Details

Time bar (total: 9.4s)

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 (21%)

Results
895.0ms4915×body256valid
790.0ms2337×body1024valid
264.0ms1004×body512valid

preprocess22.0ms (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)

simplify49.0ms (0.5%)

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
20.6b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶20.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 12 to 10 computations (16.7% saved)

localize15.0ms (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)))
✓0.2b
(/.f64 1 (sqrt.f64 x))
✓2.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 33 to 23 computations (30.3% saved)

series39.0ms (0.4%)

Counts
4 → 8
Calls

12 calls:

TimeVariablePointExpression
29.0ms
x
@0
(sqrt.f64 (+.f64 x 1))
2.0ms
x
@inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms
x
@-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
(sqrt.f64 (+.f64 x 1))

rewrite120.0ms (1.3%)

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

Useful iterations: 1 (0.0ms)

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

simplify174.0ms (1.9%)

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)

eval182.0ms (1.9%)

Compiler

Compiled 4484 to 3575 computations (20.3% saved)

prune167.0ms (1.8%)

Pruning

32 alts after pruning (31 fresh and 1 done)

PrunedKeptTotal
New21131242
Fresh000
Picked011
Done000
Total21132243
Error
19.9b
Counts
243 → 32
Alt Table
Click to see full alt table
StatusErrorProgram
28.9b
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
29.4b
(+.f64 (fma.f64 (pow.f64 x -1/2) 1 (neg.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x)))))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (/.f64 1 (cbrt.f64 (+.f64 1 x))) (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x))))))
22.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
22.4b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
20.7b
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
30.6b
(fma.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
30.9b
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
22.5b
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
25.0b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
31.0b
(/.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))))
▶31.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
28.9b
(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))
20.7b
(*.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))))
▶26.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
▶29.3b
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
25.1b
(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
28.9b
(fma.f64 (pow.f64 (+.f64 1 x) -1/4) (neg.f64 (pow.f64 (+.f64 1 x) -1/4)) (pow.f64 x -1/2))
25.3b
(/.f64 (-.f64 (/.f64 1 x) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2)) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
31.0b
(/.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))))
25.8b
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
31.2b
(/.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)))))))
20.7b
(*.f64 (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)) (-.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)))
29.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
30.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
✓20.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶44.3b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.4b
(fma.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
▶20.5b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
22.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
39.7b
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
27.0b
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
20.6b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
Compiler

Compiled 1114 to 912 computations (18.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 1 x))
✓0.1b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
✓2.8b
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓14.0b
(sqrt.f64 (*.f64 x (+.f64 1 x)))
Compiler

Compiled 44 to 28 computations (36.4% saved)

series12.0ms (0.1%)

Counts
4 → 13
Calls

12 calls:

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

rewrite146.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
558×log-prod_binary64
546×fma-def_binary64
430×pow-prod-down_binary64
275×pow2_binary64
267×fma-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01048
122442
2330341
Stop Event
1×node limit
Counts
4 → 221
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 x (+.f64 1 x)))
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(sqrt.f64 (+.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x x)) (pow.f64 (fma.f64 x x x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (*.f64 (pow.f64 x 1/6) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x x) 1/6) (cbrt.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (*.f64 (pow.f64 (+.f64 x 1) 1/6) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x x) 1/4) (pow.f64 (fma.f64 x x x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 x 1)) (cbrt.f64 x)) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 x 1/4)) (pow.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 x 1))) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x 1) 1/4)) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x x) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x x) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x x)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x x) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 x 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x x x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 x (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/6)) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 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(#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))) (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 x (-.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (exp.f64 (neg.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (exp.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 (sqrt.f64 x))) (exp.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (exp.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 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x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) 1 (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) 1 (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1 (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1 (fma.f64 (neg.f64 (pow.f64 x 1/6)) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1 (+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (neg.f64 (pow.f64 x 1/6)) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (fma.f64 x (-.f64 x 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))

simplify81.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
671×fma-neg_binary64
642×times-frac_binary64
433×cancel-sign-sub-inv_binary64
393×fma-def_binary64
385×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
045108
1129106
2371106
3920100
43432100
Stop Event
1×node limit
Counts
234 → 239
Calls
Call 1
Inputs
x
(+.f64 1/2 x)
(-.f64 (+.f64 1/2 x) (*.f64 1/8 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) x)) (*.f64 1/8 (/.f64 1 x)))
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(+.f64 1/2 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))
(+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))
1
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
Outputs
x
(+.f64 1/2 x)
(+.f64 x 1/2)
(-.f64 (+.f64 1/2 x) (*.f64 1/8 (/.f64 1 x)))
(-.f64 (+.f64 x 1/2) (/.f64 1/8 x))
(+.f64 x (-.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) x)) (*.f64 1/8 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (+.f64 x (/.f64 1/16 (*.f64 x x)))) (/.f64 1/8 x))
(+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (+.f64 1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)) (/.f64 1/16 (*.f64 x x)))
(+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x)))
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))
x
(+.f64 1/2 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(+.f64 x 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))
(-.f64 (+.f64 x 1/2) (/.f64 1/8 x))
(+.f64 x (-.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))
(+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))
(-.f64 (+.f64 1/2 (+.f64 x (/.f64 1/16 (*.f64 x x)))) (/.f64 1/8 x))
(+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (+.f64 1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)) (/.f64 1/16 (*.f64 x x)))
(+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x)))
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 (*.f64 x -1/8) (fma.f64 x 1/2 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) (fma.f64 1/2 x (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 x 1/2 (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x -1/8 1/2) (fma.f64 1/16 (pow.f64 x 3) 1))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 1))

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiled 15 to 9 computations (40% saved)

series1.0ms (0%)

Counts
1 → 2
Calls

3 calls:

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

rewrite62.0ms (0.7%)

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

Useful iterations: 1 (0.0ms)

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

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

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

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)))
✓7.8b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
✓29.0b
(pow.f64 (*.f64 x x) -1/4)
Compiler

Compiled 37 to 24 computations (35.1% saved)

series58.0ms (0.6%)

Counts
2 → 18
Calls

6 calls:

TimeVariablePointExpression
31.0ms
x
@inf
(pow.f64 (*.f64 x x) -1/4)
26.0ms
x
@0
(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)

rewrite126.0ms (1.3%)

