Details

Time bar (total: 6.3s)

analyze83.0ms (1.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%74.9%25.1%4
12.5%62.4%25.1%5
18.7%43.7%37.6%6
28.1%34.3%37.6%7
32.8%23.4%43.8%8
36.7%18.3%45%9
39.4%12.3%48.3%10
41.6%9.5%49%11
43%6.3%50.7%12
Compiler

Compiled 11 to 8 computations (27.3% saved)

sample2.1s (33.4%)

Results
2.1s8254×body256valid
53.0ms407×body256invalid
0.0ms2×body1024valid

preprocess49.0ms (0.8%)

Algorithm
2×egg-herbie
Rules
258×fma-neg_binary64
254×fma-def_binary64
74×cancel-sign-sub-inv_binary64
60×sub-neg_binary64
40×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01224
12620
26520
313020
428520
559220
698320
7114620
8120620
9121820
022
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(+.f64 (-.f64 1 y) (*.f64 x (sqrt.f64 y)))
Outputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(+.f64 (-.f64 1 y) (*.f64 x (sqrt.f64 y)))
(fma.f64 x (sqrt.f64 y) (-.f64 1 y))
(-.f64 (fma.f64 x (sqrt.f64 y) 1) y)
Compiler

Compiled 12 to 9 computations (25% saved)

simplify21.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
151×fma-def_binary64
131×fma-neg_binary64
46×cancel-sign-sub-inv_binary64
37×sub-neg_binary64
30×unsub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0812
11610
23710
37210
415010
531210
651110
763510
871710
973110
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
Outputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)

eval1.0ms (0%)

Compiler

Compiled 17 to 10 computations (41.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
0.1b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.1b
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
Compiler

Compiled 10 to 7 computations (30% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiled 22 to 10 computations (54.5% saved)

series8.0ms (0.1%)

Counts
2 → 15
Calls

12 calls:

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

rewrite58.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
969×pow1_binary64
903×add-log-exp_binary64
903×log1p-expm1-u_binary64
903×expm1-log1p-u_binary64
90×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0818
117416
2242516
Stop Event
1×node limit
Counts
2 → 52
Calls
Call 1
Inputs
(*.f64 y (sqrt.f64 x))
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 y (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (sqrt.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x))))) (/.f64 (*.f64 x (*.f64 y y)) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 y (sqrt.f64 x)) 3)) (/.f64 1 (+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 (*.f64 y (sqrt.f64 x)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (/.f64 1 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 (*.f64 y (sqrt.f64 x)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x)))) (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 y (sqrt.f64 x)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 y (sqrt.f64 x)) 3)) (+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 (*.f64 y (sqrt.f64 x)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 y (sqrt.f64 x)) 3)) (+.f64 (*.f64 x (*.f64 y y)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 y (sqrt.f64 x)) 3))) (neg.f64 (+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 (*.f64 y (sqrt.f64 x)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) (neg.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (-.f64 x (*.f64 y (sqrt.f64 x))) 3)) (+.f64 1 (+.f64 (*.f64 (-.f64 x (*.f64 y (sqrt.f64 x))) (-.f64 x (*.f64 y (sqrt.f64 x)))) (-.f64 x (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (-.f64 x (*.f64 y (sqrt.f64 x))) (-.f64 x (*.f64 y (sqrt.f64 x))))) (+.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x (*.f64 y y)) (pow.f64 (-.f64 1 x) 2)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (sqrt.f64 x) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) y (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) (cbrt.f64 (*.f64 y (sqrt.f64 x))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (cbrt.f64 (-.f64 1 x)) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 y (sqrt.f64 x))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (-.f64 1 x)) (*.f64 y (sqrt.f64 x)))))))

simplify29.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
190×fma-def_binary64
155×fma-neg_binary64
55×cancel-sign-sub-inv_binary64
34×distribute-rgt-in_binary64
33×associate--r+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011113
121113
232113
354113
488113
5147113
6283113
7436113
8595113
9733113
10825113
11831113
Stop Event
1×saturated
Counts
67 → 57
Calls
Call 1
Inputs
1
(*.f64 -1 x)
(*.f64 -1 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
Outputs
1
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

eval15.0ms (0.2%)

Compiler

Compiled 799 to 397 computations (50.3% saved)

prune15.0ms (0.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New48957
Fresh000
Picked011
Done000
Total481058
Error
0.1b
Counts
58 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
26.4b
(*.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (/.f64 1 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x))))))
19.7b
(-.f64 1 x)
19.1b
(+.f64 (-.f64 1 x) (sqrt.f64 (*.f64 x (*.f64 y y))))
41.8b
1
▶26.4b
(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))
▶41.3b
(neg.f64 x)
▶0.4b
(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
▶26.3b
(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
✓0.1b
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
▶43.1b
(*.f64 y (sqrt.f64 x))
Compiler

Compiled 233 to 166 computations (28.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
0.3b
(*.f64 y (sqrt.f64 x))
✓0.6b
(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)
✓5.2b
(cbrt.f64 (*.f64 y (sqrt.f64 x)))
Compiler

Compiled 38 to 16 computations (57.9% saved)

series59.0ms (0.9%)

Counts
3 → 39
Calls

18 calls:

TimeVariablePointExpression
26.0ms
x
@0
(cbrt.f64 (*.f64 y (sqrt.f64 x)))
11.0ms
x
@inf
(cbrt.f64 (*.f64 y (sqrt.f64 x)))
4.0ms
y
@-inf
(cbrt.f64 (*.f64 y (sqrt.f64 x)))
3.0ms
x
@-inf
(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)
2.0ms
x
@-inf
(cbrt.f64 (*.f64 y (sqrt.f64 x)))

rewrite75.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
495×fma-def_binary64
479×log-prod_binary64
354×pow-prod-down_binary64
268×pow2_binary64
207×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01126
124324
2294724
Stop Event
1×node limit
Counts
3 → 151
Calls
Call 1
Inputs
(cbrt.f64 (*.f64 y (sqrt.f64 x)))
(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)
(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
Outputs
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(#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (sqrt.f64 x) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) y (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y (sqrt.f64 x)) 1 (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) (cbrt.f64 (*.f64 x (*.f64 y y))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 x) 1 (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) (cbrt.f64 (*.f64 y (sqrt.f64 x))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 y) (*.f64 (pow.f64 x 1/6) (cbrt.f64 (*.f64 x (*.f64 y y)))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (sqrt.f64 x)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (*.f64 y y)))) (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x)))) (cbrt.f64 (*.f64 x (*.f64 y y)))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (*.f64 (pow.f64 x 1/6) y) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (cbrt.f64 (-.f64 1 x)) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 y (sqrt.f64 x))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (pow.f64 (*.f64 y x) 1/2) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 1/6) (pow.f64 (*.f64 y (sqrt.f64 x)) 5/6) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (-.f64 1 x)) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 x 3)) (/.f64 1 (+.f64 1 (fma.f64 x x x))) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (*.f64 x x)) (/.f64 1 (+.f64 x 1)) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 5/6) (pow.f64 (*.f64 y (sqrt.f64 x)) 1/6) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y (cbrt.f64 x)) (pow.f64 x 1/6) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y (pow.f64 x 1/4)) (pow.f64 x 1/4) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 x y) 1/2) (sqrt.f64 y) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) 1) (cbrt.f64 (*.f64 y (sqrt.f64 x))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) (cbrt.f64 y)) (pow.f64 x 1/6) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) (cbrt.f64 (cbrt.f64 (*.f64 x (*.f64 y y))))) (cbrt.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x)))) (-.f64 1 x))))))

simplify109.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
642×fma-def_binary64
508×unswap-sqr_binary64
477×fma-neg_binary64
442×cube-prod_binary64
400×sqr-pow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
035315
1104295
2234295
3530295
41641295
53623295
65378295
75998295
86537295
97172295
Stop Event
1×node limit
Counts
190 → 163
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) (*.f64 1 y)) 1/3))
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) (*.f64 1 y)) 1/3))
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) (*.f64 1 y)) 1/3))
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) (*.f64 1 y)) 1/3))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x)))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x)))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x)))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x)))
(+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) 1)
(+.f64 1 (+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (*.f64 -1 x)))
(+.f64 1 (+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (*.f64 -1 x)))
(+.f64 1 (+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (*.f64 -1 x)))
(*.f64 -1 x)
(+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(*.f64 -1 x)
(+.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(+.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(+.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(-.f64 1 x)
(-.f64 1 x)
(-.f64 1 x)
Outputs
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (sqrt.f64 1) (*.f64 (pow.f64 y 1/3) (pow.f64 x 1/6)))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) (*.f64 1 y)) 1/3))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) (*.f64 1 y)) 1/3))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) (*.f64 1 y)) 1/3))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (pow.f64 (*.f64 -1 x) 1/6) (pow.f64 (*.f64 (sqrt.f64 -1) (*.f64 1 y)) 1/3))
(*.f64 (cbrt.f64 y) (pow.f64 x 1/6))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) 1)
(+.f64 1 (*.f64 y (sqrt.f64 x)))
(fma.f64 y (sqrt.f64 x) 1)
(+.f64 1 (+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (*.f64 -1 x)))
(+.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(+.f64 1 (+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (*.f64 -1 x)))
(+.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(+.f64 1 (+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (*.f64 -1 x)))
(+.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(+.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(+.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(+.f64 (*.f64 (pow.f64 1 1/6) (*.f64 y (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(+.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(+.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(+.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(+.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(+.f64 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (*.f64 (pow.f64 1 1/6) (sqrt.f64 x))) (+.f64 1 (*.f64 -1 x)))
(+.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 1 x)
(-.f64 1 x)
(-.f64 1 x)

localize2.0ms (0%)

