Details

Time bar (total: 11.4s)

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)

sample2.0s (17.8%)

Results
938.0ms2328×body1024valid
808.0ms4935×body256valid
272.0ms993×body512valid

preprocess19.0ms (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)

simplify15.0ms (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
16.3b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶16.3b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 12 to 10 computations (16.7% saved)

localize14.0ms (0.1%)

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))
✓2.7b
(-.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))))
1.0ms
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))

rewrite84.0ms (0.7%)

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))))))

simplify161.0ms (1.4%)

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)

eval99.0ms (0.9%)

Compiler

Compiled 4484 to 3575 computations (20.3% saved)

prune70.0ms (0.6%)

Pruning

29 alts after pruning (28 fresh and 1 done)

PrunedKeptTotal
New21428242
Fresh000
Picked011
Done000
Total21429243
Error
15.8b
Counts
243 → 29
Alt Table
Click to see full alt table
StatusErrorProgram
▶29.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
19.3b
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.5b
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
21.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
27.4b
(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))
▶23.9b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
▶29.5b
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
27.8b
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
16.4b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
27.4b
(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
22.8b
(/.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)))))
29.6b
(/.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 3)) (+.f64 (/.f64 1 x) (-.f64 (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2) (*.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))))
▶16.2b
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
✓16.3b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
24.3b
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
41.6b
(-.f64 (pow.f64 (pow.f64 x 3/2) -1/3) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
28.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
20.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
27.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
18.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
16.3b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
40.9b
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.5b
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
18.6b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.5b
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
16.3b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
27.7b
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
▶46.1b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
Compiler

Compiled 916 to 748 computations (18.3% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 x (+.f64 1 x))
✓0.0b
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
✓2.7b
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓15.8b
(pow.f64 (*.f64 x (+.f64 1 x)) -1/2)
Compiler

Compiled 47 to 31 computations (34% saved)

series13.0ms (0.1%)

Counts
4 → 25
Calls

12 calls:

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

rewrite80.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
542×log-prod_binary64
516×fma-def_binary64
427×pow-prod-down_binary64
298×pow2_binary64
232×fma-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01151
124551
2326045
Stop Event
1×node limit
Counts
4 → 192
Calls
Call 1
Inputs
(pow.f64 (*.f64 x (+.f64 1 x)) -1/2)
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(*.f64 x (+.f64 1 x))
Outputs
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(*.f64 (cbrt.f64 x) 1) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1) (*.f64 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 3/4) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 3/4) (*.f64 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/4) (pow.f64 x 1/4) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/4) (pow.f64 x 1/4) (*.f64 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (pow.f64 (cbrt.f64 x) 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 x) (cbrt.f64 x)) (pow.f64 x 1/6) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 x) (cbrt.f64 x)) (pow.f64 x 1/6) (*.f64 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) x)))))

simplify46.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
712×times-frac_binary64
554×fma-def_binary64
473×associate-*l*_binary64
378×associate-*r*_binary64
373×associate-*r/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
045282
1119264
2285258
3713258
42119258
Stop Event
1×node limit
Counts
217 → 218
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 1 x))
(+.f64 (*.f64 -1/2 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 x)))
(+.f64 (*.f64 -1/2 (sqrt.f64 x)) (+.f64 (*.f64 3/8 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 -5/16 (sqrt.f64 (pow.f64 x 5))) (+.f64 (*.f64 -1/2 (sqrt.f64 x)) (+.f64 (*.f64 3/8 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 4))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))))
(/.f64 -1 x)
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 4))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
1
x
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
Outputs
(sqrt.f64 (/.f64 1 x))
(+.f64 (*.f64 -1/2 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 x)))
(fma.f64 -1/2 (sqrt.f64 x) (sqrt.f64 (/.f64 1 x)))
(+.f64 (*.f64 -1/2 (sqrt.f64 x)) (+.f64 (*.f64 3/8 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1/2 (sqrt.f64 x) (fma.f64 3/8 (sqrt.f64 (pow.f64 x 3)) (sqrt.f64 (/.f64 1 x))))
(fma.f64 3/8 (pow.f64 x 3/2) (fma.f64 -1/2 (sqrt.f64 x) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1/2 (sqrt.f64 x) (fma.f64 3/8 (pow.f64 x 3/2) (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 -5/16 (sqrt.f64 (pow.f64 x 5))) (+.f64 (*.f64 -1/2 (sqrt.f64 x)) (+.f64 (*.f64 3/8 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -5/16 (sqrt.f64 (pow.f64 x 5)) (fma.f64 -1/2 (sqrt.f64 x) (fma.f64 3/8 (sqrt.f64 (pow.f64 x 3)) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -5/16 (pow.f64 x 5/2) (fma.f64 3/8 (pow.f64 x 3/2) (fma.f64 -1/2 (sqrt.f64 x) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -1/2 (sqrt.f64 x) (fma.f64 3/8 (pow.f64 x 3/2) (fma.f64 -5/16 (pow.f64 x 5/2) (sqrt.f64 (/.f64 1 x)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x)))
(+.f64 (/.f64 1 x) (/.f64 (/.f64 -1/2 x) x))
(-.f64 (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3/8 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 3/8 (pow.f64 x 3)) (/.f64 1/2 (*.f64 x x))))
(+.f64 (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x))) (/.f64 3/8 (pow.f64 x 3)))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1/2 x) x)) (/.f64 3/8 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 4))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 3/8 (pow.f64 x 3))) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 5/16 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 1 x) (-.f64 (/.f64 3/8 (pow.f64 x 3)) (/.f64 5/16 (pow.f64 x 4)))) (/.f64 -1/2 (*.f64 x x)))
(+.f64 (+.f64 (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x))) (/.f64 3/8 (pow.f64 x 3))) (/.f64 -5/16 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1/2 x) x)) (+.f64 (/.f64 3/8 (pow.f64 x 3)) (/.f64 -5/16 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1/2 x) x)) (*.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 3/8 (/.f64 -5/16 x))))
(/.f64 -1 x)
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))
(-.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1 x))
(+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 -1 x))
(-.f64 (/.f64 -1 x) (/.f64 (/.f64 -1/2 x) x))
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(-.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 3/8 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 -1 x)) (/.f64 3/8 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 (*.f64 x x)) (-.f64 (/.f64 -1 x) (/.f64 3/8 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (/.f64 -1 x) (/.f64 -3/8 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 4))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(+.f64 (/.f64 5/16 (pow.f64 x 4)) (-.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 3/8 (pow.f64 x 3)))))
(+.f64 (/.f64 5/16 (pow.f64 x 4)) (-.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 -1 x)) (/.f64 3/8 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 (*.f64 x x)) (-.f64 (-.f64 (/.f64 5/16 (pow.f64 x 4)) (/.f64 1 x)) (/.f64 3/8 (pow.f64 x 3))))
(-.f64 (-.f64 (+.f64 (/.f64 5/16 (pow.f64 x 4)) (/.f64 -1 x)) (/.f64 3/8 (pow.f64 x 3))) (/.f64 (/.f64 -1/2 x) x))
(+.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (/.f64 5/16 (pow.f64 x 4)) (+.f64 (/.f64 -1 x) (/.f64 -3/8 (pow.f64 x 3)))))
1
x
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(+.f64 x (*.f64 x x))
(fma.f64 x x x)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 15 to 9 computations (40% saved)

localize22.0ms (0.2%)

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)))
✓10.1b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
✓34.1b
(pow.f64 (*.f64 x x) -1/4)
Compiler

Compiled 37 to 24 computations (35.1% saved)

series34.0ms (0.3%)

Counts
2 → 18
Calls

6 calls:

TimeVariablePointExpression
22.0ms
x
@0
(pow.f64 (*.f64 x x) -1/4)
11.0ms
x
@inf
(pow.f64 (*.f64 x x) -1/4)
0.0ms
x
@inf
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0ms
x
@-inf
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0ms
x
@-inf
(pow.f64 (*.f64 x x) -1/4)

rewrite73.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
545×prod-diff_binary64
451×log-prod_binary64
326×fma-def_binary64
295×pow-prod-down_binary64
271×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01025
122817
2301317
Stop Event
1×node limit
Counts
2 → 129
Calls
Call 1
Inputs
(pow.f64 (*.f64 x x) -1/4)
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (/.f64 -1 (sqrt.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) -1/6)) (cbrt.f64 (/.f64 1 (+.f64 x 1))) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (+.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 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 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x 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simplify46.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
940×fma-def_binary64
914×cancel-sign-sub-inv_binary64
602×unswap-sqr_binary64
580×distribute-rgt-neg-in_binary64
564×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
030174
175172
2181170
3499164
41435161
54417161
Stop Event
1×node limit
Counts
147 → 140
Calls
Call 1
Inputs
(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))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))
(-.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)
(sqrt.f64 (/.f64 1 x))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))
Outputs
(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))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 -1))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 -1))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 -1))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 -1))
(-.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 -1 (fma.f64 x 1/2 (pow.f64 x -1/2)))
(-.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 -1 (fma.f64 x 1/2 (fma.f64 -3/8 (*.f64 x x) (pow.f64 x -1/2))))
(+.f64 -1 (fma.f64 x (*.f64 x -3/8) (fma.f64 x 1/2 (pow.f64 x -1/2))))
(+.f64 -1 (fma.f64 x (fma.f64 x -3/8 1/2) (pow.f64 x -1/2)))
(fma.f64 x (fma.f64 x -3/8 1/2) (+.f64 -1 (pow.f64 x -1/2)))
(-.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 -1 (+.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) (fma.f64 -3/8 (*.f64 x x) (*.f64 5/16 (pow.f64 x 3)))))
(+.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 -1 (fma.f64 5/16 (pow.f64 x 3) (fma.f64 x (fma.f64 x -3/8 1/2) (pow.f64 x -1/2))))
(fma.f64 x (fma.f64 x (fma.f64 x 5/16 -3/8) 1/2) (+.f64 -1 (pow.f64 x -1/2)))
(sqrt.f64 (/.f64 1 x))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 -1))