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
((#(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 -1/2) 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 -1/6) (cbrt.f64 (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -1)) (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 (pow.f64 1 -1/4) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 x 4)) -1/4) (pow.f64 x -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 x -1))))) (#(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 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))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/2)))))))
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(pow.f64 (+.f64 x 1) -1/2)) 1 (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 fma.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 1 (+.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/6) (cbrt.f64 (pow.f64 x -1)) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/6) (cbrt.f64 (pow.f64 x -1)) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -1)) (pow.f64 x -1/6) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -1)) (pow.f64 x -1/6) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1))) (neg.f64 (pow.f64 (+.f64 x 1) -1/6)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 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 fma.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 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 fma.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2) (+.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2) (cbrt.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 fma.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2) (cbrt.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 fma.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2) (cbrt.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 fma.f64 (pow.f64 (+.f64 x 1) -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (sqrt.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 fma.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (sqrt.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 fma.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (sqrt.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 fma.f64 -1 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2)) (/.f64 1 (+.f64 (+.f64 (pow.f64 x -1) (/.f64 1 (+.f64 x 1))) (pow.f64 (*.f64 x (+.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 fma.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2)) (/.f64 1 (+.f64 (+.f64 (pow.f64 x -1) (/.f64 1 (+.f64 x 1))) (pow.f64 (*.f64 x (+.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 fma.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2)) (/.f64 1 (+.f64 (+.f64 (pow.f64 x -1) (/.f64 1 (+.f64 x 1))) (pow.f64 (*.f64 x (+.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 fma.f64 (-.f64 (pow.f64 x -1) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.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 fma.f64 (-.f64 (pow.f64 x -1) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.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 fma.f64 (-.f64 (pow.f64 x -1) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.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 fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.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 1 -1/4) (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 -1/4) (pow.f64 x -1/2) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (pow.f64 x 4)) -1/4) (pow.f64 x -1/6) (/.f64 -1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (pow.f64 x 4)) -1/4) (pow.f64 x -1/6) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (fma.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) 1 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (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 fma.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)) (+.f64 (/.f64 -1 (sqrt.f64 (+.f64 x 1))) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (+.f64 x 1)))) (pow.f64 (+.f64 x 1) -1/6) (pow.f64 x -1/2))))))

simplify47.0ms (0.5%)

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))

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (sqrt.f64 x))
✓0.2b
(pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2)
✓0.3b
(cbrt.f64 (+.f64 1 x))
✓13.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
Compiler

Compiled 34 to 24 computations (29.4% saved)

series11.0ms (0.1%)

Counts
3 → 8
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@0
(cbrt.f64 (+.f64 1 x))
2.0ms
x
@-inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
2.0ms
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)

rewrite90.0ms (1%)

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))
(cbrt.f64 (+.f64 1 x))
(pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 1 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (cbrt.f64 (pow.f64 (+.f64 1 x) -1)) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (+.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 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simplify171.0ms (1.8%)

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

Useful iterations: 10 (0.0ms)

IterNodesCost
03084
17578
218274
352862
4136458
5241558
6294258
7307658
8323058
9342058
10367356
11433356
12474056
13527056
14592856
15675256
16715356
17751956
18785756
Stop Event
1×node limit
Counts
165 → 170
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/3 x))
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (*.f64 1/3 x)))
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x))))
1
(+.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 1 (*.f64 1/3 x))
(fma.f64 1/3 x 1)
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (*.f64 1/3 x)))
(fma.f64 -1/9 (*.f64 x x) (+.f64 1 (*.f64 1/3 x)))
(fma.f64 -1/9 (*.f64 x x) (fma.f64 1/3 x 1))
(fma.f64 x (*.f64 x -1/9) (fma.f64 1/3 x 1))
(fma.f64 x (fma.f64 x -1/9 1/3) 1)
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x))))
(fma.f64 -1/9 (*.f64 x x) (+.f64 1 (fma.f64 5/81 (pow.f64 x 3) (*.f64 1/3 x))))
(+.f64 (fma.f64 -1/9 (*.f64 x x) (fma.f64 1/3 x 1)) (*.f64 5/81 (pow.f64 x 3)))
(fma.f64 x (*.f64 x -1/9) (fma.f64 5/81 (pow.f64 x 3) (fma.f64 1/3 x 1)))
(fma.f64 5/81 (pow.f64 x 3) (fma.f64 x (fma.f64 x -1/9 1/3) 1))
(fma.f64 x (+.f64 1/3 (*.f64 x (fma.f64 x 5/81 -1/9))) 1)
(fma.f64 x (fma.f64 x (fma.f64 x 5/81 -1/9) 1/3) 1)
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))
(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 (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)))
(fma.f64 x -1/2 (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)

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 1 x))
✓0.1b
(/.f64 -1 (sqrt.f64 (+.f64 1 x)))
✓29.1b
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
Compiler

Compiled 34 to 26 computations (23.5% saved)

series4.0ms (0%)

Counts
2 → 10
Calls

6 calls:

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

rewrite110.0ms (1.2%)

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

Useful iterations: 1 (0.0ms)

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

simplify58.0ms (0.6%)

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

Useful iterations: 5 (0.0ms)

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

eval726.0ms (7.7%)

Compiler

Compiled 15253 to 11494 computations (24.6% saved)

prune148.0ms (1.6%)

Pruning

29 alts after pruning (28 fresh and 1 done)

PrunedKeptTotal
New81122833
Fresh20626
Picked101
Done415
Total83629865
Error
19.3b
Counts
865 → 29
Alt Table
Click to see full alt table
StatusErrorProgram
24.5b
(/.f64 (-.f64 (*.f64 (pow.f64 x -1/2) (pow.f64 x -1/2)) (/.f64 1 (+.f64 x 1))) (-.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))
51.0b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)
22.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
62.8b
-1
▶24.9b
(exp.f64 (log.f64 (-.f64 (*.f64 (pow.f64 x -1/2) 1) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
29.2b
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (pow.f64 (cbrt.f64 (+.f64 x 1)) 3/2)))
22.4b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
20.7b
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
▶32.0b
(pow.f64 x -1/2)
23.3b
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
32.1b
(sqrt.f64 (/.f64 1 x))
31.1b
(/.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 3)) (+.f64 (/.f64 1 x) (-.f64 (pow.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 2) (*.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))
29.0b
(fma.f64 (/.f64 (pow.f64 (+.f64 x 1) 1/4) 1) (/.f64 (pow.f64 (+.f64 x 1) 1/4) (hypot.f64 x (sqrt.f64 x))) (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓31.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
29.3b
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))
25.9b
(-.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
25.3b
(/.f64 (-.f64 (/.f64 1 x) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2)) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
30.8b
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
20.5b
(+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))
28.9b
(fma.f64 (pow.f64 (+.f64 x 1) -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 x -1/2))
31.3b
(-.f64 (pow.f64 x -1/2) 1)
45.0b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
52.4b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
29.0b
(fma.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (fma.f64 x x x) -1/2) (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
20.6b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
▶20.0b
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
▶31.5b
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
30.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
▶50.7b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
Compiler

