/.f64 -16 (pow.f64 x 4)) (/.f64 4 (*.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (pow.f64 x 3)) (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -16 (pow.f64 x 4)))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 2 x) (/.f64 4 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -4 (*.f64 x x)))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 8 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 4 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 -4 (*.f64 x x))) (/.f64 8 (pow.f64 x 3)))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (pow.f64 x 3)) (/.f64 -4 (*.f64 x x))))
(+.f64 (/.f64 2 x) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 8 x) 4)))
(+.f64 (/.f64 2 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 8 x) -4)))
(-.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (pow.f64 x 3))) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 16 (pow.f64 x 4))))
(+.f64 (/.f64 8 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 2 x) (/.f64 -4 (*.f64 x x))) (/.f64 16 (pow.f64 x 4))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (pow.f64 x 3)) (-.f64 (/.f64 -16 (pow.f64 x 4)) (/.f64 4 (*.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (pow.f64 x 3)) (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -16 (pow.f64 x 4)))))

localize31.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (+.f64 1 x) -1/2)
0.2b
(/.f64 1 (sqrt.f64 x))
✓9.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
Compiler

Compiled 28 to 19 computations (32.1% saved)

series4.0ms (0%)

Counts
1 → 2
Calls

3 calls:

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

rewrite90.0ms (0.9%)

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
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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))))))

simplify31.0ms (0.3%)

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)))

eval333.0ms (3.2%)

Compiler

Compiled 13490 to 10432 computations (22.7% saved)

prune92.0ms (0.9%)

Pruning

29 alts after pruning (21 fresh and 8 done)

PrunedKeptTotal
New5865591
Fresh11617
Picked101
Done2810
Total59029619
Error
0b
Counts
619 → 29
Alt Table
Click to see full alt table
StatusErrorProgram
✓29.4b
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
1.5b
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (exp.f64 (*.f64 1/6 (log1p.f64 x)))))
✓34.4b
(pow.f64 x -1/2)
29.6b
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
47.5b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
34.3b
(-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
34.4b
(sqrt.f64 (/.f64 1 x))
6.5b
(/.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)))
23.1b
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
62.3b
(-.f64 (*.f64 1/2 x) 1)
✓23.2b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
28.4b
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
44.4b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (pow.f64 (+.f64 1 x) -1/2))
34.6b
(-.f64 (pow.f64 x -1/2) 1)
✓61.3b
(*.f64 1/2 x)
34.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
✓23.2b
(/.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)))))
✓34.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
29.4b
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
✓34.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
30.0b
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
✓23.0b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
36.6b
(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
29.3b
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
33.1b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
33.9b
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
6.5b
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
33.0b
(/.f64 1 (+.f64 x (sqrt.f64 x)))
62.8b
-1
Compiler

Compiled 353 to 276 computations (21.8% saved)

regimes111.0ms (1.1%)

Counts
75 → 1
Calls
Call 1
Inputs
-1
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
(-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -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 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (+.f64 1 x) 1/2)))
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
(/.f64 (/.f64 1 (*.f64 x 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 (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 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 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.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)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
(-.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 (pow.f64 (pow.f64 x 3/2) -1/3) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 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 (/.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 (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 (-.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 (*.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))))
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x)))) (pow.f64 (+.f64 1 x) -1/6) (pow.f64 x -1/2))
(*.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 (/.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)))))
(fma.f64 1/2 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (*.f64 x x)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2))))
(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 1 (cbrt.f64 (+.f64 1 x))) (/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (exp.f64 (*.f64 1/6 (log1p.f64 x)))))
(/.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)))))))
(fma.f64 1/2 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (*.f64 x x)) (fma.f64 5/16 (/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (pow.f64 x 4)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 -1 (/.f64 -1 x)) -1/2)))))
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 x))) (/.f64 (/.f64 1 (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x)))))
(fma.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 (*.f64 x (+.f64 1 x)) -1/2)))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
(+.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))))))
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (sqrt.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 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
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:

45.0ms
x
16.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
15.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.4b1x
0.4b1(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.4b1(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 1174 to 891 computations (24.1% saved)

regimes129.0ms (1.2%)

Counts
64 → 2
Calls
Call 1
Inputs
-1
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
(-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -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 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (+.f64 1 x) 1/2)))
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
(/.f64 (/.f64 1 (*.f64 x 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 (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 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 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.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)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
(-.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 (pow.f64 (pow.f64 x 3/2) -1/3) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 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 (/.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 (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 (-.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 (*.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))))
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
(fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x)))) (pow.f64 (+.f64 1 x) -1/6) (pow.f64 x -1/2))
(*.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)))
Outputs
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
Calls

3 calls:

62.0ms
x
22.0ms
(-.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
0.2b2x
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 830 to 623 computations (24.9% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.0992024391739963e-7
0.002357729061656849
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes123.0ms (1.2%)

Counts
60 → 2
Calls
Call 1
Inputs
-1
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
(-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -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 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (+.f64 1 x) 1/2)))
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 1 x) x)) 1) (sqrt.f64 (+.f64 1 x)))
(/.f64 (/.f64 1 (*.f64 x 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 (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 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 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) x) (+.f64 1 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.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)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
(-.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 (pow.f64 (pow.f64 x 3/2) -1/3) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 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 (/.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 (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 (-.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 (*.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))))
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
Outputs
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
Calls

3 calls:

64.0ms
x
19.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
18.0ms
(-.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 765 to 574 computations (25% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.0992024391739963e-7
0.002357729061656849
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes33.0ms (0.3%)

Counts
25 → 2
Calls
Call 1
Inputs
-1
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
(-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
Outputs
(-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
Calls

1 calls:

24.0ms
x
Results
ErrorSegmentsBranch
0.9b2x
Compiler

Compiled 223 to 165 computations (26% saved)

bsearch22.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
0.221759216495619
2.3047089771102423
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes30.0ms (0.3%)

Counts
22 → 2
Calls
Call 1
Inputs
-1
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
(-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
Outputs
(-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16)))))))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
Calls

1 calls:

24.0ms
x
Results
ErrorSegmentsBranch
1.1b2x
Compiler

Compiled 180 to 134 computations (25.6% saved)

bsearch23.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
0.221759216495619
2.3047089771102423
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes29.0ms (0.3%)

Counts
21 → 2
Calls
Call 1
Inputs
-1
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 (pow.f64 (/.f64 -1 (/.f64 -1 x)) 1/2) (/.f64 (*.f64 x x) 1/2))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (*.f64 2 (sqrt.f64 (/.f64 1 x))))
Outputs
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
Calls

1 calls:

23.0ms
x
Results
ErrorSegmentsBranch
1.3b2x
Compiler

Compiled 163 to 121 computations (25.8% saved)

bsearch25.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
24.0ms
0.221759216495619
2.3047089771102423
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes23.0ms (0.2%)

Counts
17 → 2
Calls
Call 1
Inputs
-1
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (sqrt.f64 (/.f64 1 x))) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
Outputs
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
Calls

1 calls:

19.0ms
x
Results
ErrorSegmentsBranch
1.7b2x
Compiler

Compiled 111 to 81 computations (27% saved)

bsearch23.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
23.0ms
0.221759216495619
2.3047089771102423
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes23.0ms (0.2%)

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

1 calls:

18.0ms
x
Results
ErrorSegmentsBranch
1.8b2x
Compiler

Compiled 100 to 72 computations (28% saved)

bsearch22.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
0.221759216495619
2.3047089771102423
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes20.0ms (0.2%)

Counts
13 → 2
Calls
Call 1
Inputs
-1
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
Outputs
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
Calls

1 calls:

17.0ms
x
Results
ErrorSegmentsBranch
2.0b2x
Compiler

Compiled 71 to 50 computations (29.6% saved)

bsearch23.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
23.0ms
0.221759216495619
2.3047089771102423
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes18.0ms (0.2%)

Counts
12 → 2
Calls
Call 1
Inputs
-1
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) 1)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(*.f64 (pow.f64 x -1/2) (/.f64 1/2 x))
(/.f64 1 (*.f64 2 (pow.f64 x 3/2)))
Outputs
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
Calls

1 calls:

15.0ms
x
Results
ErrorSegmentsBranch
2.1b2x
Compiler

Compiled 63 to 44 computations (30.2% saved)

bsearch23.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
23.0ms
0.221759216495619
2.3047089771102423
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes9.0ms (0.1%)

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

1 calls:

6.0ms
x
Results
ErrorSegmentsBranch
33.0b1x
Compiler

Compiled 42 to 28 computations (33.3% saved)

regimes7.0ms (0.1%)

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

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
34.4b1x
Compiler

Compiled 24 to 18 computations (25% saved)

regimes5.0ms (0%)

Accuracy

Total -1.6b remaining (-2.6%)

Threshold costs -1.6b (-2.6%)

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

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
61.3b1x
Compiler

Compiled 12 to 9 computations (25% saved)

simplify32.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
33×+-commutative_binary64
20×*-commutative_binary64
20×sub-neg_binary64
13×neg-sub0_binary64
13×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075434
1112434
2141434
3170434
4186434
5198434
6207434
7218434
8221434
9222434
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.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)))) 944473296573929/4722366482869645213696) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))) (fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 944473296573929/4722366482869645213696) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16))))))) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16))))))) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1))) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1))) (/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1)) (/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) 1) (/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) 1) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(pow.f64 x -1/2)
(*.f64 1/2 x)
-1
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)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 944473296573929/4722366482869645213696) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))) (fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 944473296573929/4722366482869645213696) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))) (fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2)))
(if (<=.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) 944473296573929/4722366482869645213696) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))) (fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 944473296573929/4722366482869645213696) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))) (-.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)))) 944473296573929/4722366482869645213696) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))) (-.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)))) 944473296573929/4722366482869645213696) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16))))))) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 7989717798205143/36028797018963968) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16))))))) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16))))))) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x))))
(if (<=.f64 x 7989717798205143/36028797018963968) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 3/8 (*.f64 x -5/16))))))) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1))) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x))))
(if (<=.f64 x 7989717798205143/36028797018963968) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 1 (*.f64 x 1/2)))) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1))) (/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x))))
(if (<=.f64 x 7989717798205143/36028797018963968) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 1 (*.f64 x 1/2)))) (/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1)) (/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x))))
(if (<=.f64 x 7989717798205143/36028797018963968) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x -1/2))) (/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) 1) (/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x))))
(if (<=.f64 x 7989717798205143/36028797018963968) (+.f64 (pow.f64 x -1/2) -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x))))
(if (<=.f64 x 4090735512681033216/18446744073709551616) (-.f64 (pow.f64 x -1/2) 1) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 7989717798205143/36028797018963968) (+.f64 (pow.f64 x -1/2) -1) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(pow.f64 x -1/2)
(*.f64 1/2 x)
(*.f64 x 1/2)
-1
Compiler

Compiled 307 to 235 computations (23.5% saved)

soundness107.0ms (1%)

Algorithm
1×egg-herbie
Rules
738×times-frac_binary64
478×associate-/l*_binary64
416×associate-/r*_binary64
375×unswap-sqr_binary64
362×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
099797
1268765
2687609
31971514
47380469
Stop Event
1×node limit
Compiler

Compiled 984 to 835 computations (15.1% saved)

end168.0ms (1.6%)

Compiler

Compiled 294 to 217 computations (26.2% saved)

Profiling

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