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(cbrt.f64 (+.f64 1 x))
✓0.2b
(pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2)
0.2b
(/.f64 1 (sqrt.f64 x))
✓15.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
Compiler

Compiled 34 to 24 computations (29.4% saved)

series7.0ms (0.1%)

Counts
3 → 8
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
1.0ms
x
@-inf
(cbrt.f64 (+.f64 1 x))
1.0ms
x
@-inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
1.0ms
x
@0
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
1.0ms
x
@-inf
(pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2)

rewrite84.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
595×prod-diff_binary64
442×log-prod_binary64
311×fma-def_binary64
286×pow-prod-down_binary64
267×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01032
122426
2291626
Stop Event
1×node limit
Counts
3 → 157
Calls
Call 1
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2)
(cbrt.f64 (+.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 1 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (cbrt.f64 (pow.f64 (+.f64 1 x) -1)) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (+.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (+.f64 1 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (+.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (exp.f64 (*.f64 2/3 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (*.f64 2/3 (log1p.f64 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) 1/6) (pow.f64 (+.f64 1 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 1 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x (-.f64 x 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (*.f64 2/3 (log1p.f64 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (sqrt.f64 x)) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (exp.f64 (*.f64 2/3 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/3 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 x)) 1))))))

simplify158.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
1215×fma-def_binary64
750×sqr-pow_binary64
605×cube-prod_binary64
421×fabs-mul_binary64
370×pow-sqr_binary64
Iterations

Useful iterations: 10 (0.0ms)

IterNodesCost
03084
17578
218274
352362
4135758
5241158
6293858
7307258
8322658
9341658
10367156
11432956
12473656
13526456
14592456
15675256
16715556
17751956
18785556
Stop Event
1×node limit
Counts
165 → 170
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 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))))
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 1 (*.f64 1/3 x))
(+.f64 1 (*.f64 x 1/3))
(fma.f64 x 1/3 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 x 1/3)))
(fma.f64 (*.f64 x x) -1/9 (fma.f64 x 1/3 1))
(fma.f64 x 1/3 (fma.f64 x (*.f64 x -1/9) 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 x 1/3))))
(fma.f64 (*.f64 x x) -1/9 (+.f64 1 (fma.f64 (pow.f64 x 3) 5/81 (*.f64 x 1/3))))
(fma.f64 x (*.f64 x -1/9) (fma.f64 (pow.f64 x 3) 5/81 (fma.f64 x 1/3 1)))
(fma.f64 x (fma.f64 x -1/9 1/3) (fma.f64 (pow.f64 x 3) 5/81 1))
(fma.f64 x (+.f64 1/3 (*.f64 x (fma.f64 x 5/81 -1/9))) 1)
(fma.f64 x (fma.f64 x (fma.f64 x 5/81 -1/9) 1/3) 1)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)))
✓0.6b
(cbrt.f64 (/.f64 1 x))
✓4.2b
(pow.f64 x -1/6)
✓27.5b
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 50 to 38 computations (24% saved)

series65.0ms (0.6%)

Counts
4 → 12
Calls

12 calls:

TimeVariablePointExpression
28.0ms
x
@0
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
14.0ms
x
@-inf
(pow.f64 x -1/6)
8.0ms
x
@inf
(pow.f64 x -1/6)
7.0ms
x
@0
(pow.f64 x -1/6)
4.0ms
x
@-inf
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite88.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
651×prod-diff_binary64
521×log-prod_binary64
366×fma-def_binary64
305×pow2_binary64
220×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01245
127127
2359627
Stop Event
1×node limit
Counts
4 → 207
Calls
Call 1
Inputs
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(pow.f64 x -1/6)
(cbrt.f64 (/.f64 1 x))
(*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) 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 (/.f64 1 (+.f64 x 1))) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (+.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/6) (/.f64 1 (cbrt.f64 x)) (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x)))) -1 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (pow.f64 x -1/2) (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x)))) -1 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6) (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x)))) -1 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/2) 1 (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x)))) -1 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 (cbrt.f64 (cbrt.f64 x))) (*.f64 (cbrt.f64 (pow.f64 x -1/6)) (/.f64 1 (cbrt.f64 x))) (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x)))) -1 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x -2))) (*.f64 (/.f64 1 (cbrt.f64 (cbrt.f64 x))) (pow.f64 x -1/6)) (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (cbrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (cbrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (cbrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (cbrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (cbrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/6) (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (cbrt.f64 x))) (*.f64 (cbrt.f64 (pow.f64 x -1/6)) (pow.f64 x -1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x -1/2)) (pow.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/12) (sqrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x -1/6) (/.f64 1 (cbrt.f64 (cbrt.f64 x)))) (cbrt.f64 (pow.f64 x -1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (cbrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (cbrt.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) -1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (cbrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (cbrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/3 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/3 (log.f64 x)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 x -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 x -1/6) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 x -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 x -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 x -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 x)) 1))))))

simplify51.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
625×fma-def_binary64
607×div-sub_binary64
522×associate-*r*_binary64
480×fma-neg_binary64
433×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01584
13784
27484
316584
445448
5129948
6570348
Stop Event
1×node limit
Counts
219 → 210
Calls
Call 1
Inputs
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 (/.f64 1 x) 1/6)
(exp.f64 (*.f64 -1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(exp.f64 (*.f64 -1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(exp.f64 (*.f64 -1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(exp.f64 (*.f64 -1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
Outputs
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(exp.f64 (*.f64 -1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(exp.f64 (*.f64 -1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(exp.f64 (*.f64 -1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)
(exp.f64 (*.f64 -1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (/.f64 1 x) 1/6)
(pow.f64 x -1/6)

eval1.0s (9.1%)

Compiler

Compiled 17946 to 13450 computations (25.1% saved)

prune275.0ms (2.4%)

Pruning

30 alts after pruning (29 fresh and 1 done)

PrunedKeptTotal
New87022892
Fresh16723
Picked101
Done415
Total89130921
Error
14.8b
Counts
921 → 30
Alt Table
Click to see full alt table
StatusErrorProgram
▶19.3b
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
16.3b
(*.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
28.7b
(fma.f64 (*.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 1 (cbrt.f64 (cbrt.f64 x)))) (cbrt.f64 (pow.f64 x -1/6)) (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))))
▶15.2b
(/.f64 (*.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
▶27.4b
(fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))
18.1b
(*.f64 1 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
21.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
15.2b
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
27.7b
(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x -1/2)) (sqrt.f64 (pow.f64 x -1/2)) (neg.f64 (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (/.f64 1 (cbrt.f64 (+.f64 x 1)))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2))) (/.f64 1 (cbrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (/.f64 1 (cbrt.f64 (+.f64 x 1))))))
16.3b
(fma.f64 (pow.f64 (fma.f64 x x x) -1/2) (sqrt.f64 (+.f64 x 1)) (*.f64 (pow.f64 (fma.f64 x x x) -1/2) (neg.f64 (sqrt.f64 x))))
16.4b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))
22.8b
(/.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)))))
27.4b
(fma.f64 (pow.f64 (+.f64 x 1) -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 x -1/2))
✓16.2b
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
29.0b
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
46.1b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (pow.f64 (+.f64 1 x) -1/2))
▶29.5b
(-.f64 (pow.f64 x -1/2) 1)
16.2b
(+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
27.8b
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))
28.6b
(fma.f64 (/.f64 1 (cbrt.f64 (cbrt.f64 x))) (*.f64 (cbrt.f64 (pow.f64 x -1/6)) (/.f64 1 (cbrt.f64 x))) (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))))
16.3b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 x 1))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
50.4b
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1/2 x) x)))
18.6b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
16.1b
(*.f64 (fma.f64 (pow.f64 x 1/4) (neg.f64 (pow.f64 x 1/4)) (sqrt.f64 (+.f64 x 1))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
27.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
16.3b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
29.5b
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
48.5b
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 1 x))
28.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
▶20.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
Compiler

Compiled 1024 to 804 computations (21.5% saved)

localize62.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓0.0b
(/.f64 (*.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓1.7b
(+.f64 x (-.f64 1 x))
✓15.8b
(pow.f64 (fma.f64 x x x) -1/2)
Compiler