Compiled 833 to 668 computations (19.8% saved)

localize61.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓0.1b
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
✓2.4b
(+.f64 x (-.f64 1 x))
14.0b
(sqrt.f64 (*.f64 x (+.f64 1 x)))
Compiler

Compiled 74 to 47 computations (36.5% saved)

series25.0ms (0.3%)

Counts
3 → 13
Calls

9 calls:

TimeVariablePointExpression
14.0ms
x
@-inf
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
3.0ms
x
@inf
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
3.0ms
x
@-inf
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
2.0ms
x
@0
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
1.0ms
x
@inf
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite120.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
863×fma-def_binary64
430×fma-neg_binary64
326×log-div_binary64
257×expm1-udef_binary64
257×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01458
133437
2498837
Stop Event
1×node limit
Counts
3 → 293
Calls
Call 1
Inputs
(+.f64 x (-.f64 1 x))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Outputs
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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 x 1) (-.f64 x (hypot.f64 x (sqrt.f64 x)))) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 x 1) (-.f64 x (hypot.f64 x (sqrt.f64 x)))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 (+.f64 x 1) (-.f64 x (hypot.f64 x (sqrt.f64 x)))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))))

simplify17.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0113
1413
Stop Event
1×saturated
Counts
306 → 294
Calls
Call 1
Inputs
1
1
1
1
1
1
1
1
1
1
1
1
1
Outputs
1
1
1
1
1
1
1
1
1
1
1
1
1

localize7.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize28.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiled 41 to 33 computations (19.5% saved)

series46.0ms (0.5%)

Counts
2 → 20
Calls

6 calls:

TimeVariablePointExpression
15.0ms
x
@-inf
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
9.0ms
x
@-inf
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
9.0ms
x
@inf
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
7.0ms
x
@0
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
3.0ms
x
@inf
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))

rewrite69.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
497×log-prod_binary64
441×prod-diff_binary64
314×pow-prod-down_binary64
289×pow2_binary64
245×fma-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01126
124626
2321226
Stop Event
1×node limit
Counts
2 → 83
Calls
Call 1
Inputs
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
Outputs
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(pow.f64 (+.f64 (/.f64 1 x) -1) 3) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 (/.f64 1 x) -1) (+.f64 1 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (+.f64 (/.f64 1 x) -1)) (log1p.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 (+.f64 (/.f64 1 x) -1)) (log1p.f64 (pow.f64 x -1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 (/.f64 1 x) -1) (+.f64 1 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2) (*.f64 -1 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2) (pow.f64 (*.f64 x (+.f64 1 (pow.f64 x -1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2) (/.f64 1 x) (*.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2) -1 (pow.f64 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x) -1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (+.f64 -1 (neg.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)) (cbrt.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -4)) (cbrt.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 x -1/4))) (/.f64 1 (hypot.f64 1 (pow.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 x -1/2))) -2) (cbrt.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (pow.f64 x -3/2))) (-.f64 (+.f64 1 (/.f64 1 x)) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1 (/.f64 1 x))) (-.f64 1 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (pow.f64 x -1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) 4) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 x -1/2))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (hypot.f64 1 (pow.f64 x -1/4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (+.f64 -1 (neg.f64 (pow.f64 x -1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 x -1/2)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (pow.f64 x -1/2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 (pow.f64 x -1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 1 (pow.f64 x -1/4)) -2)))))))

simplify60.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
602×fma-neg_binary64
449×fma-def_binary64
444×times-frac_binary64
312×unswap-sqr_binary64
275×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
033358
175358
2153328
3326318
4817298
52405298
67224298
Stop Event
1×node limit
Counts
103 → 95
Calls
Call 1
Inputs
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(/.f64 -1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2))))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2))))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2))))
(/.f64 -1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1))
(-.f64 (/.f64 1 (*.f64 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1) x)) (/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)))
(-.f64 (/.f64 1 (*.f64 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1) x)) (/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)))
(-.f64 (/.f64 1 (*.f64 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1) x)) (/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)))
(/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)))
(/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)))
(/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)))
(/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)))
(/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1))
(/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1))
(/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1))
(/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1))
Outputs
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))
(/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2))))
(/.f64 1 (+.f64 x (pow.f64 x 1/2)))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (pow.f64 x 1/2))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (pow.f64 x 1/2))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (pow.f64 x 1/2))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(/.f64 -1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)))
(/.f64 -1 (+.f64 1 (sqrt.f64 (/.f64 1 x))))
(/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2))))
(-.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (pow.f64 x 1/2))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2))))
(-.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (pow.f64 x 1/2))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)) x)) (/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2))))
(-.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (pow.f64 x 1/2))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(/.f64 -1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1))
(/.f64 -1 (+.f64 1 (sqrt.f64 (/.f64 1 x))))
(/.f64 -1 (+.f64 1 (pow.f64 x -1/2)))
(-.f64 (/.f64 1 (*.f64 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1) x)) (/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)))
(-.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (pow.f64 x 1/2))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1) x)) (/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)))
(-.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (pow.f64 x 1/2))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (*.f64 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1) x)) (/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)))
(-.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (*.f64 x (+.f64 1 (pow.f64 x -1/2)))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (pow.f64 x 1/2))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(+.f64 (/.f64 1 (+.f64 x (sqrt.f64 x))) (/.f64 -1 (+.f64 1 (pow.f64 x -1/2))))
(/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)))
(/.f64 1 (+.f64 1 (sqrt.f64 (/.f64 1 x))))
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
(/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)))
(/.f64 1 (+.f64 1 (sqrt.f64 (/.f64 1 x))))
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
(/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)))
(/.f64 1 (+.f64 1 (sqrt.f64 (/.f64 1 x))))
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
(/.f64 1 (+.f64 1 (pow.f64 (/.f64 1 x) 1/2)))
(/.f64 1 (+.f64 1 (sqrt.f64 (/.f64 1 x))))
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
(/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1))
(/.f64 1 (+.f64 1 (sqrt.f64 (/.f64 1 x))))
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
(/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1))
(/.f64 1 (+.f64 1 (sqrt.f64 (/.f64 1 x))))
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
(/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1))
(/.f64 1 (+.f64 1 (sqrt.f64 (/.f64 1 x))))
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))
(/.f64 1 (+.f64 (exp.f64 (*.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1))
(/.f64 1 (+.f64 1 (sqrt.f64 (/.f64 1 x))))
(/.f64 1 (+.f64 1 (pow.f64 x -1/2)))