Compiler

Compiled 5 to 3 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.3b
(*.f64 y (sqrt.f64 x))
Compiler

Compiled 10 to 4 computations (60% saved)

localize45.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 y (sqrt.f64 x))
✓2.5b
(-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))
✓8.6b
(*.f64 x (*.f64 y y))
✓20.9b
(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
Compiler

Compiled 73 to 30 computations (58.9% saved)

series20.0ms (0.3%)

Counts
3 → 63
Calls

18 calls:

TimeVariablePointExpression
8.0ms
x
@0
(-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))
2.0ms
x
@0
(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
1.0ms
x
@-inf
(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
1.0ms
x
@inf
(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
1.0ms
y
@0
(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))

rewrite258.0ms (4.1%)

Algorithm
1×batch-egg-rewrite
Rules
874×fma-def_binary64
395×fma-neg_binary64
293×expm1-udef_binary64
291×log1p-udef_binary64
240×log-pow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01553
134851
2518551
Stop Event
1×node limit
Counts
3 → 176
Calls
Call 1
Inputs
(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
(*.f64 x (*.f64 y y))
(-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (neg.f64 (/.f64 (*.f64 x (*.f64 y y)) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (/.f64 (*.f64 x (*.f64 y y)) (-.f64 1 (fma.f64 y (sqrt.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 (*.f64 y y) (neg.f64 x) (pow.f64 (-.f64 1 x) 2)) (-.f64 1 (fma.f64 y (sqrt.f64 x) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (fma.f64 (*.f64 y y) (neg.f64 x) (pow.f64 (-.f64 1 x) 2)) (-.f64 1 (fma.f64 y (sqrt.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (*.f64 y y) (neg.f64 x) (pow.f64 (-.f64 1 x) 2)) (/.f64 1 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 (*.f64 y y) (neg.f64 x) (pow.f64 (-.f64 1 x) 2)) (-.f64 1 (fma.f64 y 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fma.f64 (-.f64 (pow.f64 (-.f64 1 x) 6) (pow.f64 (*.f64 x (*.f64 y y)) 3)) (/.f64 1 (fma.f64 (*.f64 x (*.f64 y y)) (fma.f64 x (*.f64 y y) (pow.f64 (-.f64 1 x) 2)) (pow.f64 (-.f64 1 x) 4))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x (*.f64 y y)))) (cbrt.f64 (*.f64 (*.f64 x x) (pow.f64 y 4))) (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (-.f64 1 x) 6) (pow.f64 (*.f64 x (*.f64 y y)) 3)) (/.f64 1 (fma.f64 (*.f64 x (*.f64 y y)) (fma.f64 x (*.f64 y y) (pow.f64 (-.f64 1 x) 2)) (pow.f64 (-.f64 1 x) 4))) (fma.f64 (neg.f64 y) (*.f64 x y) (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 x) (*.f64 y y) (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (-.f64 1 x) 4) (*.f64 (*.f64 x x) (pow.f64 y 4))) (/.f64 1 (fma.f64 x (*.f64 y y) (pow.f64 (-.f64 1 x) 2))) (fma.f64 (*.f64 (*.f64 y y) (neg.f64 x)) 1 (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (-.f64 1 x) 4) (*.f64 (*.f64 x x) (pow.f64 y 4))) (/.f64 1 (fma.f64 x (*.f64 y y) (pow.f64 (-.f64 1 x) 2))) (fma.f64 (neg.f64 x) (*.f64 y y) (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (-.f64 1 x) 4) (*.f64 (*.f64 x x) (pow.f64 y 4))) (/.f64 1 (fma.f64 x (*.f64 y y) (pow.f64 (-.f64 1 x) 2))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x (*.f64 y y)))) (cbrt.f64 (*.f64 (*.f64 x x) (pow.f64 y 4))) (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (-.f64 1 x) 4) (*.f64 (*.f64 x x) (pow.f64 y 4))) (/.f64 1 (fma.f64 x (*.f64 y y) (pow.f64 (-.f64 1 x) 2))) (fma.f64 (neg.f64 y) (*.f64 x y) (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x y) (neg.f64 y) (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (-.f64 1 x) (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (-.f64 1 x)) (*.f64 (*.f64 y y) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (-.f64 1 x) (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (-.f64 1 x)) (*.f64 (*.f64 (*.f64 y y) (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 y y) (neg.f64 x))) (cbrt.f64 (*.f64 (*.f64 y y) (neg.f64 x)))) (cbrt.f64 (*.f64 (*.f64 y y) (neg.f64 x))) (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (*.f64 y y) (neg.f64 x))) (sqrt.f64 (*.f64 (*.f64 y y) (neg.f64 x))) (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (*.f64 y (sqrt.f64 x))) (*.f64 y (sqrt.f64 x)) (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (*.f64 y y)) x (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 x (*.f64 y y)) (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (fma.f64 (*.f64 (*.f64 y y) (neg.f64 x)) 1 (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (fma.f64 (neg.f64 x) (*.f64 y y) (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x (*.f64 y y)))) (cbrt.f64 (*.f64 (*.f64 x x) (pow.f64 y 4))) (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (fma.f64 (neg.f64 y) (*.f64 x y) (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (*.f64 (*.f64 x x) (pow.f64 y 4)))) (cbrt.f64 (*.f64 x (*.f64 y y))) (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (*.f64 x y)) y (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 x) 1) (*.f64 y y) (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (-.f64 1 x) (cbrt.f64 (pow.f64 (-.f64 1 x) 2))) (cbrt.f64 (-.f64 1 x)) (*.f64 (*.f64 y y) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (-.f64 1 x) (cbrt.f64 (pow.f64 (-.f64 1 x) 2))) (cbrt.f64 (-.f64 1 x)) (*.f64 (*.f64 (*.f64 y y) (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 x) y) y (pow.f64 (-.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 x) (cbrt.f64 (pow.f64 y 4))) (pow.f64 (cbrt.f64 y) 2) (pow.f64 (-.f64 1 x) 2))))))

simplify75.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
496×unsub-neg_binary64
409×fma-def_binary64
296×difference-of-squares_binary64
283×sub-neg_binary64
256×distribute-rgt-out--_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
030664
186592
2218528
3628528
42522528
55604528
Stop Event
1×node limit
Counts
239 → 199
Calls
Call 1
Inputs
1
(*.f64 -1 x)
(*.f64 -1 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 (pow.f64 y 2) x)
1
(+.f64 1 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))))
(+.f64 1 (+.f64 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2))
(+.f64 1 (+.f64 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 (-.f64 2 (*.f64 -1 (pow.f64 y 2))) x)))
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 (-.f64 2 (*.f64 -1 (pow.f64 y 2))) x))))
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 (-.f64 2 (*.f64 -1 (pow.f64 y 2))) x))))
(pow.f64 (-.f64 1 x) 2)
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(*.f64 -1 (*.f64 (pow.f64 y 2) x))
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(*.f64 -1 (*.f64 (pow.f64 y 2) x))
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
Outputs
1
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
(*.f64 (pow.f64 y 2) x)
(*.f64 x (*.f64 y y))
1
(+.f64 1 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))))
(+.f64 1 (*.f64 (neg.f64 x) (+.f64 2 (*.f64 y y))))
(-.f64 1 (*.f64 x (fma.f64 y y 2)))
(+.f64 1 (+.f64 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 1 (+.f64 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2))
(fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x))
(*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2))))
(*.f64 x (-.f64 x (fma.f64 y y 2)))
(+.f64 1 (+.f64 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 1 (+.f64 (*.f64 -1 (*.f64 x (+.f64 2 (pow.f64 y 2)))) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 (-.f64 2 (*.f64 -1 (pow.f64 y 2))) x)))
(fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x))
(*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2))))
(*.f64 x (-.f64 x (fma.f64 y y 2)))
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 (-.f64 2 (*.f64 -1 (pow.f64 y 2))) x))))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 (-.f64 2 (*.f64 -1 (pow.f64 y 2))) x))))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(pow.f64 (-.f64 1 x) 2)
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(*.f64 -1 (*.f64 (pow.f64 y 2) x))
(*.f64 (neg.f64 (*.f64 y y)) x)
(*.f64 x (*.f64 y (neg.f64 y)))
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(*.f64 -1 (*.f64 (pow.f64 y 2) x))
(*.f64 (neg.f64 (*.f64 y y)) x)
(*.f64 x (*.f64 y (neg.f64 y)))
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)
(+.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 1 (fma.f64 -1 (*.f64 x (+.f64 2 (*.f64 y y))) (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x (neg.f64 (fma.f64 y y 2)))))
(fma.f64 x (-.f64 x (fma.f64 y y 2)) 1)