Compiled 70 to 38 computations (45.7% saved)

series24.0ms (0.2%)

Counts
4 → 25
Calls

12 calls:

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

rewrite158.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
730×fma-def_binary64
395×fma-neg_binary64
274×expm1-udef_binary64
274×log1p-udef_binary64
231×log-pow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01456
133050
2493450
Stop Event
1×node limit
Counts
4 → 218
Calls
Call 1
Inputs
(pow.f64 (fma.f64 x x x) -1/2)
(+.f64 x (-.f64 1 x))
(/.f64 (*.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
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egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (*.f64 x x))) (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x x)) 1/2) (pow.f64 (cbrt.f64 x) 1/2) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2) (sqrt.f64 x))))))

simplify109.0ms (1%)

Algorithm
1×egg-herbie
Rules
712×times-frac_binary64
505×fma-def_binary64
453×associate-*l*_binary64
372×associate-*r/_binary64
366×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
044222
1117222
2279216
3698216
42073216
Stop Event
1×node limit
Counts
243 → 240
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 1 x))
(+.f64 (*.f64 -1/2 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 x)))
(+.f64 (*.f64 -1/2 (sqrt.f64 x)) (+.f64 (*.f64 3/8 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 -5/16 (sqrt.f64 (pow.f64 x 5))) (+.f64 (*.f64 -1/2 (sqrt.f64 x)) (+.f64 (*.f64 3/8 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 4))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))))
(/.f64 -1 x)
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 4))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
1
1
1
1
1
1
1
1
1
1
1
1
1
Outputs
(sqrt.f64 (/.f64 1 x))
(+.f64 (*.f64 -1/2 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 x)))
(fma.f64 -1/2 (sqrt.f64 x) (sqrt.f64 (/.f64 1 x)))
(+.f64 (*.f64 -1/2 (sqrt.f64 x)) (+.f64 (*.f64 3/8 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1/2 (sqrt.f64 x) (fma.f64 3/8 (sqrt.f64 (pow.f64 x 3)) (sqrt.f64 (/.f64 1 x))))
(fma.f64 3/8 (pow.f64 x 3/2) (fma.f64 -1/2 (sqrt.f64 x) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1/2 (sqrt.f64 x) (fma.f64 3/8 (pow.f64 x 3/2) (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 -5/16 (sqrt.f64 (pow.f64 x 5))) (+.f64 (*.f64 -1/2 (sqrt.f64 x)) (+.f64 (*.f64 3/8 (sqrt.f64 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -5/16 (sqrt.f64 (pow.f64 x 5)) (fma.f64 -1/2 (sqrt.f64 x) (fma.f64 3/8 (sqrt.f64 (pow.f64 x 3)) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -5/16 (pow.f64 x 5/2) (fma.f64 3/8 (pow.f64 x 3/2) (fma.f64 -1/2 (sqrt.f64 x) (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -1/2 (sqrt.f64 x) (fma.f64 3/8 (pow.f64 x 3/2) (fma.f64 -5/16 (pow.f64 x 5/2) (sqrt.f64 (/.f64 1 x)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x)))
(+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x)))
(-.f64 (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3/8 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 3/8 (pow.f64 x 3)) (/.f64 -1/2 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))) (/.f64 3/8 (pow.f64 x 3)))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2)))
(-.f64 (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 4))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 3/8 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 5/16 (pow.f64 x 4)))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 3/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 5/16 (pow.f64 x 4)))))
(+.f64 (/.f64 3/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 -5/16 (pow.f64 x 4)))))
(+.f64 (-.f64 (/.f64 1 x) (/.f64 -3/8 (pow.f64 x 3))) (-.f64 (/.f64 -1/2 (*.f64 x x)) (/.f64 5/16 (pow.f64 x 4))))
(-.f64 (/.f64 -5/16 (pow.f64 x 4)) (-.f64 (/.f64 -1 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2))))
(/.f64 -1 x)
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))
(-.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1 x))
(+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 -1 x))
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(-.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 3/8 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 -1 x)) (/.f64 3/8 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (/.f64 -1 x) (/.f64 -3/8 (pow.f64 x 3))))
(-.f64 (/.f64 -1 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2)))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 4))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 3/8 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(+.f64 (/.f64 5/16 (pow.f64 x 4)) (-.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 3/8 (pow.f64 x 3)))))
(+.f64 (/.f64 5/16 (pow.f64 x 4)) (-.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 -1 x)) (/.f64 3/8 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (/.f64 5/16 (pow.f64 x 4)) (+.f64 (/.f64 -1 x) (/.f64 -3/8 (pow.f64 x 3)))))
(+.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 -1 x)) (+.f64 (/.f64 5/16 (pow.f64 x 4)) (/.f64 -3/8 (pow.f64 x 3))))
(+.f64 (/.f64 5/16 (pow.f64 x 4)) (-.f64 (/.f64 -1 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2))))
1
1
1
1
1
1
1
1
1
1
1
1
1

localize16.0ms (0.1%)

Compiler

Compiled 12 to 9 computations (25% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(sqrt.f64 (/.f64 1 x))
0.1b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓9.8b
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 34 to 26 computations (23.5% saved)

series5.0ms (0%)

Counts
2 → 0
Calls

6 calls:

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

rewrite230.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
564×prod-diff_binary64
431×log-prod_binary64
342×fma-def_binary64
294×pow-prod-down_binary64
246×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0923
120417
2281417
Stop Event
1×node limit
Counts
2 → 147
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(sqrt.f64 (/.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) 1 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 x)))) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (+.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 x))))) (pow.f64 (+.f64 1 x) -1/6) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (pow.f64 x -1/2) (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x)))) -1 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/2) 1 (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x)))) -1 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/6) (/.f64 1 (cbrt.f64 x)) (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x)))) -1 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6) (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x)))) -1 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1))) (fma.f64 (neg.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x)))) -1 (*.f64 (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (pow.f64 x -1/2) (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))))))))) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.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 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/6) (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/4) (pow.f64 x -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 x)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) -1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 x -1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 x -1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 x -3/2)) 1/3))))))

simplify15.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
147 → 147
Calls
Call 1
Inputs
Outputs

localize65.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2))
✓0.2b
(pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)
0.2b
(/.f64 1 (sqrt.f64 x))
✓11.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
Compiler

Compiled 49 to 38 computations (22.4% saved)

series42.0ms (0.4%)

Counts
3 → 16
Calls

9 calls:

TimeVariablePointExpression
33.0ms
x
@-inf
(pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)
3.0ms
x
@inf
(pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)
1.0ms
x
@inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
1.0ms
x
@-inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
1.0ms
x
@0
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))

rewrite149.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
900×prod-diff_binary64
534×log-prod_binary64
391×fma-def_binary64
215×expm1-udef_binary64
215×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01235
128326
2377826
Stop Event
1×node limit
Counts
3 → 222
Calls
Call 1
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
(pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)
(/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2))) (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2))))) (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) -1/4) (pow.f64 (+.f64 1 x) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)) (cbrt.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)) (*.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 (+.f64 1 x) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 -1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/8) (*.f64 (pow.f64 (+.f64 1 x) -1/8) (pow.f64 (+.f64 1 x) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 (+.f64 1 x) -1/8)) (pow.f64 (+.f64 1 x) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/4) (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2))) (cbrt.f64 (pow.f64 (+.f64 1 x) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -1/4) 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 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -3) 1/3)))) (#(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 (sqrt.f64 (+.f64 1 x)) -3))))) (#(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 -1/4 (log1p.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log1p.f64 x)) 1))))))