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 1 x))
✓0.0b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
2.8b
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
Compiler

Compiled 34 to 22 computations (35.3% saved)

series22.0ms (0.2%)

Counts
1 → 1
Calls

3 calls:

TimeVariablePointExpression
19.0ms
x
@-inf
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
2.0ms
x
@inf
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
1.0ms
x
@0
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))

rewrite67.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
529×log-prod_binary64
519×fma-def_binary64
357×pow-prod-down_binary64
297×pow2_binary64
267×fma-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01017
123017
2336017
Stop Event
1×node limit
Counts
1 → 57
Calls
Call 1
Inputs
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2)) (/.f64 (sqrt.f64 x) (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (/.f64 1 (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2)) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))) (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (neg.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 x 1/2)) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x 1/2)) -2) (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (cbrt.f64 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1/2) -1/2) (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (pow.f64 (cbrt.f64 (+.f64 x 1/2)) 2)) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 x 1/2)) 2)) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (sqrt.f64 (+.f64 x 1/2))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 1/8 (pow.f64 x 3))) (-.f64 (fma.f64 x x 1/4) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (fma.f64 x x -1/4)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3) (pow.f64 (+.f64 x 1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (neg.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 x 1/2) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3) (pow.f64 (+.f64 x 1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 1 (+.f64 x 1/2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2))) 2) (cbrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x 1/2)) -2) (/.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1/2) -1/2) (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (+.f64 1 x)) 1) (/.f64 (pow.f64 (+.f64 1 x) 1/6) (+.f64 x 1/2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (+.f64 1 x) 1/4) 1) (/.f64 (pow.f64 (+.f64 1 x) 1/4) (+.f64 x 1/2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 x 1/2)) 2)) (/.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (cbrt.f64 (+.f64 x 1/2)) 2)) (/.f64 (pow.f64 (+.f64 1 x) 1/4) (cbrt.f64 (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 x 1/2))) (/.f64 (pow.f64 (+.f64 1 x) 1/6) (sqrt.f64 (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (+.f64 1 x) 1/4) (sqrt.f64 (+.f64 x 1/2))) (/.f64 (pow.f64 (+.f64 1 x) 1/4) (sqrt.f64 (+.f64 x 1/2))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 1/8 (pow.f64 x 3))) (-.f64 (fma.f64 x x 1/4) (*.f64 x 1/2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (fma.f64 x x -1/4)) (+.f64 x -1/2) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x 1/2))))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011
Stop Event
1×saturated
Counts
58 → 58
Calls
Call 1
Inputs
2
Outputs
2

localize176.0ms (1.9%)

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)))
✓2.8b
(exp.f64 (log.f64 (-.f64 (*.f64 (pow.f64 x -1/2) 1) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
✓7.8b
(-.f64 (*.f64 (pow.f64 x -1/2) 1) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 64 to 52 computations (18.8% saved)

series5.0ms (0.1%)

Counts
2 → 0
Calls

6 calls:

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

rewrite210.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
524×prod-diff_binary64
454×log-prod_binary64
296×fma-def_binary64
288×pow-prod-down_binary64
271×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01230
125526
2295226
Stop Event
1×node limit
Counts
2 → 260
Calls
Call 1
Inputs
(-.f64 (*.f64 (pow.f64 x -1/2) 1) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(exp.f64 (log.f64 (-.f64 (*.f64 (pow.f64 x -1/2) 1) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
Outputs
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simplify10.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
260 → 134
Calls
Call 1
Inputs
Outputs

eval541.0ms (5.8%)

Compiler

Compiled 19431 to 13798 computations (29% saved)

prune242.0ms (2.6%)

Pruning

30 alts after pruning (26 fresh and 4 done)

PrunedKeptTotal
New83314847
Fresh111223
Picked101
Done145
Total84630876
Error
5.9b
Counts
876 → 30
Alt Table
Click to see full alt table
StatusErrorProgram
22.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
51.0b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)
62.8b
-1
20.5b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
✓32.0b
(pow.f64 x -1/2)
20.0b
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (*.f64 (*.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 x 1))) (pow.f64 (+.f64 x 1) 1/6)))
✓31.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
30.3b
(/.f64 1 (+.f64 x (sqrt.f64 x)))
✓31.5b
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
30.4b
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))
▶25.9b
(-.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
50.8b
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
30.8b
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
60.1b
2
31.3b
(-.f64 (pow.f64 x -1/2) 1)
45.0b
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
50.3b
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
20.0b
(*.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x)))))
▶52.4b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
20.6b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
55.5b
(/.f64 (-.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 3/2) (sqrt.f64 x)) (+.f64 x 1/2))
51.9b
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
▶30.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
54.7b
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)) (+.f64 x 1/2))
▶59.1b
(/.f64 1 (+.f64 x 1/2))
✓50.7b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
▶6.0b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
51.2b
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x))))
22.4b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
23.3b
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
Compiler

Compiled 727 to 554 computations (23.8% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓0.1b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓0.2b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
14.0b
(sqrt.f64 (*.f64 x (+.f64 1 x)))
Compiler

Compiled 58 to 38 computations (34.5% saved)

series7.0ms (0.1%)

Counts
3 → 2
Calls

9 calls:

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

rewrite96.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
597×log-prod_binary64
581×fma-def_binary64
303×pow2_binary64
289×fma-neg_binary64
226×pow-unpow_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01250
127847
2382146
Stop Event
1×node limit
Counts
3 → 129
Calls
Call 1
Inputs
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 -1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (-.f64 x x))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 1 x) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 x (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (/.f64 1 (-.f64 (+.f64 (+.f64 1 x) x) (hypot.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (-.f64 x x)) (/.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 (+.f64 1 x) x) (hypot.f64 x (sqrt.f64 x))) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 1 (-.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.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 /.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 x (-.f64 (+.f64 1 x) (hypot.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (-.f64 x x)) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (neg.f64 (-.f64 (+.f64 (+.f64 1 x) x) (hypot.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (-.f64 x x))) (neg.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x (+.f64 1 x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (+.f64 (+.f64 1 x) x) (hypot.f64 x (sqrt.f64 x))) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 1 (-.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x)))) (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x)))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (exp.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 x)) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) 1 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))))

simplify23.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
012
142
Stop Event
1×saturated
Counts
131 → 130
Calls
Call 1
Inputs
1
1
Outputs
1
1

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite95.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
622×pow1_binary64
582×add-log-exp_binary64
582×log1p-expm1-u_binary64
582×expm1-log1p-u_binary64
572×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11307
215747
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(/.f64 1 (+.f64 x 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 x 1/2))) (cbrt.f64 (pow.f64 (+.f64 x 1/2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1/2) -2)) (/.f64 1 (cbrt.f64 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1/2) -1/2) (pow.f64 (+.f64 x 1/2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (+.f64 -1/2 (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1/2)) 2) -1) (pow.f64 (cbrt.f64 (+.f64 x 1/2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1/2)) -1) (pow.f64 (sqrt.f64 (+.f64 x 1/2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1/8 (pow.f64 x 3))) (fma.f64 x x (-.f64 1/4 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 x 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1/2) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x 1/2) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 x 1/2))))))))

simplify197.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
753×distribute-neg-frac_binary64
747×associate-*l*_binary64
721×fma-def_binary64
496×associate-*r*_binary64
415×times-frac_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
036183
194181
2230178
3608171
41924168
57340168
Stop Event
1×node limit
Counts
34 → 36
Calls
Call 1
Inputs
2
(+.f64 2 (*.f64 -4 x))
(+.f64 2 (+.f64 (*.f64 -4 x) (*.f64 8 (pow.f64 x 2))))
(+.f64 2 (+.f64 (*.f64 -4 x) (+.f64 (*.f64 -16 (pow.f64 x 3)) (*.f64 8 (pow.f64 x 2)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 (pow.f64 x 4)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 (pow.f64 x 4)))))
Outputs
2
(+.f64 2 (*.f64 -4 x))
(fma.f64 -4 x 2)
(+.f64 2 (+.f64 (*.f64 -4 x) (*.f64 8 (pow.f64 x 2))))
(+.f64 2 (fma.f64 -4 x (*.f64 8 (*.f64 x x))))
(fma.f64 -4 x (fma.f64 8 (*.f64 x x) 2))
(fma.f64 x (fma.f64 x 8 -4) 2)
(+.f64 2 (+.f64 (*.f64 -4 x) (+.f64 (*.f64 -16 (pow.f64 x 3)) (*.f64 8 (pow.f64 x 2)))))
(+.f64 2 (fma.f64 -4 x (fma.f64 -16 (pow.f64 x 3) (*.f64 8 (*.f64 x x)))))
(+.f64 2 (fma.f64 -4 x (fma.f64 8 (*.f64 x x) (*.f64 -16 (pow.f64 x 3)))))
(+.f64 (fma.f64 -4 x 2) (*.f64 (*.f64 x x) (+.f64 8 (*.f64 x -16))))
(fma.f64 -4 x (fma.f64 (*.f64 x x) (fma.f64 x -16 8) 2))
(fma.f64 x (fma.f64 x (fma.f64 x -16 8) -4) 2)
(/.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 1/4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 1/4 (pow.f64 x 3))) (/.f64 -1/2 (*.f64 x x)))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))) (/.f64 1/4 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 (pow.f64 x 4)))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1/4 (pow.f64 x 3))) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/8 (pow.f64 x 4))))
(-.f64 (+.f64 (+.f64 (/.f64 1 x) (/.f64 1/4 (pow.f64 x 3))) (/.f64 -1/2 (*.f64 x x))) (/.f64 1/8 (pow.f64 x 4)))
(+.f64 (/.f64 -1/2 (*.f64 x x)) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/8 (pow.f64 x 4)))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 -1/8 (pow.f64 x 4)) (/.f64 (/.f64 1/2 x) x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 -1/2 (*.f64 x x)) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/8 (pow.f64 x 4)))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 (*.f64 x x)) (/.f64 -1/8 (pow.f64 x 4)))))
(/.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 1/4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 1/4 (pow.f64 x 3))) (/.f64 -1/2 (*.f64 x x)))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))) (/.f64 1/4 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 (pow.f64 x 4)))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1/4 (pow.f64 x 3))) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 1/8 (pow.f64 x 4))))
(-.f64 (+.f64 (+.f64 (/.f64 1 x) (/.f64 1/4 (pow.f64 x 3))) (/.f64 -1/2 (*.f64 x x))) (/.f64 1/8 (pow.f64 x 4)))
(+.f64 (/.f64 -1/2 (*.f64 x x)) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/8 (pow.f64 x 4)))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 -1/8 (pow.f64 x 4)) (/.f64 (/.f64 1/2 x) x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 -1/2 (*.f64 x x)) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/8 (pow.f64 x 4)))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 (*.f64 x x)) (/.f64 -1/8 (pow.f64 x 4)))))

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiled 37 to 27 computations (27% saved)

series43.0ms (0.5%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
38.0ms
x
@inf
(/.f64 1 (+.f64 (*.f64 1/2 x) 1))
3.0ms
x
@0
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
1.0ms
x
@-inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
1.0ms
x
@inf
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
1.0ms
x
@-inf
(/.f64 1 (+.f64 (*.f64 1/2 x) 1))

rewrite133.0ms (1.4%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01024
122922
2324322
Stop Event
1×node limit
Counts
2 → 165
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (*.f64 1/2 x) 1))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
Outputs
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simplify99.0ms (1.1%)

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

Useful iterations: 4 (0.0ms)

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

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 1 x))
✓0.1b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
2.8b
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
Compiler

Compiled 49 to 33 computations (32.7% saved)

series4.0ms (0%)