localize56.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 y (sqrt.f64 x))
2.5b
(-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))
8.6b
(*.f64 x (*.f64 y y))
✓20.9b
(/.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))
Compiler

Compiled 95 to 40 computations (57.9% saved)

series7.0ms (0.1%)

Counts
1 → 15
Calls

6 calls:

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

rewrite75.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
865×fma-def_binary64
388×fma-neg_binary64
291×expm1-udef_binary64
289×log1p-udef_binary64
239×log-pow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01530
134728
2510228
Stop Event
1×node limit
Counts
1 → 43
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) (neg.f64 (/.f64 (fma.f64 y (sqrt.f64 x) x) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) (/.f64 (fma.f64 y (sqrt.f64 x) x) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (-.f64 1 x) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) (/.f64 (*.f64 y (sqrt.f64 x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) 2) (cbrt.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) 2)) (*.f64 (cbrt.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) (sqrt.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (*.f64 (sqrt.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (/.f64 1 (neg.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) 2))) (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (cbrt.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 (-.f64 1 x) (sqrt.f64 (*.f64 (*.f64 x y) (neg.f64 y))))) (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (hypot.f64 (-.f64 1 x) (sqrt.f64 (*.f64 (*.f64 x y) (neg.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) 2)) 1) (/.f64 (cbrt.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) 2)) (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) 2))) (cbrt.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) 2))) (/.f64 (sqrt.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (cbrt.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) 2)) (hypot.f64 (-.f64 1 x) (sqrt.f64 (*.f64 (*.f64 x y) (neg.f64 y))))) (/.f64 (cbrt.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) (hypot.f64 (-.f64 1 x) (sqrt.f64 (*.f64 (*.f64 x y) (neg.f64 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 6) (pow.f64 (*.f64 x (*.f64 y y)) 3))) (fma.f64 (*.f64 x (*.f64 y y)) (fma.f64 x (*.f64 y y) (pow.f64 (-.f64 1 x) 2)) (pow.f64 (-.f64 1 x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 4) (*.f64 (pow.f64 y 4) (*.f64 x x)))) (fma.f64 x (*.f64 y y) (pow.f64 (-.f64 1 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (fma.f64 y (sqrt.f64 x) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (neg.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) 3) (pow.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 (fma.f64 y (sqrt.f64 x) x)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) (neg.f64 (/.f64 (fma.f64 y (sqrt.f64 x) x) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) (cbrt.f64 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))) (cbrt.f64 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) (neg.f64 (/.f64 (fma.f64 y (sqrt.f64 x) x) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))) (neg.f64 (/.f64 (fma.f64 y (sqrt.f64 x) x) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 6) (pow.f64 (*.f64 x (*.f64 y y)) 3))) (fma.f64 (*.f64 x (*.f64 y y)) (fma.f64 x (*.f64 y y) (pow.f64 (-.f64 1 x) 2)) (pow.f64 (-.f64 1 x) 4)) (neg.f64 (/.f64 (fma.f64 y (sqrt.f64 x) x) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (-.f64 (pow.f64 (-.f64 1 x) 4) (*.f64 (pow.f64 y 4) (*.f64 x x)))) (fma.f64 x (*.f64 y y) (pow.f64 (-.f64 1 x) 2)) (neg.f64 (/.f64 (fma.f64 y (sqrt.f64 x) x) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))))))))))

simplify127.0ms (2%)

Algorithm
1×egg-herbie
Rules
570×cancel-sign-sub-inv_binary64
547×associate-/l/_binary64
536×fma-neg_binary64
464×associate-/r/_binary64
318×times-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
051486
1148451
2515441
32842429
Stop Event
1×node limit
Counts
58 → 60
Calls
Call 1
Inputs
1
(/.f64 -1 x)
(/.f64 -1 x)
(/.f64 1 (-.f64 1 x))
(+.f64 (/.f64 1 (-.f64 1 x)) (*.f64 -1 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))
(+.f64 (/.f64 (*.f64 (pow.f64 y 2) x) (pow.f64 (-.f64 1 x) 3)) (+.f64 (/.f64 1 (-.f64 1 x)) (*.f64 -1 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))))
(+.f64 (*.f64 -1 (*.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 4)) (sqrt.f64 (pow.f64 x 3)))) (+.f64 (/.f64 (*.f64 (pow.f64 y 2) x) (pow.f64 (-.f64 1 x) 3)) (+.f64 (/.f64 1 (-.f64 1 x)) (*.f64 -1 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (+.f64 (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (+.f64 (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 (pow.f64 y 4) (pow.f64 x 2)))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (+.f64 (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (+.f64 (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 (pow.f64 y 4) (pow.f64 x 2)))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
Outputs
1
(/.f64 -1 x)
(/.f64 -1 x)
(/.f64 1 (-.f64 1 x))
(+.f64 (/.f64 1 (-.f64 1 x)) (*.f64 -1 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))
(+.f64 (/.f64 1 (-.f64 1 x)) (neg.f64 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))
(-.f64 (/.f64 1 (-.f64 1 x)) (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))
(fma.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (neg.f64 (sqrt.f64 x)) (/.f64 1 (-.f64 1 x)))
(+.f64 (/.f64 (*.f64 (pow.f64 y 2) x) (pow.f64 (-.f64 1 x) 3)) (+.f64 (/.f64 1 (-.f64 1 x)) (*.f64 -1 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))))
(+.f64 (+.f64 (/.f64 (*.f64 y y) (/.f64 (pow.f64 (-.f64 1 x) 3) x)) (/.f64 1 (-.f64 1 x))) (neg.f64 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))
(+.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))) (/.f64 x (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 y y))))
(-.f64 (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 1 x) 3) y)) x (/.f64 1 (-.f64 1 x))) (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))
(-.f64 (/.f64 1 (-.f64 1 x)) (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (-.f64 (sqrt.f64 x) (/.f64 (*.f64 x y) (-.f64 1 x)))))
(+.f64 (*.f64 -1 (*.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 4)) (sqrt.f64 (pow.f64 x 3)))) (+.f64 (/.f64 (*.f64 (pow.f64 y 2) x) (pow.f64 (-.f64 1 x) 3)) (+.f64 (/.f64 1 (-.f64 1 x)) (*.f64 -1 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))))))
(fma.f64 -1 (*.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 4)) (sqrt.f64 (pow.f64 x 3))) (+.f64 (+.f64 (/.f64 (*.f64 y y) (/.f64 (pow.f64 (-.f64 1 x) 3) x)) (/.f64 1 (-.f64 1 x))) (neg.f64 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))))
(+.f64 (-.f64 (/.f64 1 (-.f64 1 x)) (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x))) (fma.f64 (neg.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 4))) (sqrt.f64 (pow.f64 x 3)) (/.f64 x (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 y y)))))
(-.f64 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 4)) (neg.f64 (pow.f64 x 3/2)) (fma.f64 (/.f64 y (/.f64 (pow.f64 (-.f64 1 x) 3) y)) x (/.f64 1 (-.f64 1 x)))) (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (sqrt.f64 x)))
(-.f64 (/.f64 1 (-.f64 1 x)) (+.f64 (*.f64 (/.f64 y (pow.f64 (-.f64 1 x) 2)) (-.f64 (sqrt.f64 x) (/.f64 (*.f64 x y) (-.f64 1 x)))) (/.f64 (pow.f64 y 3) (/.f64 (pow.f64 (-.f64 1 x) 4) (pow.f64 x 3/2)))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (*.f64 x (*.f64 y y))))
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (+.f64 (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (sqrt.f64 (/.f64 1 x)) y)) (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (*.f64 (/.f64 (-.f64 1 x) (*.f64 y y)) (+.f64 (/.f64 -1 x) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (-.f64 1 x) y)))))
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (+.f64 (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 (pow.f64 y 4) (pow.f64 x 2)))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)) (fma.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 (pow.f64 y 4) (*.f64 x x))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y)))) (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (neg.f64 (pow.f64 (-.f64 1 x) 3)) (*.f64 x (*.f64 x (pow.f64 y 4))))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 x (*.f64 x (pow.f64 y 4)))))) (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 (pow.f64 y 4) (*.f64 x x)))) (*.f64 (/.f64 (-.f64 1 x) (*.f64 y y)) (+.f64 (/.f64 -1 x) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (-.f64 1 x) y)))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))) (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (+.f64 -1 x) (*.f64 x (*.f64 y y))))
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (+.f64 (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (sqrt.f64 (/.f64 1 x)) y)) (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (*.f64 (/.f64 (-.f64 1 x) (*.f64 y y)) (+.f64 (/.f64 -1 x) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (-.f64 1 x) y)))))
(+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (*.f64 (pow.f64 y 2) x))) (+.f64 (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 (pow.f64 y 4) (pow.f64 x 2)))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 -1 (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)) (fma.f64 -1 (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 (pow.f64 y 4) (*.f64 x x))) (*.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y)))) (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (neg.f64 (pow.f64 (-.f64 1 x) 3)) (*.f64 x (*.f64 x (pow.f64 y 4))))))
(-.f64 (fma.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 x (*.f64 x (pow.f64 y 4)))))) (/.f64 (-.f64 1 x) (*.f64 x (*.f64 y y))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (pow.f64 (-.f64 1 x) 3) (*.f64 (pow.f64 y 4) (*.f64 x x)))) (*.f64 (/.f64 (-.f64 1 x) (*.f64 y y)) (+.f64 (/.f64 -1 x) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 (-.f64 1 x) y)))))