simplify95.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
504×fma-def_binary64
414×unswap-sqr_binary64
380×distribute-rgt-in_binary64
363×distribute-lft-in_binary64
363×distribute-rgt-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0100516
1280495
2932441
34187305
Stop Event
1×node limit
Counts
238 → 250
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 -2 (*.f64 (+.f64 (*.f64 -1/16 (pow.f64 (*.f64 1 x) 1/4)) (*.f64 5/32 (pow.f64 (*.f64 1 x) 1/4))) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))))
(+.f64 (*.f64 -2 (*.f64 (+.f64 (*.f64 -1/16 (pow.f64 (*.f64 1 x) 1/4)) (*.f64 5/32 (pow.f64 (*.f64 1 x) 1/4))) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))) (+.f64 (*.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (+.f64 (*.f64 1/4 (+.f64 (*.f64 -1/16 (pow.f64 (*.f64 1 x) 1/4)) (*.f64 5/32 (pow.f64 (*.f64 1 x) 1/4)))) (+.f64 (*.f64 5/128 (pow.f64 (*.f64 1 x) 1/4)) (*.f64 -15/128 (pow.f64 (*.f64 1 x) 1/4)))))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -1/2 (*.f64 (+.f64 (*.f64 -1/16 (pow.f64 (*.f64 1 x) 1/4)) (*.f64 5/32 (pow.f64 (*.f64 1 x) 1/4))) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4))))))))
(/.f64 1 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))) (/.f64 1 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))) (/.f64 1 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))) (/.f64 1 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))
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)))))
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) 1))
(fma.f64 1/2 x (fma.f64 -1/8 (*.f64 x x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 1) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) 1)))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))
(+.f64 (*.f64 -2 (*.f64 (+.f64 (*.f64 -1/16 (pow.f64 (*.f64 1 x) 1/4)) (*.f64 5/32 (pow.f64 (*.f64 1 x) 1/4))) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))))
(fma.f64 -2 (*.f64 (*.f64 (pow.f64 x 1/4) 3/32) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))))
(fma.f64 -2 (*.f64 (*.f64 (pow.f64 x 1/4) 3/32) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (*.f64 (pow.f64 x 1/4) -3/16) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (*.f64 (pow.f64 x 1/4) -3/16) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))))
(+.f64 (*.f64 -2 (*.f64 (+.f64 (*.f64 -1/16 (pow.f64 (*.f64 1 x) 1/4)) (*.f64 5/32 (pow.f64 (*.f64 1 x) 1/4))) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))) (+.f64 (*.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (+.f64 (*.f64 1/4 (+.f64 (*.f64 -1/16 (pow.f64 (*.f64 1 x) 1/4)) (*.f64 5/32 (pow.f64 (*.f64 1 x) 1/4)))) (+.f64 (*.f64 5/128 (pow.f64 (*.f64 1 x) 1/4)) (*.f64 -15/128 (pow.f64 (*.f64 1 x) 1/4)))))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -1/2 (*.f64 (+.f64 (*.f64 -1/16 (pow.f64 (*.f64 1 x) 1/4)) (*.f64 5/32 (pow.f64 (*.f64 1 x) 1/4))) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4))))))))
(fma.f64 -2 (*.f64 (*.f64 (pow.f64 x 1/4) 3/32) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)) (fma.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (fma.f64 1/4 (*.f64 (pow.f64 x 1/4) 3/32) (*.f64 (pow.f64 x 1/4) -5/64))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (*.f64 (*.f64 (pow.f64 x 1/4) 3/32) (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4))))))))
(fma.f64 -2 (*.f64 (*.f64 (pow.f64 x 1/4) 3/32) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)) (fma.f64 -2 (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (fma.f64 (pow.f64 x 1/4) -5/64 (*.f64 (pow.f64 x 1/4) 3/128))) (+.f64 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))) (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (*.f64 (*.f64 (pow.f64 x 1/4) 3/32) -1/2)))))
(fma.f64 -2 (fma.f64 (*.f64 (pow.f64 x 1/4) 3/32) (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (*.f64 (pow.f64 x 1/4) -7/128))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (*.f64 (pow.f64 x 1/4) -3/64) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (*.f64 (pow.f64 x 1/4) -3/16) (+.f64 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))) (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (+.f64 (*.f64 (pow.f64 x 1/4) -3/64) (*.f64 -2 (*.f64 (pow.f64 x 1/4) -7/128))))))
(/.f64 1 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(/.f64 1 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(/.f64 1 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(exp.f64 (neg.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -1/2)))
(exp.f64 (*.f64 (log.f64 x) 1/2))
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))) (/.f64 1 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))
(+.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) (/.f64 1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))))
(+.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (/.f64 (/.f64 1/2 x) (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))
(+.f64 (exp.f64 (neg.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -1/2))) (/.f64 (/.f64 1/2 x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2)))
(*.f64 (+.f64 (/.f64 1/2 x) 1) (exp.f64 (*.f64 (log.f64 x) 1/2)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))) (/.f64 1 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))
(+.f64 (/.f64 1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))) (-.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) (/.f64 1/8 (*.f64 (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)))))
(+.f64 (/.f64 (/.f64 1/2 x) (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (+.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (/.f64 -1/8 (*.f64 (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))))
(+.f64 (exp.f64 (neg.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -1/2))) (+.f64 (/.f64 (/.f64 1/2 x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2)) (/.f64 -1/8 (*.f64 (*.f64 x x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2)))))
(+.f64 (exp.f64 (*.f64 (log.f64 x) 1/2)) (*.f64 (/.f64 (exp.f64 (*.f64 (log.f64 x) 1/2)) x) (-.f64 1/2 (/.f64 1/8 x))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))) (/.f64 1 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (exp.f64 (*.f64 -1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))
(+.f64 (/.f64 1/16 (*.f64 (pow.f64 x 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))) (+.f64 (/.f64 1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))) (-.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) (/.f64 1/8 (*.f64 (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 -1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))))))
(+.f64 (+.f64 (/.f64 (/.f64 1/2 x) (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (+.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (/.f64 -1/8 (*.f64 (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))))) (/.f64 1/16 (*.f64 (pow.f64 x 3) (pow.f64 (pow.f64 (exp.f64 -1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))))
(+.f64 (exp.f64 (neg.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -1/2))) (+.f64 (/.f64 (/.f64 1/2 x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2)) (+.f64 (/.f64 (/.f64 1/16 (pow.f64 x 3)) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2)) (/.f64 -1/8 (*.f64 (*.f64 x x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) 1/4) (pow.f64 -1 -1/4)) 2))))))
(+.f64 (*.f64 (+.f64 (/.f64 1/2 x) 1) (exp.f64 (*.f64 (log.f64 x) 1/2))) (*.f64 (/.f64 (exp.f64 (*.f64 (log.f64 x) 1/2)) (*.f64 x x)) (-.f64 (/.f64 1/16 x) 1/8)))
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))
(fma.f64 x -1/2 (fma.f64 x (*.f64 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 (*.f64 x -5/16) 3/8)))))

localize180.0ms (1.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (+.f64 x 1))
✓0.3b
(cbrt.f64 (/.f64 1 (+.f64 x 1)))
✓0.3b
(cbrt.f64 (pow.f64 (+.f64 x 1) -1/2))
✓27.4b
(fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))
Compiler

Compiled 56 to 45 computations (19.6% saved)

series19.0ms (0.2%)

Counts
4 → 34
Calls

12 calls:

TimeVariablePointExpression
6.0ms
x
@0
(cbrt.f64 (pow.f64 (+.f64 x 1) -1/2))
3.0ms
x
@-inf
(fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))
3.0ms
x
@inf
(fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))
1.0ms
x
@0
(fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))
1.0ms
x
@inf
(cbrt.f64 (pow.f64 (+.f64 x 1) -1/2))

rewrite154.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
451×log-prod_binary64
294×prod-diff_binary64
289×pow-prod-down_binary64
265×pow2_binary64
198×pow-to-exp_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01251
125736
2314135
Stop Event
1×node limit
Counts
4 → 215
Calls
Call 1
Inputs
(fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))
(cbrt.f64 (pow.f64 (+.f64 x 1) -1/2))
(cbrt.f64 (/.f64 1 (+.f64 x 1)))
(/.f64 1 (+.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 2) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4)) (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 x) -3/2) (pow.f64 x -3/2)) (+.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (pow.f64 x -1) (pow.f64 (*.f64 (+.f64 1 x) x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 x -1)) (-.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2))) (exp.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)) (+.f64 1 (expm1.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2))) (+.f64 1 (expm1.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (pow.f64 x -1/2))) (exp.f64 (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (pow.f64 x -1/2)) (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (pow.f64 x -1/2))) (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 (pow.f64 (+.f64 1 x) -1/4) (pow.f64 x -1/4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 x -1/2))) 1) 1))))))
((#(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 (pow.f64 (pow.f64 (+.f64 1 x) -1/18) 2) (pow.f64 (+.f64 1 x) -1/18))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/18) (pow.f64 (pow.f64 (+.f64 1 x) -1/18) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/12) (pow.f64 (+.f64 1 x) -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 -1) (pow.f64 (+.f64 1 x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (pow.f64 (+.f64 1 x) -1/18) 4)) (sqrt.f64 (pow.f64 (pow.f64 (+.f64 1 x) -1/18) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) -1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 x)) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (*.f64 -1/3 (log1p.f64 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -1/2) 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 (pow.f64 (+.f64 1 x) -3) 1/18)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -3/2) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 2) -1/12)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 3) -1/18)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (+.f64 1 x) -1/18) 2) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -1/18) 3)))) (#(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 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) -1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -1/12) 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) -1/4) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (exp.f64 (*.f64 -1/3 (log1p.f64 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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (*.f64 1/3 (log1p.f64 x))) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/3 (log1p.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 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2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 -1/6 (log1p.f64 x)) 1) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 x)))) 2)) (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 (exp.f64 (*.f64 -1/3 (log1p.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 x)) -2))))) (#(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 (pow.f64 (cbrt.f64 (+.f64 1 x)) -2) (exp.f64 (*.f64 -1/3 (log1p.f64 x))))))) 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(+.f64 1 x) -1/6))))) (#(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 (exp.f64 (*.f64 -1/3 (log1p.f64 x))) 3)))) (#(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) -1/6) 6)))) (#(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 (pow.f64 (+.f64 1 x) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -3/2) 2/3)))) (#(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 (pow.f64 (+.f64 1 x) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (+.f64 1 x) -1/18) 2) 9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 x)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 4) -1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 1 (+.f64 1 x)))))) (#(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 log.f64 (/.f64 1 (+.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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/3 (log1p.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log1p.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (neg.f64 (log1p.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log1p.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 x)) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 -1/3 (log1p.f64 x)) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 -1/2 (log1p.f64 x)) 1) 2))))))