Counts
1 → 1
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
1.0ms
x
@-inf
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
1.0ms
x
@0
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))

rewrite79.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
747×fma-def_binary64
697×log-prod_binary64
401×fma-neg_binary64
286×log-div_binary64
269×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01323
130923
2468623
Stop Event
1×node limit
Counts
1 → 54
Calls
Call 1
Inputs
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))))) (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 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x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) 2) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 x (+.f64 1/2 (/.f64 -1/8 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(2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (pow.f64 (cbrt.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) 2)) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) 2)) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (sqrt.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (pow.f64 (+.f64 x 1/2) 3) (/.f64 -1/512 (pow.f64 x 3)))) (fma.f64 (/.f64 -1/8 x) (-.f64 (/.f64 -1/8 x) (+.f64 x 1/2)) (pow.f64 (+.f64 x 1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (-.f64 (pow.f64 (+.f64 x 1/2) 2) (/.f64 1/64 (*.f64 x x)))) (-.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 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x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3) (pow.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 1 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) (cbrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))))) (cbrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) 2)) (/.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (+.f64 1 x)) 1) (/.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (+.f64 1 x) 1/4) 1) (/.f64 (pow.f64 (+.f64 1 x) 1/4) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 x (+.f64 1/2 (/.f64 -1/8 x)))) 2)) (/.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1/2) 3) (/.f64 -1/512 (pow.f64 x 3)))) (fma.f64 (/.f64 -1/8 x) (-.f64 (/.f64 -1/8 x) (+.f64 x 1/2)) (pow.f64 (+.f64 x 1/2) 2)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 (pow.f64 (+.f64 x 1/2) 2) (/.f64 1/64 (*.f64 x x)))) (-.f64 (+.f64 x 1/2) (/.f64 -1/8 x)) (neg.f64 (/.f64 (sqrt.f64 x) (+.f64 x (+.f64 1/2 (/.f64 -1/8 x))))))))))

simplify13.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
044
154
Stop Event
1×saturated
Counts
55 → 55
Calls
Call 1
Inputs
(*.f64 -8 x)
Outputs
(*.f64 -8 x)

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2)
0.3b
(cbrt.f64 (+.f64 1 x))
✓12.1b
(-.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
Compiler

Compiled 31 to 24 computations (22.6% saved)

series2.0ms (0%)

Counts
1 → 4
Calls

3 calls:

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

rewrite72.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
553×prod-diff_binary64
421×log-prod_binary64
305×fma-def_binary64
268×pow2_binary64
266×pow-prod-down_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01015
122413
2282313
Stop Event
1×node limit
Counts
1 → 103
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
Outputs
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#<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2) (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2) (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/6)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2) (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/6) (cbrt.f64 (pow.f64 x -1)) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/6) (cbrt.f64 (pow.f64 x -1)) (*.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -1)) (pow.f64 x -1/6) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -1)) (pow.f64 x -1/6) (*.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/6)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2)) (/.f64 1 (+.f64 (+.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2))) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2)) (/.f64 1 (+.f64 (+.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2))) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/6)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2)) (/.f64 1 (+.f64 (+.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2))) (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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))) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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))) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/6)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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))) (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) -1/4) (neg.f64 (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) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (*.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))) 2) (cbrt.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))) (sqrt.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2))) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.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 (cbrt.f64 x) -1) (pow.f64 x -1/6) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 x -1/6) (*.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1))))) (#(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 (+.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)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/6)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1))) (pow.f64 (+.f64 x 1) -1/6) (pow.f64 x -1/2))))))

simplify55.0ms (0.6%)

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

Useful iterations: 4 (0.0ms)

IterNodesCost
02565
17063
217661
349855
4143052
5443652
Stop Event
1×node limit
Counts
107 → 111
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)
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 -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)) -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 (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 (fma.f64 x (fma.f64 x 5/16 -3/8) 1/2) -1))

eval647.0ms (6.9%)

Compiler

Compiled 17002 to 12651 computations (25.6% saved)

prune242.0ms (2.6%)

Pruning

43 alts after pruning (36 fresh and 7 done)

PrunedKeptTotal
New75827785
Fresh12921
Picked101
Done178
Total77243815
Error
0.0b
Counts
815 → 43
Alt Table
Click to see full alt table
StatusErrorProgram
6.1b
(/.f64 (/.f64 1 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
59.1b
(pow.f64 (pow.f64 (+.f64 x 1/2) -1/2) 2)
30.6b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
30.1b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
10.3b
(sqrt.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) (fma.f64 x x x)))
51.0b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)
0.5b
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (sqrt.f64 x)) (/.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x))))
62.8b
-1
30.8b
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
22.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
59.1b
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 x 1/2))) 3)
5.9b
(+.f64 0 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
32.2b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
20.5b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
✓32.0b
(pow.f64 x -1/2)
61.3b
(+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x)))
31.5b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x))))
0.8b
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1)
51.0b
(*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2))
6.1b
(/.f64 (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) (sqrt.f64 (*.f64 x (+.f64 1 x))))
0.3b
(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
59.2b
(/.f64 1 x)
✓31.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
6.3b
(/.f64 (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3) (sqrt.f64 (*.f64 x (+.f64 1 x))))
6.8b
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
30.3b
(/.f64 1 (+.f64 x (sqrt.f64 x)))
✓31.5b
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
31.3b
(-.f64 (pow.f64 x -1/2) 1)
59.1b
(exp.f64 (neg.f64 (log.f64 (+.f64 x 1/2))))
✓52.4b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
51.1b
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x 1/2)) 3))
60.1b
2
20.6b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
6.0b
(/.f64 (*.f64 (/.f64 1 (+.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)))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
51.5b
(log.f64 (exp.f64 (/.f64 1 (+.f64 x 1/2))))
31.1b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
✓59.1b
(/.f64 1 (+.f64 x 1/2))
✓50.7b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
✓6.0b
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
51.5b
(-.f64 (+.f64 1 (/.f64 1 (+.f64 x 1/2))) 1)
22.4b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
30.4b
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))
20.0b
(*.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x)))))
Compiler

Compiled 555 to 428 computations (22.9% saved)

regimes239.0ms (2.5%)