eval364.0ms (5.7%)

Compiler

Compiled 15525 to 7349 computations (52.7% saved)

prune125.0ms (2%)

Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New60110611
Fresh224
Picked101
Done235
Total60615621
Error
0.0b
Counts
621 → 15
Alt Table
Click to see full alt table
StatusErrorProgram
48.0b
(/.f64 (*.f64 x (-.f64 x (fma.f64 y y 2))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
41.4b
(/.f64 1 (/.f64 -1 x))
▶19.1b
(+.f64 (-.f64 1 x) (sqrt.f64 (*.f64 x (*.f64 y y))))
41.8b
1
▶33.8b
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 (*.f64 x y) 1/2) (sqrt.f64 y)))
▶59.5b
(sqrt.f64 (*.f64 x (*.f64 y y)))
▶0.2b
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y)))
✓0.1b
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
▶19.7b
(-.f64 1 x)
0.4b
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))
✓41.3b
(neg.f64 x)
43.4b
(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)
43.1b
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
43.1b
(/.f64 1 (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
✓43.1b
(*.f64 y (sqrt.f64 x))
Compiler

Compiled 277 to 201 computations (27.4% saved)

localize67.0ms (1.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y)))
✓0.2b
(*.f64 (pow.f64 x 1/4) y)
✓0.3b
(*.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y))
Compiler

Compiled 39 to 26 computations (33.3% saved)

series74.0ms (1.2%)

Counts
3 → 51
Calls

18 calls:

TimeVariablePointExpression
45.0ms
y
@0
(*.f64 (pow.f64 x 1/4) y)
14.0ms
x
@-inf
(*.f64 (pow.f64 x 1/4) y)
8.0ms
x
@0
(*.f64 (pow.f64 x 1/4) y)
1.0ms
x
@inf
(*.f64 (pow.f64 x 1/4) y)
1.0ms
x
@0
(*.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y))

rewrite81.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
511×log-prod_binary64
442×fma-def_binary64
359×pow-prod-down_binary64
282×pow2_binary64
194×pow-to-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01039
122323
2302123
Stop Event
1×node limit
Counts
3 → 117
Calls
Call 1
Inputs
(*.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y))
(*.f64 (pow.f64 x 1/4) y)
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 y (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 y y)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 y) (pow.f64 x 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 y (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 y (sqrt.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 y (sqrt.f64 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 y (sqrt.f64 x))) 3) 1/3))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 x 1/4) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (pow.f64 x 1/4))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (pow.f64 x 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (pow.f64 x 1/4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (pow.f64 x 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x 1/4) y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 1/4) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (*.f64 y (sqrt.f64 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 y 3) (pow.f64 x 3/4)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 1/4) y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 y) (pow.f64 x 1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 y (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 1/4) y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 y 3) (pow.f64 x 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 1/4) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 1/4) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x 1/4) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 1/4) y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (pow.f64 x 1/4) y))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 x 1/4) y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 y) (pow.f64 x 1/8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 1/4) y)) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))) (/.f64 (*.f64 x (*.f64 y y)) (-.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 y (sqrt.f64 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> 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y)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 x 1/4) (*.f64 (sqrt.f64 y) (pow.f64 x 1/8))) (*.f64 (sqrt.f64 y) (pow.f64 x 1/8)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (pow.f64 x 1/4) y) (cbrt.f64 (sqrt.f64 x))) (pow.f64 x 1/12) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (pow.f64 x 1/4) y) (pow.f64 x 1/8)) (pow.f64 x 1/8) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 x y) 1/2) (sqrt.f64 y) (-.f64 1 x))))))

simplify61.0ms (1%)

Algorithm
1×egg-herbie
Rules
749×fma-neg_binary64
675×div-sub_binary64
411×times-frac_binary64
297×fma-def_binary64
232×unswap-sqr_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
023353
157353
2123353
3264353
4689353
51913353
65960353
Stop Event
1×node limit
Counts
168 → 126
Calls
Call 1
Inputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) y)
(*.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) y)
(*.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) y)
(*.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
1
(*.f64 -1 x)
(*.f64 -1 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
Outputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
(*.f64 (pow.f64 (*.f64 1 x) 1/4) y)
(*.f64 y (pow.f64 x 1/4))
1
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

localize3.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
8.6b
(*.f64 x (*.f64 y y))
✓20.4b
(sqrt.f64 (*.f64 x (*.f64 y y)))
Compiler

Compiled 18 to 5 computations (72.2% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@0
(sqrt.f64 (*.f64 x (*.f64 y y)))
0.0ms
x
@-inf
(sqrt.f64 (*.f64 x (*.f64 y y)))
0.0ms
x
@inf
(sqrt.f64 (*.f64 x (*.f64 y y)))
0.0ms
y
@-inf
(sqrt.f64 (*.f64 x (*.f64 y y)))
0.0ms
y
@inf
(sqrt.f64 (*.f64 x (*.f64 y y)))

rewrite44.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
537×pow1_binary64
511×add-sqr-sqrt_binary64
496×add-log-exp_binary64
496×log1p-expm1-u_binary64
496×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
069
11216
214486
Stop Event
1×node limit
Counts
1 → 24
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 x (*.f64 y y)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 y (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) (cbrt.f64 (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) (cbrt.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x y) 1/2) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 y y)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 x)) y))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (sqrt.f64 x))))))))

simplify14.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
38×fma-def_binary64
9×sub-neg_binary64
6×+-commutative_binary64
4×*-commutative_binary64
4×distribute-lft-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0780
11280
22580
32980
43380
55180
67380
78480
89680
912180
Stop Event
1×saturated
Counts
36 → 26
Calls
Call 1
Inputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 y (sqrt.f64 x)))
(*.f64 -1 (*.f64 y (sqrt.f64 x)))
(*.f64 -1 (*.f64 y (sqrt.f64 x)))
(*.f64 -1 (*.f64 y (sqrt.f64 x)))
Outputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 y (sqrt.f64 x)))
(neg.f64 (*.f64 y (sqrt.f64 x)))
(*.f64 y (neg.f64 (sqrt.f64 x)))
(*.f64 -1 (*.f64 y (sqrt.f64 x)))
(neg.f64 (*.f64 y (sqrt.f64 x)))
(*.f64 y (neg.f64 (sqrt.f64 x)))
(*.f64 -1 (*.f64 y (sqrt.f64 x)))
(neg.f64 (*.f64 y (sqrt.f64 x)))
(*.f64 y (neg.f64 (sqrt.f64 x)))
(*.f64 -1 (*.f64 y (sqrt.f64 x)))
(neg.f64 (*.f64 y (sqrt.f64 x)))
(*.f64 y (neg.f64 (sqrt.f64 x)))