simplify100.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
831×fma-neg_binary64
447×associate-*l*_binary64
403×fma-def_binary64
375×associate-*r*_binary64
316×times-frac_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0108660
1288644
2777567
32336504
46733503
Stop Event
1×node limit
Counts
249 → 266
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)
(sqrt.f64 (/.f64 1 x))
(exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
1
(+.f64 1 (*.f64 -1/6 x))
(+.f64 1 (+.f64 (*.f64 7/72 (pow.f64 x 2)) (*.f64 -1/6 x)))
(+.f64 1 (+.f64 (*.f64 7/72 (pow.f64 x 2)) (+.f64 (*.f64 -1/6 x) (*.f64 -91/1296 (pow.f64 x 3)))))
(pow.f64 (/.f64 1 x) 1/6)
(+.f64 (pow.f64 (/.f64 1 x) 1/6) (*.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6)))
(+.f64 (pow.f64 (/.f64 1 x) 1/6) (+.f64 (*.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6)) (*.f64 7/72 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/6))))
(+.f64 (*.f64 -91/1296 (pow.f64 (/.f64 1 (pow.f64 x 19)) 1/6)) (+.f64 (pow.f64 (/.f64 1 x) 1/6) (+.f64 (*.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6)) (*.f64 7/72 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/6)))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(+.f64 (*.f64 -1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x)) (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(+.f64 (*.f64 7/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 -1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x)) (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(+.f64 (*.f64 7/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 -1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x)) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (*.f64 -91/1296 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (pow.f64 x 3))))))
1
(+.f64 1 (*.f64 -1/3 x))
(+.f64 1 (+.f64 (*.f64 -1/3 x) (*.f64 2/9 (pow.f64 x 2))))
(+.f64 (*.f64 -14/81 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 -1/3 x) (*.f64 2/9 (pow.f64 x 2)))))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (+.f64 (*.f64 -1 x) (pow.f64 x 2)))
(+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 -1 x) (pow.f64 x 2))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
Outputs
(-.f64 (pow.f64 x -1/2) 1)
(+.f64 (pow.f64 x -1/2) -1)
(-.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 x (*.f64 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))
(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 x -1/2)
1
(+.f64 1 (*.f64 -1/6 x))
(+.f64 1 (*.f64 x -1/6))
(fma.f64 x -1/6 1)
(+.f64 1 (+.f64 (*.f64 7/72 (pow.f64 x 2)) (*.f64 -1/6 x)))
(+.f64 1 (fma.f64 7/72 (*.f64 x x) (*.f64 x -1/6)))
(+.f64 1 (fma.f64 (*.f64 x x) 7/72 (*.f64 x -1/6)))
(fma.f64 x -1/6 (fma.f64 (*.f64 x x) 7/72 1))
(fma.f64 x -1/6 (fma.f64 x (*.f64 x 7/72) 1))
(+.f64 1 (+.f64 (*.f64 7/72 (pow.f64 x 2)) (+.f64 (*.f64 -1/6 x) (*.f64 -91/1296 (pow.f64 x 3)))))
(+.f64 1 (fma.f64 7/72 (*.f64 x x) (fma.f64 -1/6 x (*.f64 (pow.f64 x 3) -91/1296))))
(+.f64 1 (fma.f64 (*.f64 x x) 7/72 (fma.f64 (pow.f64 x 3) -91/1296 (*.f64 x -1/6))))
(+.f64 1 (fma.f64 x -1/6 (*.f64 (*.f64 x x) (+.f64 7/72 (*.f64 x -91/1296)))))
(+.f64 1 (*.f64 x (+.f64 -1/6 (*.f64 x (+.f64 7/72 (*.f64 x -91/1296))))))
(pow.f64 (/.f64 1 x) 1/6)
(+.f64 (pow.f64 (/.f64 1 x) 1/6) (*.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6)))
(fma.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6) (pow.f64 (/.f64 1 x) 1/6))
(+.f64 (pow.f64 (/.f64 1 x) 1/6) (+.f64 (*.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6)) (*.f64 7/72 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/6))))
(+.f64 (pow.f64 (/.f64 1 x) 1/6) (fma.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6) (*.f64 7/72 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/6))))
(fma.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6) (fma.f64 7/72 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/6) (pow.f64 (/.f64 1 x) 1/6)))
(+.f64 (*.f64 -91/1296 (pow.f64 (/.f64 1 (pow.f64 x 19)) 1/6)) (+.f64 (pow.f64 (/.f64 1 x) 1/6) (+.f64 (*.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6)) (*.f64 7/72 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/6)))))
(fma.f64 -91/1296 (pow.f64 (/.f64 1 (pow.f64 x 19)) 1/6) (+.f64 (pow.f64 (/.f64 1 x) 1/6) (fma.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6) (*.f64 7/72 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/6)))))
(+.f64 (fma.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6) (*.f64 7/72 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/6))) (fma.f64 -91/1296 (pow.f64 (/.f64 1 (pow.f64 x 19)) 1/6) (pow.f64 (/.f64 1 x) 1/6)))
(fma.f64 -91/1296 (pow.f64 (/.f64 1 (pow.f64 x 19)) 1/6) (fma.f64 -1/6 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/6) (fma.f64 7/72 (pow.f64 (/.f64 1 (pow.f64 x 13)) 1/6) (pow.f64 (/.f64 1 x) 1/6))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(pow.f64 (/.f64 1 x) 1/6)
(+.f64 (*.f64 -1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x)) (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(fma.f64 -1/6 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(fma.f64 -1/6 (/.f64 (pow.f64 (/.f64 -1 x) 1/6) (/.f64 x (pow.f64 -1 1/6))) (*.f64 (pow.f64 (/.f64 -1 x) 1/6) (pow.f64 -1 1/6)))
(*.f64 (+.f64 (/.f64 -1/6 x) 1) (pow.f64 (/.f64 1 x) 1/6))
(+.f64 (*.f64 7/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 -1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x)) (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(fma.f64 7/72 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (fma.f64 -1/6 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(fma.f64 (pow.f64 (/.f64 -1 x) 1/6) (pow.f64 -1 1/6) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) 1/6) (/.f64 x (pow.f64 -1 1/6))) (+.f64 -1/6 (/.f64 7/72 x))))
(+.f64 (pow.f64 (/.f64 1 x) 1/6) (*.f64 (/.f64 (pow.f64 (/.f64 1 x) 1/6) x) (+.f64 -1/6 (/.f64 7/72 x))))
(+.f64 (*.f64 7/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 -1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x)) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (*.f64 -91/1296 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (pow.f64 x 3))))))
(fma.f64 7/72 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (+.f64 (fma.f64 -1/6 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (*.f64 -91/1296 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)))))
(fma.f64 7/72 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (fma.f64 -1/6 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (fma.f64 -91/1296 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(+.f64 (fma.f64 -1/6 (/.f64 (pow.f64 (/.f64 -1 x) 1/6) (/.f64 x (pow.f64 -1 1/6))) (*.f64 (pow.f64 (/.f64 -1 x) 1/6) (pow.f64 -1 1/6))) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) 1/6) (/.f64 (*.f64 x x) (pow.f64 -1 1/6))) (+.f64 (/.f64 -91/1296 x) 7/72)))
(+.f64 (pow.f64 (/.f64 1 x) 1/6) (*.f64 (/.f64 (pow.f64 (/.f64 1 x) 1/6) x) (+.f64 (+.f64 -1/6 (/.f64 -91/1296 (*.f64 x x))) (/.f64 7/72 x))))
1
(+.f64 1 (*.f64 -1/3 x))
(+.f64 1 (*.f64 x -1/3))
(fma.f64 x -1/3 1)
(+.f64 1 (+.f64 (*.f64 -1/3 x) (*.f64 2/9 (pow.f64 x 2))))
(+.f64 1 (fma.f64 -1/3 x (*.f64 (*.f64 x x) 2/9)))
(+.f64 1 (fma.f64 x -1/3 (*.f64 x (*.f64 x 2/9))))
(fma.f64 x -1/3 (fma.f64 (*.f64 x x) 2/9 1))
(+.f64 (*.f64 -14/81 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 -1/3 x) (*.f64 2/9 (pow.f64 x 2)))))
(fma.f64 -14/81 (pow.f64 x 3) (+.f64 1 (fma.f64 -1/3 x (*.f64 (*.f64 x x) 2/9))))
(+.f64 (fma.f64 x -1/3 (*.f64 x (*.f64 x 2/9))) (fma.f64 (pow.f64 x 3) -14/81 1))
(fma.f64 (pow.f64 x 3) -14/81 (fma.f64 x -1/3 (fma.f64 (*.f64 x x) 2/9 1)))
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)
(fma.f64 x (-.f64 x 1) 1)
(+.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 (*.f64 x (fma.f64 x (-.f64 x 1) 1)))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x)))
(+.f64 (/.f64 1 x) (/.f64 -1 (*.f64 x x)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 -1 (*.f64 x x))))
(-.f64 (/.f64 1 x) (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3))))
(-.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 1 x) (-.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 -1 (*.f64 x x))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 -1 (pow.f64 x 4))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 4)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x)))
(+.f64 (/.f64 1 x) (/.f64 -1 (*.f64 x x)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 -1 (*.f64 x x))))
(-.f64 (/.f64 1 x) (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3))))
(-.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 1 x) (-.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 -1 (*.f64 x x))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 -1 (pow.f64 x 4))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (/.f64 -1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 4)))))

eval1.7s (15%)