Counts
95 → 1
Calls
Call 1
Inputs
(+.f64 (fma.f64 (pow.f64 x -1/2) 1 (neg.f64 (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x)))))) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (/.f64 1 (cbrt.f64 (+.f64 1 x))) (*.f64 (pow.f64 (+.f64 1 x) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 x))))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (sqrt.f64 x)) (/.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x))))
(fma.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2) (fma.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/6)) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 3)) (+.f64 (/.f64 1 x) (-.f64 (pow.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 2) (*.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))
(/.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 3)) (+.f64 (/.f64 1 x) (-.f64 (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2) (*.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))))
(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 (/.f64 (pow.f64 (+.f64 x 1) 1/4) 1) (/.f64 (pow.f64 (+.f64 x 1) 1/4) (hypot.f64 x (sqrt.f64 x))) (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
(/.f64 (*.f64 (/.f64 1 (+.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)))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (*.f64 (*.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 x 1))) (pow.f64 (+.f64 x 1) 1/6)))
(/.f64 (/.f64 1 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(fma.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (fma.f64 x x x) -1/2) (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
(sqrt.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) (fma.f64 x x x)))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (pow.f64 (cbrt.f64 (+.f64 x 1)) 3/2)))
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x))) -1)
(/.f64 (-.f64 (*.f64 (pow.f64 x -1/2) (pow.f64 x -1/2)) (/.f64 1 (+.f64 x 1))) (-.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))
(/.f64 (-.f64 (/.f64 1 x) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 2)) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
(*.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x)))))
(*.f64 (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)) (-.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)))
(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
(+.f64 0 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 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))
(exp.f64 (log.f64 (-.f64 (*.f64 (pow.f64 x -1/2) 1) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
(fma.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(/.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))))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)) (+.f64 x 1/2))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (-.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 3/2) (sqrt.f64 x)) (+.f64 x 1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
(*.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 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 x 1/2))) 3)
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x 1/2)) 3))
(pow.f64 (pow.f64 (+.f64 x 1/2) -1/2) 2)
(log.f64 (exp.f64 (/.f64 1 (+.f64 x 1/2))))
(exp.f64 (neg.f64 (log.f64 (+.f64 x 1/2))))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (pow.f64 x -1/2) 1)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x)))
(-.f64 (+.f64 1 (/.f64 1 (+.f64 x 1/2))) 1)
(/.f64 1 (+.f64 x 1/2))
(/.f64 1 x)
2
2
-1
Outputs
(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
Calls

3 calls:

86.0ms
x
40.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
31.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.3b1x
0.3b1(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.3b1(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 1399 to 1033 computations (26.2% saved)

regimes232.0ms (2.5%)

Counts
73 → 2
Calls
Call 1
Inputs
(+.f64 0 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 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))
(exp.f64 (log.f64 (-.f64 (*.f64 (pow.f64 x -1/2) 1) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
(fma.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/6) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))
(fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
(/.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))))
(/.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 1 x) -3/2)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (pow.f64 (*.f64 x (+.f64 1 x)) -1/2))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)) (+.f64 x 1/2))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 (-.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 3/2) (sqrt.f64 x)) (+.f64 x 1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -2))
(-.f64 (pow.f64 (pow.f64 x 1/4) -2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (pow.f64 x -1/4) 2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -3/2)))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (cbrt.f64 (pow.f64 x -3/2)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 (cbrt.f64 x) -3/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) -3/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (exp.f64 (*.f64 -1/2 (log1p.f64 x))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x))))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
(*.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 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 x 1/2))) 3)
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x 1/2)) 3))
(pow.f64 (pow.f64 (+.f64 x 1/2) -1/2) 2)
(log.f64 (exp.f64 (/.f64 1 (+.f64 x 1/2))))
(exp.f64 (neg.f64 (log.f64 (+.f64 x 1/2))))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (pow.f64 x -1/2) 1)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x)))
(-.f64 (+.f64 1 (/.f64 1 (+.f64 x 1/2))) 1)
(/.f64 1 (+.f64 x 1/2))
(/.f64 1 x)
2
2
-1
Outputs
(+.f64 0 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x))))
Calls

3 calls:

94.0ms
x
46.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
45.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.1b2x
0.2b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 882 to 654 computations (25.9% saved)

bsearch43.0ms (0.5%)

Algorithm
1×binary-search
Steps
TimeLeftRight
42.0ms
5.055835627447984e+124
1.6910452721298822e+128
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes99.0ms (1.1%)

Counts
48 → 2
Calls
Call 1
Inputs
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))))
(*.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 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
(/.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 x 1/2))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x 1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(-.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 x 1/2))) 3)
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x 1/2)) 3))
(pow.f64 (pow.f64 (+.f64 x 1/2) -1/2) 2)
(log.f64 (exp.f64 (/.f64 1 (+.f64 x 1/2))))
(exp.f64 (neg.f64 (log.f64 (+.f64 x 1/2))))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (pow.f64 x -1/2) 1)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x)))
(-.f64 (+.f64 1 (/.f64 1 (+.f64 x 1/2))) 1)
(/.f64 1 (+.f64 x 1/2))
(/.f64 1 x)
2
2
-1
Outputs
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x)))
(+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))
Calls

3 calls:

46.0ms
x
20.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
18.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.2b2x
0.2b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b2(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 499 to 372 computations (25.5% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.5528874697853107e-7
0.010037002864838607
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes24.0ms (0.3%)

Counts
30 → 1
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 x 1/2))) 3)
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x 1/2)) 3))
(pow.f64 (pow.f64 (+.f64 x 1/2) -1/2) 2)
(log.f64 (exp.f64 (/.f64 1 (+.f64 x 1/2))))
(exp.f64 (neg.f64 (log.f64 (+.f64 x 1/2))))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (pow.f64 x -1/2) 1)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x)))
(-.f64 (+.f64 1 (/.f64 1 (+.f64 x 1/2))) 1)
(/.f64 1 (+.f64 x 1/2))
(/.f64 1 x)
2
2
-1
Outputs
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
Calls

1 calls:

16.0ms
x
Results
ErrorSegmentsBranch
20.5b1x
Compiler

Compiled 219 to 168 computations (23.3% saved)

regimes37.0ms (0.4%)