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (-.f64 1 x) (sqrt.f64 (*.f64 x (*.f64 y y))))
8.6b
(*.f64 x (*.f64 y y))
20.4b
(sqrt.f64 (*.f64 x (*.f64 y y)))
Compiler

Compiled 32 to 11 computations (65.6% saved)

series2.0ms (0%)

Counts
1 → 15
Calls

6 calls:

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

rewrite62.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
506×fma-def_binary64
464×log-prod_binary64
348×pow-prod-down_binary64
337×exp-prod_binary64
252×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0915
119710
2280310
Stop Event
1×node limit
Counts
1 → 64
Calls
Call 1
Inputs
(+.f64 (-.f64 1 x) (sqrt.f64 (*.f64 x (*.f64 y y))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x))))) (/.f64 (*.f64 x (*.f64 y y)) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 y (sqrt.f64 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 3/2) (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3)) (/.f64 1 (fma.f64 (*.f64 y (sqrt.f64 x)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x)) (pow.f64 (-.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (/.f64 1 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (*.f64 y (sqrt.f64 x)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x)) (pow.f64 (-.f64 1 x) 2)) (fma.f64 (pow.f64 x 3/2) (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3/2) (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3)) (fma.f64 (*.f64 y (sqrt.f64 x)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x)) (pow.f64 (-.f64 1 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3/2) (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3)) (fma.f64 x (*.f64 y y) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 3/2) (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3))) (neg.f64 (fma.f64 (*.f64 y (sqrt.f64 x)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x)) (pow.f64 (-.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) (neg.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (-.f64 x (*.f64 y (sqrt.f64 x))) 3)) (+.f64 1 (+.f64 (pow.f64 (-.f64 x (*.f64 y (sqrt.f64 x))) 2) (-.f64 x (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (-.f64 x (*.f64 y (sqrt.f64 x))) 2)) (+.f64 1 (-.f64 x (*.f64 y (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x (*.f64 y y)) (pow.f64 (-.f64 1 x) 2)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (*.f64 y (sqrt.f64 x)) (-.f64 (*.f64 y (sqrt.f64 x)) (-.f64 1 x)) (pow.f64 (-.f64 1 x) 2)) (fma.f64 (pow.f64 x 3/2) (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 2)) (cbrt.f64 (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))) (sqrt.f64 (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 x))) (pow.f64 (exp.f64 y) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (-.f64 1 x)) (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 x))) (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 x)))) (exp.f64 (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)) (+.f64 1 (expm1.f64 (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 x)))) (+.f64 1 (expm1.f64 (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y (sqrt.f64 x)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 x) 1 (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (sqrt.f64 x) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y (sqrt.f64 x)) 1 (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) (cbrt.f64 (*.f64 x (*.f64 y y))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) (cbrt.f64 (*.f64 y (sqrt.f64 x))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (cbrt.f64 (-.f64 1 x)) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 y (sqrt.f64 x))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) y (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (-.f64 1 x)) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 x 3)) (/.f64 1 (+.f64 1 (fma.f64 x x x))) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (*.f64 x x)) (/.f64 1 (+.f64 1 x)) (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 y) (-.f64 1 x))))))

simplify36.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
224×fma-neg_binary64
110×fma-def_binary64
73×cancel-sign-sub-inv_binary64
44×sub-neg_binary64
34×associate--r+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
014124
132121
267121
3140115
4264115
5423115
6702115
7848115
8893115
9897115
Stop Event
1×saturated
Counts
79 → 74
Calls
Call 1
Inputs
1
(*.f64 -1 x)
(*.f64 -1 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 -1 (*.f64 y (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 -1 (*.f64 y (sqrt.f64 x))) 1) x)
(-.f64 (+.f64 (*.f64 -1 (*.f64 y (sqrt.f64 x))) 1) x)
(-.f64 (+.f64 (*.f64 -1 (*.f64 y (sqrt.f64 x))) 1) x)
Outputs
1
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(*.f64 -1 (*.f64 y (sqrt.f64 x)))
(neg.f64 (*.f64 y (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (neg.f64 y))
(*.f64 y (neg.f64 (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 -1 (*.f64 y (sqrt.f64 x))) 1) x)
(-.f64 (fma.f64 -1 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) 1) x)
(-.f64 1 (+.f64 (*.f64 y (sqrt.f64 x)) x))
(-.f64 1 (fma.f64 y (sqrt.f64 x) x))
(-.f64 (+.f64 (*.f64 -1 (*.f64 y (sqrt.f64 x))) 1) x)
(-.f64 (fma.f64 -1 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) 1) x)
(-.f64 1 (+.f64 (*.f64 y (sqrt.f64 x)) x))
(-.f64 1 (fma.f64 y (sqrt.f64 x) x))
(-.f64 (+.f64 (*.f64 -1 (*.f64 y (sqrt.f64 x))) 1) x)
(-.f64 (fma.f64 -1 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 (neg.f64 y) (sqrt.f64 x) 1) x)
(-.f64 1 (+.f64 (*.f64 y (sqrt.f64 x)) x))
(-.f64 1 (fma.f64 y (sqrt.f64 x) x))

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 (*.f64 x y) 1/2) (sqrt.f64 y)))
✓0.2b
(*.f64 (pow.f64 (*.f64 x y) 1/2) (sqrt.f64 y))
✓11.8b
(pow.f64 (*.f64 x y) 1/2)
Compiler

Compiled 39 to 19 computations (51.3% saved)

series10.0ms (0.2%)

Counts
3 → 27
Calls

18 calls:

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

rewrite73.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
547×log-prod_binary64
426×pow-prod-down_binary64
413×fma-def_binary64
297×pow2_binary64
215×pow-to-exp_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01134
124224
2315622
Stop Event
1×node limit
Counts
3 → 117
Calls
Call 1
Inputs
(pow.f64 (*.f64 x y) 1/2)
(*.f64 (pow.f64 (*.f64 x y) 1/2) (sqrt.f64 y))
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 (*.f64 x y) 1/2) (sqrt.f64 y)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 x y)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 x y))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 x y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 y) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x y) 1/6) (cbrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x y)) (pow.f64 (*.f64 x y) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x y) 1/4) (pow.f64 (*.f64 x y) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) 1) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (cbrt.f64 y)) (pow.f64 y 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (pow.f64 y 1/4)) (pow.f64 y 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x y) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 x y))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 x y))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x y) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 x y))) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 x) y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 x) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (*.f64 x y)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 x) y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 x) y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 y y)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 y (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 x) y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 y (*.f64 x y))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sqrt.f64 x) y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sqrt.f64 x) y))) 1/3))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 x (*.f64 (sqrt.f64 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (-.f64 1 x) 2) (-.f64 (-.f64 1 x) (*.f64 (sqrt.f64 x) y))) (/.f64 (*.f64 y (*.f64 x y)) (-.f64 (-.f64 1 x) (*.f64 (sqrt.f64 x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 (sqrt.f64 x) y 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)) 2) (cbrt.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)) (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 (sqrt.f64 x) y) 3)) (/.f64 1 (fma.f64 (*.f64 (sqrt.f64 x) y) (-.f64 (*.f64 (sqrt.f64 x) y) (-.f64 1 x)) (pow.f64 (-.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 y (*.f64 x y))) (/.f64 1 (-.f64 (-.f64 1 x) (*.f64 (sqrt.f64 x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (*.f64 (sqrt.f64 x) y) (-.f64 (*.f64 (sqrt.f64 x) y) (-.f64 1 x)) (pow.f64 (-.f64 1 x) 2)) (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 (sqrt.f64 x) y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (-.f64 1 x) (*.f64 (sqrt.f64 x) y)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 y (*.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 (sqrt.f64 x) y) 3)) (fma.f64 (*.f64 (sqrt.f64 x) y) (-.f64 (*.f64 (sqrt.f64 x) y) (-.f64 1 x)) (pow.f64 (-.f64 1 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 (sqrt.f64 x) y) 3)) (fma.f64 y (*.f64 x y) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 (*.f64 (sqrt.f64 x) y) (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 y (*.f64 x y))) (-.f64 (-.f64 1 x) (*.f64 (sqrt.f64 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 (sqrt.f64 x) y) 3))) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 x) y) (-.f64 (*.f64 (sqrt.f64 x) y) (-.f64 1 x)) (pow.f64 (-.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 y (*.f64 x y)))) (neg.f64 (-.f64 (-.f64 1 x) (*.f64 (sqrt.f64 x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (-.f64 x (*.f64 (sqrt.f64 x) y)) 3)) (+.f64 1 (+.f64 (pow.f64 (-.f64 x (*.f64 (sqrt.f64 x) y)) 2) (-.f64 x (*.f64 (sqrt.f64 x) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (-.f64 x (*.f64 (sqrt.f64 x) y)) 2)) (+.f64 1 (-.f64 x (*.f64 (sqrt.f64 x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 y (*.f64 x y)) (pow.f64 (-.f64 1 x) 2)) (-.f64 (*.f64 (sqrt.f64 x) y) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (*.f64 (sqrt.f64 x) y) (-.f64 (*.f64 (sqrt.f64 x) y) (-.f64 1 x)) (pow.f64 (-.f64 1 x) 2)) (+.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (*.f64 (sqrt.f64 x) y) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (-.f64 1 x) (*.f64 (sqrt.f64 x) y)) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 y (*.f64 x y)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 x) y))) (exp.f64 (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)) (+.f64 1 (expm1.f64 (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 x) y))) (+.f64 1 (expm1.f64 (-.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 x))) (pow.f64 (exp.f64 y) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (-.f64 1 x)) (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 x) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 x))) (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 x) y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 x) y 1) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 y) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 (*.f64 x y)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 x) y) 1 (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (sqrt.f64 x) y) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 x) (*.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 x) 1 (*.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) y)) (cbrt.f64 (*.f64 y (*.f64 x y))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 y (*.f64 x y))) (cbrt.f64 (*.f64 (sqrt.f64 x) y)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 y) (*.f64 (pow.f64 y 1/6) (sqrt.f64 (*.f64 x y))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (*.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (cbrt.f64 (-.f64 1 x)) (*.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x y)) (*.f64 (pow.f64 (*.f64 x y) 1/6) (sqrt.f64 y)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (sqrt.f64 x) y)) (sqrt.f64 (*.f64 (sqrt.f64 x) y)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) y (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (-.f64 1 x)) (*.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 y 1/4) (*.f64 (pow.f64 y 1/4) (sqrt.f64 (*.f64 x y))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 x 3)) (/.f64 1 (fma.f64 x (+.f64 x 1) 1)) (*.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (*.f64 x x)) (/.f64 1 (+.f64 x 1)) (*.f64 (sqrt.f64 x) y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 x y) 1/4) (*.f64 (pow.f64 (*.f64 x y) 1/4) (sqrt.f64 y)) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (*.f64 x y)) (cbrt.f64 y)) (pow.f64 y 1/6) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (*.f64 x y)) (pow.f64 y 1/4)) (pow.f64 y 1/4) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 y) (cbrt.f64 (*.f64 x y))) (pow.f64 (*.f64 x y) 1/6) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 y) (pow.f64 (*.f64 x y) 1/4)) (pow.f64 (*.f64 x y) 1/4) (-.f64 1 x))))))