Compiler

Compiled 23579 to 17625 computations (25.3% saved)

prune430.0ms (3.8%)

Pruning

26 alts after pruning (25 fresh and 1 done)

PrunedKeptTotal
New1010131023
Fresh121224
Picked101
Done415
Total1027261053
Error
5.0b
Counts
1053 → 26
Alt Table
Click to see full alt table
StatusErrorProgram
21.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) -1/4) 2))
15.2b
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
▶29.6b
(pow.f64 x -1/2)
29.7b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
15.3b
(*.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (/.f64 (+.f64 x (-.f64 1 x)) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))))
29.6b
(sqrt.f64 (/.f64 1 x))
49.0b
(/.f64 (*.f64 (+.f64 (/.f64 1 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2))) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
46.1b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (pow.f64 (+.f64 1 x) -1/2))
✓29.5b
(-.f64 (pow.f64 x -1/2) 1)
▶20.1b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
▶47.8b
(/.f64 (*.f64 (/.f64 1 x) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
▶16.2b
(+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
27.8b
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))
29.0b
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
▶5.1b
(/.f64 (*.f64 (pow.f64 (fma.f64 x x x) -1/2) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
16.3b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 x 1))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
50.4b
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1/2 x) x)))
28.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
18.6b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
27.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
16.9b
(-.f64 (sqrt.f64 (/.f64 1 x)) (pow.f64 (+.f64 1 x) -1/2))
29.5b
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
48.5b
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 1 x))
18.1b
(*.f64 1 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
27.4b
(fma.f64 (pow.f64 (+.f64 x 1) -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 x -1/2))
49.6b
(/.f64 (*.f64 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Compiler

Compiled 774 to 597 computations (22.9% saved)

localize71.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓0.1b
(/.f64 (*.f64 (pow.f64 (fma.f64 x x x) -1/2) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
15.8b
(pow.f64 (fma.f64 x x x) -1/2)
Compiler

Compiled 54 to 29 computations (46.3% saved)

series4.0ms (0%)

Counts
1 → 0
Calls

3 calls:

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

rewrite92.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
532×log-prod_binary64
436×fma-def_binary64
358×pow-prod-down_binary64
298×pow2_binary64
258×fma-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01221
127021
2339221
Stop Event
1×node limit
Counts
1 → 43
Calls
Call 1
Inputs
(/.f64 (*.f64 (pow.f64 (fma.f64 x x x) -1/2) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x x) -1/2) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -2)) (cbrt.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 x x x) -1)) (*.f64 (pow.f64 (fma.f64 x x x) -1/6) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1/2) (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x x) -1/4) (*.f64 (pow.f64 (fma.f64 x x x) -1/4) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (fma.f64 x x x) -1/2)) (/.f64 1 (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (pow.f64 (fma.f64 x x x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) 1) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (fma.f64 x x x) -1)) 1) (/.f64 (pow.f64 (fma.f64 x x x) -1/6) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/4) 1) (/.f64 (pow.f64 (fma.f64 x x x) -1/4) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) -2) (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2))) (/.f64 1 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (fma.f64 x x x) -1)) (cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2))) (cbrt.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/4) (cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2))) (/.f64 (pow.f64 (fma.f64 x x x) -1/4) (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) -1/2) (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (fma.f64 x x x) -1)) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (/.f64 (pow.f64 (fma.f64 x x x) -1/6) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 x (+.f64 1 (-.f64 x (hypot.f64 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 x (-.f64 1 x))) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (fma.f64 x x x) -3/2) (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (fma.f64 x x x) -3/2) (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))))) 1))))))

simplify14.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
43 → 43
Calls
Call 1
Inputs
Outputs

localize11.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize88.0ms (0.8%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓2.7b
(+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
Compiler

Compiled 31 to 24 computations (22.6% saved)

series4.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite82.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
926×pow1_binary64
868×add-log-exp_binary64
867×log1p-expm1-u_binary64
867×expm1-log1p-u_binary64
103×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
120513
2285013
Stop Event
1×node limit
Counts
1 → 40
Calls
Call 1
Inputs
(+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.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 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x -1) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (/.f64 (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 (+.f64 (pow.f64 x -1/2) 0) (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.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) (pow.f64 (+.f64 x 1) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (cbrt.f64 (+.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))) (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (pow.f64 (+.f64 x 1) -1/4) (pow.f64 x -1/4)) (hypot.f64 (pow.f64 (+.f64 x 1) -1/4) (pow.f64 x -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (pow.f64 (+.f64 x 1) -1/2) 3)) (/.f64 1 (+.f64 (pow.f64 x -1) (+.f64 (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 (+.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) (*.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))) (+.f64 (pow.f64 x -3/2) (pow.f64 (pow.f64 (+.f64 x 1) -1/2) 3))))))) (#(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 -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 (+.f64 (pow.f64 x -3/2) (pow.f64 (pow.f64 (+.f64 x 1) -1/2) 3)) (+.f64 (pow.f64 x -1) (+.f64 (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 (+.f64 (pow.f64 x -3/2) (pow.f64 (pow.f64 (+.f64 x 1) -1/2) 3)) (+.f64 (pow.f64 (+.f64 x 1) -1) (-.f64 (pow.f64 x -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 (pow.f64 (+.f64 x 1) -1/2) 3))) (neg.f64 (+.f64 (pow.f64 x -1) (+.f64 (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 -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 (pow.f64 (+.f64 x 1) -1/2) 3)) (+.f64 (pow.f64 x -1) (+.f64 (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 (-.f64 (pow.f64 (+.f64 x 1) -1) (pow.f64 x -1)) (-.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -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 (hypot.f64 (pow.f64 (+.f64 x 1) -1/4) (pow.f64 x -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)))))) (#(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) (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -1)) (cbrt.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 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/4) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/2))))))

simplify109.0ms (1%)

Algorithm
1×egg-herbie
Rules
719×fma-def_binary64
583×times-frac_binary64
549×distribute-rgt-out_binary64
375×unswap-sqr_binary64
343×associate-/l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
070433
1184421
2464333
31331281
45992260
Stop Event
1×node limit
Counts
52 → 63
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))))))
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)
(fma.f64 x 1/2 (+.f64 (pow.f64 x -1/2) -1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x 1/2 -1))
(+.f64 (fma.f64 x 1/2 (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 (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 (*.f64 x -3/8) (pow.f64 x -1/2)) (fma.f64 x 1/2 -1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x (fma.f64 x -3/8 1/2) -1))
(fma.f64 x (fma.f64 x -3/8 1/2) (+.f64 -1 (pow.f64 x -1/2)))
(-.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 (+.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) (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) (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))
(*.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 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))
(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 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 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 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))))))
(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 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.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 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) x))
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(+.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 (exp.f64 (*.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 (/.f64 5/16 x) -3/8)))
(*.f64 (/.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) x) (+.f64 (+.f64 1/2 (/.f64 -3/8 x)) (/.f64 5/16 (*.f64 x 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)))))
(fma.f64 (/.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) x) (+.f64 1/2 (/.f64 -3/8 x)) (*.f64 (/.f64 (exp.f64 (*.f64 -1/2 (log.f64 x))) (pow.f64 x 3)) (+.f64 5/16 (/.f64 -35/128 x))))
(fma.f64 1/2 (/.f64 (pow.f64 x -1/2) x) (*.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 -3/8 (+.f64 (/.f64 -35/128 (*.f64 x x)) (/.f64 5/16 x)))))

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓0.0b
(/.f64 (*.f64 (/.f64 1 x) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
1.7b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 56 to 36 computations (35.7% saved)

series4.0ms (0%)

Counts
1 → 1
Calls

3 calls:

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

rewrite77.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
749×fma-def_binary64
715×log-prod_binary64
365×fma-neg_binary64
291×log-div_binary64
242×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01223
129020
2466920
Stop Event
1×node limit
Counts
1 → 48
Calls
Call 1
Inputs
(/.f64 (*.f64 (/.f64 1 x) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) (cbrt.f64 (exp.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 1 (/.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (*.f64 (+.f64 1 (-.f64 x x)) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (-.f64 x x)) (*.f64 (/.f64 1 x) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (/.f64 (-.f64 1 x) x)) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (pow.f64 (cbrt.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) 2) (cbrt.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) 2) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) (/.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) (*.f64 (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (neg.f64 (+.f64 1 (-.f64 x x))) x) (/.f64 1 (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (+.f64 1 (/.f64 (-.f64 1 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (-.f64 x x)) 1) (/.f64 (/.f64 1 x) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (+.f64 1 (-.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) 1) (/.f64 (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2))) (/.f64 (+.f64 1 (/.f64 (-.f64 1 x) x)) (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2))) (/.f64 (+.f64 1 (-.f64 x x)) (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (-.f64 x x)) (cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2))) (/.f64 (/.f64 1 x) (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) 2) (cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2))) (cbrt.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) (cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2))) (/.f64 (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (/.f64 (+.f64 1 (/.f64 (-.f64 1 x) x)) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (/.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) 2) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (/.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 x) x))) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (/.f64 (-.f64 1 x) x)) (+.f64 1 (-.f64 x x))) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (/.f64 (-.f64 1 x) x)) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (/.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 1 (/.f64 (-.f64 1 x) x)) (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1 (/.f64 (-.f64 1 x) x)) 3) (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (/.f64 1 x) 1) (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (*.f64 x (/.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (*.f64 x (/.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) 1))))))

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
044
164
Stop Event
1×saturated
Counts
49 → 49
Calls
Call 1
Inputs
(/.f64 1 x)
Outputs
(/.f64 1 x)

localize29.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2))
0.2b
(pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)
✓14.4b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
Compiler

Compiled 46 to 38 computations (17.4% saved)

series1.0ms (0%)

Counts
1 → 6
Calls

3 calls:

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

rewrite84.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
578×prod-diff_binary64
501×log-prod_binary64
318×pow2_binary64
318×fma-def_binary64
211×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01216
128013
2347213
Stop Event
1×node limit
Counts
1 → 148
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1/2) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
Outputs
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simplify56.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
594×associate-*l*_binary64
518×times-frac_binary64
430×fma-def_binary64
387×associate-*r*_binary64
231×fma-neg_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
03577
19475
223473
363967
4187566
5517062
Stop Event
1×node limit
Counts
154 → 159
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)
(sqrt.f64 (/.f64 1 x))
(exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
Outputs
(-.f64 (pow.f64 x -1/2) 1)
(+.f64 (pow.f64 x -1/2) -1)
(-.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)
(fma.f64 x 1/2 (+.f64 (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 x (*.f64 x -3/8) -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 (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 5/16 (pow.f64 x 3) (fma.f64 -3/8 (*.f64 x x) (pow.f64 x -1/2))) (fma.f64 x 1/2 -1))
(+.f64 (fma.f64 x (fma.f64 x -3/8 1/2) (pow.f64 x -1/2)) (fma.f64 5/16 (pow.f64 x 3) -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)
(exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)

eval682.0ms (6%)

Compiler

Compiled 17675 to 12669 computations (28.3% saved)

prune571.0ms (5%)

Pruning

21 alts after pruning (18 fresh and 3 done)

PrunedKeptTotal
New73116747
Fresh18220
Picked101
Done235
Total75221773
Error
0b
Counts
773 → 21
Alt Table
Click to see full alt table
StatusErrorProgram
32.7b
(*.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (/.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))
7.7b
(*.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 x (+.f64 1 (-.f64 x (hypot.f64 x (sqrt.f64 x))))))
16.2b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
28.3b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
34.3b
(fma.f64 1/2 (/.f64 (pow.f64 x -1/2) x) (*.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 -3/8 (+.f64 (/.f64 -35/128 (*.f64 x x)) (/.f64 5/16 x)))))
✓29.6b
(pow.f64 x -1/2)
34.0b
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
43.5b
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
29.0b
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
0.8b
(pow.f64 (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1/2) 2)
34.5b
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
✓5.1b
(/.f64 (*.f64 (pow.f64 (fma.f64 x x x) -1/2) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
16.3b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 x 1))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
32.6b
(*.f64 (/.f64 (neg.f64 (+.f64 1 (-.f64 x x))) x) (/.f64 1 (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))
59.3b
(/.f64 1 x)
32.7b
(/.f64 (*.f64 (/.f64 1 x) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
29.6b
(-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
15.2b
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
✓29.5b
(-.f64 (pow.f64 x -1/2) 1)
0.6b
(pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1)
33.6b
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
Compiler

Compiled 317 to 232 computations (26.8% saved)

regimes107.0ms (0.9%)

Counts
80 → 1
Calls
Call 1
Inputs
(/.f64 1 x)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(*.f64 1 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 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 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.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) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(-.f64 (sqrt.f64 (/.f64 1 x)) (pow.f64 (+.f64 1 x) -1/2))
(+.f64 (pow.f64 x -1/2) (neg.f64 (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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.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 (/.f64 1 x) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (*.f64 (/.f64 1 x) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1/2 x) x)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 x 1))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -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 1 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 (*.f64 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (*.f64 (+.f64 (/.f64 1 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2))) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.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 3/2) -1/3) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(*.f64 (/.f64 (neg.f64 (+.f64 1 (-.f64 x x))) x) (/.f64 1 (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(fma.f64 1/2 (/.f64 (pow.f64 x -1/2) x) (*.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 -3/8 (+.f64 (/.f64 -35/128 (*.f64 x x)) (/.f64 5/16 x)))))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))
(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)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(fma.f64 (pow.f64 (+.f64 x 1) -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 x -1/2))
(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 (pow.f64 (fma.f64 x x x) -1/2) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (*.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 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 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))
(*.f64 (fma.f64 (pow.f64 x 1/4) (neg.f64 (pow.f64 x 1/4)) (sqrt.f64 (+.f64 x 1))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(*.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1)
(*.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 x (+.f64 1 (-.f64 x (hypot.f64 x (sqrt.f64 x))))))
(pow.f64 (pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1/2) 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))
(fma.f64 (pow.f64 (fma.f64 x x x) -1/2) (sqrt.f64 (+.f64 x 1)) (*.f64 (pow.f64 (fma.f64 x x x) -1/2) (neg.f64 (sqrt.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 (*.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 1 (cbrt.f64 (cbrt.f64 x)))) (cbrt.f64 (pow.f64 x -1/6)) (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))))
(fma.f64 (/.f64 1 (cbrt.f64 (cbrt.f64 x))) (*.f64 (cbrt.f64 (pow.f64 x -1/6)) (/.f64 1 (cbrt.f64 x))) (/.f64 -1 (hypot.f64 1 (sqrt.f64 x))))
(*.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (/.f64 (+.f64 1 (-.f64 x x)) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))) (/.f64 (+.f64 x (-.f64 1 x)) (hypot.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4))))
(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x -1/2)) (sqrt.f64 (pow.f64 x -1/2)) (neg.f64 (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (/.f64 1 (cbrt.f64 (+.f64 x 1)))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2))) (/.f64 1 (cbrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (/.f64 1 (cbrt.f64 (+.f64 x 1))))))
Outputs
(pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1)
Calls

2 calls:

45.0ms
x
27.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.6b1x
0.6b1(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 1259 to 914 computations (27.4% saved)

regimes129.0ms (1.1%)

Counts
69 → 2
Calls
Call 1
Inputs
(/.f64 1 x)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(*.f64 1 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 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 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.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) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(-.f64 (sqrt.f64 (/.f64 1 x)) (pow.f64 (+.f64 1 x) -1/2))
(+.f64 (pow.f64 x -1/2) (neg.f64 (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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.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 (/.f64 1 x) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (*.f64 (/.f64 1 x) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1/2 x) x)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 x 1))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -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 1 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 (*.f64 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (*.f64 (+.f64 (/.f64 1 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2))) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.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 3/2) -1/3) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(*.f64 (/.f64 (neg.f64 (+.f64 1 (-.f64 x x))) x) (/.f64 1 (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(fma.f64 1/2 (/.f64 (pow.f64 x -1/2) x) (*.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 -3/8 (+.f64 (/.f64 -35/128 (*.f64 x x)) (/.f64 5/16 x)))))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2))))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))
(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)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
(fma.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(fma.f64 (pow.f64 (+.f64 x 1) -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 x -1/2))
(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 (pow.f64 (fma.f64 x x x) -1/2) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (*.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 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 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))
(*.f64 (fma.f64 (pow.f64 x 1/4) (neg.f64 (pow.f64 x 1/4)) (sqrt.f64 (+.f64 x 1))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(*.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
Outputs
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(fma.f64 1/2 (/.f64 (pow.f64 x -1/2) x) (*.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 -3/8 (+.f64 (/.f64 -35/128 (*.f64 x x)) (/.f64 5/16 x)))))
Calls

2 calls:

70.0ms
x
26.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.1b2x
0.1b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 973 to 721 computations (25.9% saved)

bsearch23.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
279.12834226240955
123040.3876905906
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes90.0ms (0.8%)

Counts
54 → 2
Calls
Call 1
Inputs
(/.f64 1 x)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(*.f64 1 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 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 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.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) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(-.f64 (sqrt.f64 (/.f64 1 x)) (pow.f64 (+.f64 1 x) -1/2))
(+.f64 (pow.f64 x -1/2) (neg.f64 (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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.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 (/.f64 1 x) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (*.f64 (/.f64 1 x) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1/2 x) x)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 x 1))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -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 1 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 (*.f64 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (*.f64 (+.f64 (/.f64 1 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2))) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.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 3/2) -1/3) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(*.f64 (/.f64 (neg.f64 (+.f64 1 (-.f64 x x))) x) (/.f64 1 (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
Outputs
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x))))
Calls