Counts
28 → 2
Calls
Call 1
Inputs
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 x 1/2))) 3)
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x 1/2)) 3))
(pow.f64 (pow.f64 (+.f64 x 1/2) -1/2) 2)
(log.f64 (exp.f64 (/.f64 1 (+.f64 x 1/2))))
(exp.f64 (neg.f64 (log.f64 (+.f64 x 1/2))))
(-.f64 (pow.f64 (*.f64 x x) -1/4) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (+.f64 (/.f64 1 x) -1) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2))
(-.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (*.f64 -1/2 x) 1))
(-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1))
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x))))
(/.f64 1 (+.f64 x (sqrt.f64 x)))
(-.f64 (/.f64 1 (sqrt.f64 x)) 1)
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (pow.f64 x -1/2) 1)
(sqrt.f64 (/.f64 1 x))
(pow.f64 x -1/2)
(+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x)))
(-.f64 (+.f64 1 (/.f64 1 (+.f64 x 1/2))) 1)
(/.f64 1 (+.f64 x 1/2))
(/.f64 1 x)
2
2
-1
Outputs
(-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2))
Calls

1 calls:

30.0ms
x
Results
ErrorSegmentsBranch
21.3b2x
Compiler

Compiled 201 to 156 computations (22.4% saved)

bsearch22.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
21.0ms
0.015014295139124887
13.046402988192021
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes31.0ms (0.3%)

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

1 calls:

27.0ms
x
Results
ErrorSegmentsBranch
21.3b2x
Compiler

Compiled 96 to 73 computations (24% saved)

bsearch22.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
0.015014295139124887
13.046402988192021
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes18.0ms (0.2%)

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

1 calls:

15.0ms
x
Results
ErrorSegmentsBranch
22.0b2x
Compiler

Compiled 61 to 46 computations (24.6% saved)

bsearch23.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
22.0ms
0.015014295139124887
13.046402988192021
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes6.0ms (0.1%)

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

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
59.1b1x
Compiler

Compiled 14 to 11 computations (21.4% saved)

regimes6.0ms (0.1%)

Counts
4 → 1
Calls
Call 1
Inputs
(/.f64 1 x)
2
2
-1
Outputs
(/.f64 1 x)
Calls

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
59.2b1x
Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes5.0ms (0%)

Accuracy

Total -2.6b remaining (-4.4%)

Threshold costs -2.6b (-4.4%)

Counts
3 → 1
Calls
Call 1
Inputs
2
2
-1
Outputs
2
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
60.1b1x
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify17.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
27×+-commutative_binary64
12×*-commutative_binary64
12×sub-neg_binary64
7×neg-sub0_binary64
7×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077269
1112269
2132269
3149269
4157269
5160269
6161269
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
(if (<=.f64 x 50558356274479844083943733932624910637421157741983599214904101064424620718876711999697626572606423930910064066730834136137728) (+.f64 0 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 944473296573929/4722366482869645213696) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))) (+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(if (<=.f64 x 276964859878578144/18446744073709551616) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1))) (*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2)))
(if (<=.f64 x 276964859878578144/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1)) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
(if (<=.f64 x 276964859878578144/18446744073709551616) (-.f64 (pow.f64 x -1/2) 1) (-.f64 (+.f64 1 (/.f64 1 (+.f64 x 1/2))) 1))
(/.f64 1 (+.f64 x 1/2))
(/.f64 1 x)
2
-1
Outputs
(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
(*.f64 (/.f64 -1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (/.f64 1 (neg.f64 (hypot.f64 x (sqrt.f64 x)))))
(if (<=.f64 x 50558356274479844083943733932624910637421157741983599214904101064424620718876711999697626572606423930910064066730834136137728) (+.f64 0 (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x)))))
(if (<=.f64 x 50558356274479844083943733932624910637421157741983599214904101064424620718876711999697626572606423930910064066730834136137728) (/.f64 (pow.f64 (fma.f64 x x x) -1/2) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 1/2 (+.f64 (+.f64 x (/.f64 1/16 (*.f64 x x))) (/.f64 -1/8 x)))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 944473296573929/4722366482869645213696) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))) (+.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))
(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) 944473296573929/4722366482869645213696) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (/.f64 -1/8 x) (+.f64 x 1/2))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(if (<=.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) 944473296573929/4722366482869645213696) (/.f64 (/.f64 1 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (+.f64 (/.f64 -1/8 x) (+.f64 x 1/2))) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
(if (<=.f64 x 276964859878578144/18446744073709551616) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 (*.f64 1/2 x) 1))) (*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2)))
(if (<=.f64 x 8655151871205567/576460752303423488) (-.f64 (pow.f64 x -1/2) (/.f64 1 (+.f64 1 (*.f64 x 1/2)))) (*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2)))
(if (<=.f64 x 8655151871205567/576460752303423488) (+.f64 (pow.f64 x -1/2) (/.f64 -1 (+.f64 1 (*.f64 x 1/2)))) (*.f64 (/.f64 1 (fma.f64 x x -1/4)) (+.f64 x -1/2)))
(if (<=.f64 x 276964859878578144/18446744073709551616) (-.f64 (pow.f64 x -1/2) (+.f64 (*.f64 -1/2 x) 1)) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
(if (<=.f64 x 8655151871205567/576460752303423488) (-.f64 (pow.f64 x -1/2) (+.f64 1 (*.f64 x -1/2))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
(if (<=.f64 x 8655151871205567/576460752303423488) (+.f64 (pow.f64 x -1/2) (+.f64 -1 (*.f64 x 1/2))) (/.f64 1 (sqrt.f64 (*.f64 x (+.f64 1 x)))))
(if (<=.f64 x 276964859878578144/18446744073709551616) (-.f64 (pow.f64 x -1/2) 1) (-.f64 (+.f64 1 (/.f64 1 (+.f64 x 1/2))) 1))
(if (<=.f64 x 8655151871205567/576460752303423488) (+.f64 (pow.f64 x -1/2) -1) (+.f64 (+.f64 1 (/.f64 1 (+.f64 x 1/2))) -1))
(if (<=.f64 x 8655151871205567/576460752303423488) (+.f64 -1 (pow.f64 x -1/2)) (+.f64 -1 (+.f64 1 (/.f64 1 (+.f64 x 1/2)))))
(/.f64 1 (+.f64 x 1/2))
(/.f64 1 x)
2
-1
Compiler

Compiled 192 to 147 computations (23.4% saved)

soundness96.0ms (1%)

Algorithm
1×egg-herbie
Rules
671×fma-neg_binary64
642×times-frac_binary64
433×cancel-sign-sub-inv_binary64
393×fma-def_binary64
385×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
045108
1129106
2371106
3920100
43432100
Stop Event
1×node limit
Compiler

Compiled 187 to 152 computations (18.7% saved)

end118.0ms (1.3%)

Compiler

Compiled 182 to 135 computations (25.8% saved)

Profiling

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