simplify83.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
861×fma-neg_binary64
627×fma-def_binary64
446×cube-prod_binary64
399×distribute-rgt-neg-in_binary64
345×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
019185
144185
2113185
3288185
41063185
52462185
63708185
74460185
85531185
97234185
Stop Event
1×unsound
Counts
144 → 126
Calls
Call 1
Inputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
1
(*.f64 -1 x)
(*.f64 -1 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(-.f64 (+.f64 1 (*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))) x)
(-.f64 (+.f64 1 (*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))) x)
(-.f64 (+.f64 1 (*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))) x)
Outputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
1
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(-.f64 1 x)
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 (*.f64 y (sqrt.f64 x)) 1) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(-.f64 (+.f64 1 (*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 1 (*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
(-.f64 (+.f64 1 (*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))) x)
(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

eval206.0ms (3.3%)

Compiler

Compiled 5504 to 2833 computations (48.5% saved)

prune65.0ms (1%)

Pruning

16 alts after pruning (10 fresh and 6 done)

PrunedKeptTotal
New4035408
Fresh257
Picked101
Done167
Total40716423
Error
0.0b
Counts
423 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
48.0b
(/.f64 (*.f64 x (-.f64 x (fma.f64 y y 2))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
41.8b
1
▶41.4b
(/.f64 1 (/.f64 -1 x))
17.1b
(+.f64 (-.f64 1 x) (sqrt.f64 (*.f64 y (*.f64 x y))))
✓41.3b
(neg.f64 x)
▶43.4b
(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)
▶55.0b
(*.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 y))
✓0.2b
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y)))
✓0.1b
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓43.1b
(*.f64 y (sqrt.f64 x))
62.3b
(*.f64 y (neg.f64 (sqrt.f64 x)))
✓19.7b
(-.f64 1 x)
▶0.4b
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))
✓59.5b
(sqrt.f64 (*.f64 x (*.f64 y y)))
▶43.1b
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
31.9b
(+.f64 (-.f64 1 x) (*.f64 (*.f64 (*.f64 (sqrt.f64 x) (pow.f64 y 1/4)) (pow.f64 y 1/4)) (sqrt.f64 y)))
Compiler

Compiled 267 to 191 computations (28.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (sqrt.f64 x)))
✓0.4b
(*.f64 (cbrt.f64 y) (sqrt.f64 x))
✓0.5b
(pow.f64 (cbrt.f64 y) 2)
✓0.5b
(cbrt.f64 y)
Compiler

Compiled 46 to 20 computations (56.5% saved)

series13.0ms (0.2%)

Counts
4 → 12
Calls

18 calls:

TimeVariablePointExpression
2.0ms
y
@-inf
(*.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (sqrt.f64 x)))
2.0ms
y
@0
(*.f64 (cbrt.f64 y) (sqrt.f64 x))
1.0ms
x
@-inf
(*.f64 (cbrt.f64 y) (sqrt.f64 x))
1.0ms
y
@-inf
(pow.f64 (cbrt.f64 y) 2)
1.0ms
y
@-inf
(*.f64 (cbrt.f64 y) (sqrt.f64 x))

rewrite110.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
747×pow1_binary64
691×add-log-exp_binary64
691×log1p-expm1-u_binary64
691×expm1-log1p-u_binary64
673×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0923
118223
2200723
Stop Event
1×node limit
Counts
4 → 63
Calls
Call 1
Inputs
(cbrt.f64 y)
(pow.f64 (cbrt.f64 y) 2)
(*.f64 (cbrt.f64 y) (sqrt.f64 x))
(*.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 2) (cbrt.f64 (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 y)) (pow.f64 (cbrt.f64 (cbrt.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 y 1/6) (pow.f64 y 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 y (cbrt.f64 y)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 y) 1/3) (pow.f64 (sqrt.f64 y) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 y 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 y) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 y 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 y)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (cbrt.f64 y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 y) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 y) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (cbrt.f64 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 2) (cbrt.f64 (*.f64 y (cbrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 2) (*.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (cbrt.f64 y))) (pow.f64 (cbrt.f64 (cbrt.f64 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 y) (pow.f64 y 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 y 1/6) (*.f64 (pow.f64 y 1/6) (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 y) (pow.f64 (cbrt.f64 (cbrt.f64 y)) 2)) (cbrt.f64 (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 y (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cbrt.f64 y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (cbrt.f64 y))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (cbrt.f64 y) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 y) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cbrt.f64 y) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 y 1/6) (pow.f64 x 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (cbrt.f64 y) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cbrt.f64 y)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cbrt.f64 y) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 y (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3/2) y))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 y) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cbrt.f64 y) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cbrt.f64 y) (sqrt.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 y (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 y y) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 y 3) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 y y) (pow.f64 (*.f64 (cbrt.f64 y) (sqrt.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (cbrt.f64 y) (sqrt.f64 x)) 3) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (sqrt.f64 x))))))))

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0572
1672
Stop Event
1×saturated
Counts
75 → 64
Calls
Call 1
Inputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
Outputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))

localize56.0ms (0.9%)

Local error

Found 1 expressions with local error:

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

Compiled 13 to 10 computations (23.1% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite43.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
370×pow1_binary64
359×add-sqr-sqrt_binary64
351×*-un-lft-identity_binary64
343×add-log-exp_binary64
342×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
064
11201
214121
Stop Event
1×node limit
Counts
1 → 50
Calls
Call 1
Inputs
(/.f64 1 (/.f64 -1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (log.f64 (cbrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 x))) (log.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (neg.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (pow.f64 (neg.f64 (/.f64 1 (cbrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (pow.f64 (neg.f64 (pow.f64 x -1/2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 -1) 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (neg.f64 (pow.f64 x -1/2)) -1) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (neg.f64 (cbrt.f64 (pow.f64 x -2))) -1) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 x 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 x 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 x x) -1) 1/3) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 2) 1/3) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 x 5/2) 1/3) (cbrt.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) 3) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 x)) 3) (pow.f64 (sqrt.f64 (cbrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 x)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x . x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) 2))))))

simplify11.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0436
1636
2836
3936
41136
51536
61936
72436
Stop Event
1×saturated
Counts
62 → 50
Calls
Call 1
Inputs
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
(*.f64 -1 x)
Outputs
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)
(*.f64 -1 x)
(neg.f64 x)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(sqrt.f64 (/.f64 1 x))
✓0.2b
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
✓0.7b
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
Compiler

Compiled 26 to 18 computations (30.8% saved)

series10.0ms (0.2%)

Counts
3 → 24
Calls

15 calls:

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

rewrite68.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
796×pow1_binary64
737×add-log-exp_binary64
737×log1p-expm1-u_binary64
737×expm1-log1p-u_binary64
717×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0827
117017
2219217
Stop Event
1×node limit
Counts
3 → 94
Calls
Call 1
Inputs
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(sqrt.f64 (/.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 y (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 y (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) (cbrt.f64 (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 y y))) (cbrt.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (pow.f64 (/.f64 1 y) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 -1 (*.f64 y (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x -1/2) y)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x -1/2) y)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 x -1/2) y)) -1) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 x -1/2) y)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) 1) (/.f64 (cbrt.f64 y) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 1 (cbrt.f64 x))) (/.f64 y (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) (/.f64 1 (cbrt.f64 x))) (/.f64 (cbrt.f64 y) (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 y) (/.f64 1 (cbrt.f64 x))) (/.f64 (sqrt.f64 y) (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (pow.f64 x -1/2))) (/.f64 y (sqrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 y) 2) (sqrt.f64 (pow.f64 x -1/2))) (/.f64 (cbrt.f64 y) (sqrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 (pow.f64 x -1/2))) (/.f64 (sqrt.f64 y) (sqrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 y 1) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 -1 (sqrt.f64 x))) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) 1) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x -1/2) y) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 x)) y))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 y 3) (pow.f64 (/.f64 1 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (sqrt.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (pow.f64 x -1/2) y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 x -1/2) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 1 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x -1/2) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 x -1/2) y)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x -1/2) y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x -1/2) y)) 2) (cbrt.f64 (/.f64 (pow.f64 x -1/2) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 x)) (*.f64 (cbrt.f64 (pow.f64 x -1/2)) (/.f64 1 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x -1/2)) (*.f64 (sqrt.f64 (pow.f64 x -1/2)) (/.f64 1 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 x -1/2) y)) (sqrt.f64 (/.f64 (pow.f64 x -1/2) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (sqrt.f64 x)) (/.f64 1 (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 y) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (cbrt.f64 x)) 1) (/.f64 (cbrt.f64 (pow.f64 x -1/2)) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 x -1/2)) 1) (/.f64 (sqrt.f64 (pow.f64 x -1/2)) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 y) 2)) (/.f64 (pow.f64 x -1/2) (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 (/.f64 (pow.f64 x -1/2) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 x -1/2)) (pow.f64 (cbrt.f64 y) 2)) (/.f64 (sqrt.f64 (pow.f64 x -1/2)) (cbrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 y)) (/.f64 (pow.f64 x -1/2) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (cbrt.f64 x)) (sqrt.f64 y)) (/.f64 (cbrt.f64 (pow.f64 x -1/2)) (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x -1/2) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (sqrt.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 x -1/2) y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 x -1/2) y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 x -1/2) y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 x -1/2) (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (*.f64 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 x -1/2) y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 x -1/2) y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 1 x) 3/2) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 x -1/2) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 x -1/2) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 x -1/2) y)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -1/2)) (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x -1/2)) (sqrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x -2))) (sqrt.f64 (/.f64 1 (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 x -2)) 1/2) (pow.f64 (/.f64 1 (cbrt.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 x -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 x -1/2)))))))

simplify17.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
4×associate-/l*_binary64
3×*-commutative_binary64
3×associate-*l/_binary64
3×associate-/r*_binary64
3×*-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
010216
116180
221180
332180
432180
533180
636180
743180
843180
Stop Event
1×saturated
Counts
118 → 96
Calls
Call 1
Inputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
Outputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x)))
(/.f64 (sqrt.f64 (/.f64 1 x)) y)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 y))
✓10.4b
(sqrt.f64 (*.f64 x y))
Compiler

Compiled 20 to 6 computations (70% saved)

series6.0ms (0.1%)

Counts
2 → 12
Calls

12 calls:

TimeVariablePointExpression
1.0ms
y
@-inf
(*.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 y))
1.0ms
x
@-inf
(sqrt.f64 (*.f64 x y))
1.0ms
y
@-inf
(sqrt.f64 (*.f64 x y))
1.0ms
x
@0
(sqrt.f64 (*.f64 x y))
0.0ms
x
@-inf
(*.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 y))

rewrite53.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
619×pow1_binary64
569×add-log-exp_binary64
569×log1p-expm1-u_binary64
569×expm1-log1p-u_binary64
552×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0715
114012
2164112
Stop Event
1×node limit
Counts
2 → 37
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 x y))
(*.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 y) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x y))) (cbrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x y)) (cbrt.f64 (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x y) 1/4) (pow.f64 (*.f64 x y) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) 1) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (cbrt.f64 y)) (cbrt.f64 (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (pow.f64 y 1/4)) (pow.f64 y 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x y) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x y) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x y) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x y))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 x) y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 x) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (*.f64 x y)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 x) y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 x) y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 y (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (sqrt.f64 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 x) y)))))))

simplify73.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
899×fma-def_binary64
445×cube-prod_binary64
388×distribute-rgt-neg-in_binary64
388×fma-neg_binary64
330×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01272
12572
27472
317972
470672
5154872
6257172
7371872
8485772
9671272
Stop Event
1×unsound
Counts
49 → 39
Calls
Call 1
Inputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
Outputs
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))
(*.f64 -1 (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 x)))
(*.f64 y (sqrt.f64 x))

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.3b
(*.f64 y (sqrt.f64 x))
0.6b
(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)
5.2b
(cbrt.f64 (*.f64 y (sqrt.f64 x)))
Compiler

Compiled 23 to 8 computations (65.2% saved)

eval267.0ms (4.2%)

Compiler

Compiled 4010 to 2065 computations (48.5% saved)

prune82.0ms (1.3%)

Pruning

17 alts after pruning (10 fresh and 7 done)

PrunedKeptTotal
New3547361
Fresh235
Picked011
Done4610
Total36017377
Error
0b
Counts
377 → 17
Alt Table
Click to see full alt table
StatusErrorProgram
43.1b
(/.f64 1 (/.f64 (pow.f64 x -1/2) y))
48.0b
(/.f64 (*.f64 x (-.f64 x (fma.f64 y y 2))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
41.8b
1
✓41.4b
(/.f64 1 (/.f64 -1 x))
57.5b
(sqrt.f64 (*.f64 y (*.f64 x y)))
✓41.3b
(neg.f64 x)
✓43.4b
(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)
✓55.0b
(*.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 y))
19.1b
(+.f64 (-.f64 1 x) (sqrt.f64 (*.f64 (*.f64 y y) x)))
43.3b
(*.f64 (/.f64 1 (/.f64 1 (cbrt.f64 x))) (/.f64 y (cbrt.f64 (pow.f64 x -1/2))))
12.6b
(+.f64 (-.f64 1 x) (*.f64 (cbrt.f64 (*.f64 y y)) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))
✓0.1b
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
43.1b
(*.f64 (sqrt.f64 x) (pow.f64 (/.f64 1 y) -1))
✓43.1b
(*.f64 y (sqrt.f64 x))
62.3b
(*.f64 y (neg.f64 (sqrt.f64 x)))
✓19.7b
(-.f64 1 x)
62.2b
(+.f64 0 x)
Compiler

Compiled 154 to 112 computations (27.3% saved)

regimes78.0ms (1.2%)