2 calls:

50.0ms
x
20.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.1b2x
0.1b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 691 to 509 computations (26.3% saved)

bsearch25.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
24.0ms
123040.3876905906
4043595.7277765786
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes89.0ms (0.8%)

Counts
53 → 2
Calls
Call 1
Inputs
(/.f64 1 x)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(*.f64 1 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 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 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.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) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(-.f64 (sqrt.f64 (/.f64 1 x)) (pow.f64 (+.f64 1 x) -1/2))
(+.f64 (pow.f64 x -1/2) (neg.f64 (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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.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 (/.f64 1 x) 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (*.f64 (/.f64 1 x) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -1/2 x) x)))
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 x 1))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -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 1 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(/.f64 (*.f64 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (*.f64 (+.f64 (/.f64 1 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2))) (+.f64 x (-.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.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 3/2) -1/3) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (pow.f64 (pow.f64 (+.f64 1 x) -1/4) -2)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(-.f64 (*.f64 (pow.f64 x -1/6) (cbrt.f64 (/.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(*.f64 (/.f64 (neg.f64 (+.f64 1 (-.f64 x x))) x) (/.f64 1 (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 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 x 1) -1/2))
Calls

2 calls:

49.0ms
x
20.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.1b2x
0.1b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 670 to 495 computations (26.1% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.1584994201365578e-8
0.0001069298826259224
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes26.0ms (0.2%)

Counts
19 → 2
Calls
Call 1
Inputs
(/.f64 1 x)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(*.f64 1 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 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 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.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) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8))))))
(*.f64 1/2 (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 (*.f64 x -5/16) 3/8))))))
(*.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:

20.0ms
x
Results
ErrorSegmentsBranch
0.4b2x
Compiler

Compiled 183 to 138 computations (24.6% saved)

bsearch24.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
24.0ms
2.7555410670793095e-6
35.32850276590207
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes21.0ms (0.2%)

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

1 calls:

15.0ms
x
Results
ErrorSegmentsBranch
0.4b2x
Compiler

Compiled 140 to 105 computations (25% saved)

bsearch22.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
2.7555410670793095e-6
35.32850276590207
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes22.0ms (0.2%)

Counts
15 → 2
Calls
Call 1
Inputs
(/.f64 1 x)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(*.f64 1 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 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 (/.f64 1 (sqrt.f64 x)) (/.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 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
Calls

1 calls:

16.0ms
x
Results
ErrorSegmentsBranch
0.6b2x
Compiler

Compiled 123 to 93 computations (24.4% saved)

bsearch22.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
2.7555410670793095e-6
35.32850276590207
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes18.0ms (0.2%)

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

1 calls:

14.0ms
x
Results
ErrorSegmentsBranch
0.9b2x
Compiler

Compiled 88 to 67 computations (23.9% saved)

bsearch23.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
23.0ms
2.7555410670793095e-6
35.32850276590207
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes15.0ms (0.1%)

Counts
11 → 2
Calls
Call 1
Inputs
(/.f64 1 x)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(/.f64 (pow.f64 x -1/2) (/.f64 x 1/2))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(*.f64 1 (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 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 (pow.f64 x -1/2) (/.f64 x 1/2))
Calls

1 calls:

12.0ms
x
Results
ErrorSegmentsBranch
0.9b2x
Compiler

Compiled 77 to 58 computations (24.7% saved)

bsearch22.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
2.7555410670793095e-6
35.32850276590207
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes12.0ms (0.1%)

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

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
1.2b2x
Compiler

Compiled 31 to 23 computations (25.8% saved)

bsearch22.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
2.7555410670793095e-6
35.32850276590207
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes18.0ms (0.2%)

Counts
5 → 2
Calls
Call 1
Inputs
(/.f64 1 x)
(pow.f64 x -1/2)
(sqrt.f64 (/.f64 1 x))
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
Outputs
(-.f64 (pow.f64 x -1/2) 1)
(/.f64 1 x)
Calls

1 calls:

16.0ms
x
Results
ErrorSegmentsBranch
27.9b2x
Compiler

Compiled 24 to 18 computations (25% saved)

bsearch22.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
2.7555410670793095e-6
35.32850276590207
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes7.0ms (0.1%)

Accuracy

Total -30.5b remaining (-103%)

Threshold costs -30.5b (-103%)

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

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
29.6b1x
Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify33.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
34×+-commutative_binary64
23×*-commutative_binary64
19×sub-neg_binary64
12×neg-sub0_binary64
12×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
088468
1130468
2157468
3185468
4201468
5213468
6222468
7233468
8236468
9237468
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1)
(if (<=.f64 x 2455238863674867/8796093022208) (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2)) (fma.f64 1/2 (/.f64 (pow.f64 x -1/2) x) (*.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 -3/8 (+.f64 (/.f64 -35/128 (*.f64 x x)) (/.f64 5/16 x))))))
(if (<=.f64 x 4227635529745981/34359738368) (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2)) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 3022314549036573/151115727451828646838272) (*.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 x 1) -1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8)))))) (*.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 3253168694336547/1180591620717411303424) (-.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 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.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 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1))) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1)) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) 1) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) 1) (/.f64 1 x))
(pow.f64 x -1/2)
(/.f64 1 x)
Outputs
(pow.f64 (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1)
(pow.f64 (*.f64 (+.f64 (sqrt.f64 x) (hypot.f64 1 (sqrt.f64 x))) (hypot.f64 x (sqrt.f64 x))) -1)
(if (<=.f64 x 2455238863674867/8796093022208) (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2)) (fma.f64 1/2 (/.f64 (pow.f64 x -1/2) x) (*.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 -3/8 (+.f64 (/.f64 -35/128 (*.f64 x x)) (/.f64 5/16 x))))))
(if (<=.f64 x 2455238863674867/8796093022208) (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2)) (fma.f64 1/2 (/.f64 (pow.f64 x -1/2) x) (*.f64 (/.f64 1 (pow.f64 x 5/2)) (+.f64 -3/8 (+.f64 (/.f64 -35/128 (*.f64 x x)) (/.f64 5/16 x))))))
(if (<=.f64 x 4227635529745981/34359738368) (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2)) (*.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 4227635529745981/34359738368) (*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2)) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (+.f64 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 3022314549036573/151115727451828646838272) (*.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 x 1) -1/2)))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 3022314549036573/151115727451828646838272) (*.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)))) 3022314549036573/151115727451828646838272) (*.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 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8)))))) (*.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 3253168694336547/1180591620717411303424) (+.f64 (pow.f64 x -1/2) (-.f64 -1 (*.f64 x (+.f64 -1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8)))))) (*.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 3253168694336547/1180591620717411303424) (+.f64 (pow.f64 x -1/2) (+.f64 -1 (*.f64 x (-.f64 1/2 (*.f64 x (+.f64 (*.f64 x -5/16) 3/8)))))) (*.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 3253168694336547/1180591620717411303424) (+.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 3253168694336547/1180591620717411303424) (-.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 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.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 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (+.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 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (+.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 (/.f64 5/16 (*.f64 x x)) (/.f64 -3/8 x)))))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.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 3253168694336547/1180591620717411303424) (-.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 3253168694336547/1180591620717411303424) (+.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 3253168694336547/1180591620717411303424) (+.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 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1))) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 1 (*.f64 x 1/2)))) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (+.f64 (pow.f64 x -1/2) (/.f64 -1 (+.f64 1 (*.f64 x 1/2)))) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (+.f64 (pow.f64 x -1/2) (/.f64 -1 (-.f64 1 (*.f64 x -1/2)))) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1)) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x -1/2))) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (+.f64 (pow.f64 x -1/2) (-.f64 -1 (*.f64 x -1/2))) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) 1) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (+.f64 (pow.f64 x -1/2) -1) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (+.f64 -1 (pow.f64 x -1/2)) (/.f64 (pow.f64 x -1/2) (/.f64 x 1/2)))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (-.f64 (pow.f64 x -1/2) 1) (/.f64 1 x))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (+.f64 (pow.f64 x -1/2) -1) (/.f64 1 x))
(if (<=.f64 x 3253168694336547/1180591620717411303424) (+.f64 -1 (pow.f64 x -1/2)) (/.f64 1 x))
(pow.f64 x -1/2)
(/.f64 1 x)
Compiler

Compiled 330 to 247 computations (25.2% saved)

soundness181.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
719×fma-def_binary64
583×times-frac_binary64
549×distribute-rgt-out_binary64
375×unswap-sqr_binary64
343×associate-/l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
070433
1184421
2464333
31331281
45992260
Stop Event
1×node limit
Compiler

Compiled 3636 to 3068 computations (15.6% saved)

end168.0ms (1.5%)

Compiler

Compiled 318 to 228 computations (28.3% saved)

Profiling

Loading profile data...