Counts
32 → 1
Calls
Call 1
Inputs
1
1
(neg.f64 x)
(+.f64 0 x)
(-.f64 1 x)
(-.f64 1 x)
(/.f64 1 (/.f64 -1 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (neg.f64 (sqrt.f64 x)))
(sqrt.f64 (*.f64 y (*.f64 x y)))
(sqrt.f64 (*.f64 x (*.f64 y y)))
(/.f64 1 (/.f64 (pow.f64 x -1/2) y))
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(+.f64 (-.f64 1 x) (sqrt.f64 (*.f64 (*.f64 y y) x)))
(+.f64 (-.f64 1 x) (sqrt.f64 (*.f64 y (*.f64 x y))))
(/.f64 1 (*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 x))))
(+.f64 (-.f64 1 x) (sqrt.f64 (*.f64 x (*.f64 y y))))
(*.f64 (sqrt.f64 (*.f64 x y)) (sqrt.f64 y))
(*.f64 (sqrt.f64 x) (pow.f64 (/.f64 1 y) -1))
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 (*.f64 x y) 1/2) (sqrt.f64 y)))
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) y)))
(/.f64 (*.f64 x (-.f64 x (fma.f64 y y 2))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
(/.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))))
(*.f64 (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y))) (/.f64 1 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x))))))
(/.f64 1 (/.f64 (-.f64 1 (+.f64 x (*.f64 y (sqrt.f64 x)))) (-.f64 (pow.f64 (-.f64 1 x) 2) (*.f64 x (*.f64 y y)))))
(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3)
(+.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 x))) 3))
(*.f64 (/.f64 1 (/.f64 1 (cbrt.f64 x))) (/.f64 y (cbrt.f64 (pow.f64 x -1/2))))
(+.f64 (-.f64 1 x) (*.f64 (cbrt.f64 (*.f64 y y)) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))
(+.f64 (-.f64 1 x) (*.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))
(+.f64 (-.f64 1 x) (*.f64 (*.f64 (*.f64 (sqrt.f64 x) (pow.f64 y 1/4)) (pow.f64 y 1/4)) (sqrt.f64 y)))
Outputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
Calls

3 calls:

34.0ms
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
17.0ms
y
17.0ms
x
Results
ErrorSegmentsBranch
0.1b1x
0.1b1y
0.1b1(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
Compiler

Compiled 317 to 169 computations (46.7% saved)

regimes176.0ms (2.8%)

Counts
13 → 5
Calls
Call 1
Inputs
1
1
(neg.f64 x)
(+.f64 0 x)
(-.f64 1 x)
(-.f64 1 x)
(/.f64 1 (/.f64 -1 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (neg.f64 (sqrt.f64 x)))
(sqrt.f64 (*.f64 y (*.f64 x y)))
(sqrt.f64 (*.f64 x (*.f64 y y)))
(/.f64 1 (/.f64 (pow.f64 x -1/2) y))
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 x)) y))
Outputs
(*.f64 y (sqrt.f64 x))
(-.f64 1 x)
(sqrt.f64 (*.f64 y (*.f64 x y)))
(-.f64 1 x)
(*.f64 y (sqrt.f64 x))
Calls

2 calls:

90.0ms
x
83.0ms
y
Results
ErrorSegmentsBranch
15.9b7x
3.0b5y
Compiler

Compiled 62 to 40 computations (35.5% saved)

bsearch121.0ms (1.9%)

Algorithm
4×binary-search
Steps
TimeLeftRight
23.0ms
2.384083704531881e+101
2.0571026403639536e+108
20.0ms
2.0565636600531313e+64
1.3223393490181915e+73
58.0ms
1.0129847952114264e+45
1.6294966538382952e+50
20.0ms
-1.1909481088986603e+103
-3.1395683161133554e+98
Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes126.0ms (2%)

Counts
9 → 5
Calls
Call 1
Inputs
1
1
(neg.f64 x)
(+.f64 0 x)
(-.f64 1 x)
(-.f64 1 x)
(/.f64 1 (/.f64 -1 x))
(*.f64 y (sqrt.f64 x))
(*.f64 y (neg.f64 (sqrt.f64 x)))
Outputs
(*.f64 y (sqrt.f64 x))
(-.f64 1 x)
(*.f64 y (sqrt.f64 x))
(-.f64 1 x)
(*.f64 y (sqrt.f64 x))
Calls

2 calls:

72.0ms
x
52.0ms
y
Results
ErrorSegmentsBranch
15.9b7x
3.0b5y
Compiler

Compiled 35 to 23 computations (34.3% saved)

bsearch83.0ms (1.3%)

Algorithm
4×binary-search
Steps
TimeLeftRight
20.0ms
2.384083704531881e+101
2.0571026403639536e+108
19.0ms
2.0565636600531313e+64
1.3223393490181915e+73
21.0ms
1.0129847952114264e+45
1.6294966538382952e+50
22.0ms
-1.1909481088986603e+103
-3.1395683161133554e+98
Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes13.0ms (0.2%)

Counts
7 → 1
Calls
Call 1
Inputs
1
1
(neg.f64 x)
(+.f64 0 x)
(-.f64 1 x)
(-.f64 1 x)
(/.f64 1 (/.f64 -1 x))
Outputs
(-.f64 1 x)
Calls

2 calls:

6.0ms
x
5.0ms
y
Results
ErrorSegmentsBranch
19.7b1x
19.7b1y
Compiler

Compiled 26 to 19 computations (26.9% saved)

regimes40.0ms (0.6%)

Counts
4 → 2
Calls
Call 1
Inputs
1
1
(neg.f64 x)
(+.f64 0 x)
Outputs
1
(neg.f64 x)
Calls

2 calls:

22.0ms
y
16.0ms
x
Results
ErrorSegmentsBranch
20.3b2x
35.6b6y
Compiler

Compiled 15 to 11 computations (26.7% saved)

bsearch19.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
19.0ms
0.05125377519440065
10285.14555189847
Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes9.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

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

2 calls:

5.0ms
y
3.0ms
x
Results
ErrorSegmentsBranch
41.8b1x
41.8b1y
Compiler

Compiled 10 to 8 computations (20% saved)

simplify10.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
031130
141130
244130
345130
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(if (<=.f64 y -11909481088986603267766819359008664315815880559655662723614344664130616909579916382615280457020606513152) (*.f64 y (sqrt.f64 x)) (if (<=.f64 y 1012984795211426438423504470453662921107963904) (-.f64 1 x) (if (<=.f64 y 20565636600531313241868772548960238221066578103474564163818225664) (sqrt.f64 (*.f64 y (*.f64 x y))) (if (<=.f64 y 238408370453188095124296013959598380340307032672159324661309224017857001137646288896719456547347890176) (-.f64 1 x) (*.f64 y (sqrt.f64 x))))))
(if (<=.f64 y -11909481088986603267766819359008664315815880559655662723614344664130616909579916382615280457020606513152) (*.f64 y (sqrt.f64 x)) (if (<=.f64 y 1012984795211426438423504470453662921107963904) (-.f64 1 x) (if (<=.f64 y 20565636600531313241868772548960238221066578103474564163818225664) (*.f64 y (sqrt.f64 x)) (if (<=.f64 y 238408370453188095124296013959598380340307032672159324661309224017857001137646288896719456547347890176) (-.f64 1 x) (*.f64 y (sqrt.f64 x))))))
(-.f64 1 x)
(if (<=.f64 x 945465273822551808/18446744073709551616) 1 (neg.f64 x))
1
Outputs
(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
(if (<=.f64 y -11909481088986603267766819359008664315815880559655662723614344664130616909579916382615280457020606513152) (*.f64 y (sqrt.f64 x)) (if (<=.f64 y 1012984795211426438423504470453662921107963904) (-.f64 1 x) (if (<=.f64 y 20565636600531313241868772548960238221066578103474564163818225664) (sqrt.f64 (*.f64 y (*.f64 x y))) (if (<=.f64 y 238408370453188095124296013959598380340307032672159324661309224017857001137646288896719456547347890176) (-.f64 1 x) (*.f64 y (sqrt.f64 x))))))
(if (<=.f64 y -11909481088986603267766819359008664315815880559655662723614344664130616909579916382615280457020606513152) (*.f64 y (sqrt.f64 x)) (if (<=.f64 y 1012984795211426438423504470453662921107963904) (-.f64 1 x) (if (<=.f64 y 20565636600531313241868772548960238221066578103474564163818225664) (*.f64 y (sqrt.f64 x)) (if (<=.f64 y 238408370453188095124296013959598380340307032672159324661309224017857001137646288896719456547347890176) (-.f64 1 x) (*.f64 y (sqrt.f64 x))))))
(-.f64 1 x)
(if (<=.f64 x 945465273822551808/18446744073709551616) 1 (neg.f64 x))
(if (<=.f64 x 3693223725869343/72057594037927936) 1 (neg.f64 x))
1
Compiler

Compiled 101 to 64 computations (36.6% saved)

soundness0.0ms (0%)

end55.0ms (0.9%)

Compiler

Compiled 91 to 50 computations (45.1% saved)

Profiling

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