Details

Time bar (total: 2.2s)

analyze126.0ms (5.7%)

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%99.9%0.1%4
25%74.9%0.1%5
25%62.4%12.6%6
37.5%50%12.6%7
46.8%37.5%15.7%8
53.1%30.4%16.5%9
58.5%20.7%20.8%10
62%16.2%21.8%11
65%10.8%24.2%12
Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.2s (52.8%)

Results
1.0s8256×body256valid
77.0ms470×body256invalid

preprocess73.0ms (3.3%)

Algorithm
2×egg-herbie
Rules
513×fma-def_binary64
355×fma-neg_binary64
106×distribute-rgt-in_binary64
92×cancel-sign-sub-inv_binary64
84×unsub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
13320
27120
316120
431220
552420
6100620
7144520
8189620
9204620
10204820
11204820
022
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(*.f64 2 (-.f64 (*.f64 x x) (*.f64 x y)))
(*.f64 2 (-.f64 (*.f64 y y) (*.f64 y x)))
Outputs
(*.f64 2 (-.f64 (*.f64 x x) (*.f64 x y)))
(*.f64 2 (*.f64 x (-.f64 x y)))
(*.f64 (*.f64 x -2) (-.f64 y x))
(*.f64 (-.f64 y x) (*.f64 x -2))
(*.f64 2 (-.f64 (*.f64 y y) (*.f64 y x)))
(*.f64 2 (*.f64 y (-.f64 y x)))
(*.f64 (-.f64 y x) (*.f64 2 y))
Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify42.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
388×fma-def_binary64
286×fma-neg_binary64
70×distribute-rgt-in_binary64
68×cancel-sign-sub-inv_binary64
67×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11810
24310
310210
420710
529410
650110
787110
8125410
9145110
10150110
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(*.f64 2 (-.f64 (*.f64 x x) (*.f64 x y)))
Outputs
(*.f64 2 (-.f64 (*.f64 x x) (*.f64 x y)))
(*.f64 2 (*.f64 x (-.f64 x y)))
(*.f64 (*.f64 2 x) (-.f64 x y))

eval1.0ms (0%)

Compiler

Compiled 18 to 11 computations (38.9% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0b
Counts
3 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(*.f64 2 (-.f64 (*.f64 x x) (*.f64 x y)))
▶0.0b
(*.f64 (*.f64 2 x) (-.f64 x y))
Compiler

Compiled 20 to 13 computations (35% saved)

localize9.0ms (0.4%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (*.f64 x x) (*.f64 x y))
Compiler

Compiled 27 to 8 computations (70.4% saved)

series4.0ms (0.2%)

Counts
1 → 24
Calls

6 calls:

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

rewrite67.0ms (3.1%)

Algorithm
1×batch-egg-rewrite
Rules
781×pow1_binary64
729×add-log-exp_binary64
729×log1p-expm1-u_binary64
729×expm1-log1p-u_binary64
713×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11437
220527
Stop Event
1×node limit
Counts
1 → 51
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) (*.f64 x y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 (*.f64 y (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (+.f64 (*.f64 y (neg.f64 x)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 x) y (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (*.f64 y (neg.f64 x)) 1 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (sqrt.f64 (*.f64 x y))) (sqrt.f64 (*.f64 x y)) (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (*.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (+.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (*.f64 x (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (neg.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (-.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2) (cbrt.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2)) (/.f64 1 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 x y) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (sqrt.f64 (*.f64 x y))) (-.f64 x (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y)))) (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x (+.f64 x y)) (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3)) (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2)) (*.f64 x (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2))) (neg.f64 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (*.f64 y (neg.f64 x)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 y (neg.f64 x)) (*.f64 y (neg.f64 x))) (*.f64 (*.f64 x x) (*.f64 y (neg.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) 3)) (+.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2) (-.f64 (*.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))) (*.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 y (neg.f64 x)) (*.f64 y (neg.f64 x)))) (-.f64 (*.f64 x x) (*.f64 y (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2) (*.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y)))) (-.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (-.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2) (cbrt.f64 (*.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))))))

simplify81.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
559×associate-*r*_binary64
553×fma-neg_binary64
459×cancel-sign-sub-inv_binary64
416×unswap-sqr_binary64
328×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
09246
120192
249156
398156
4243156
5762156
62499156
76401156
87500156
Stop Event
1×node limit
Counts
75 → 56
Calls
Call 1
Inputs
(*.f64 -1 (*.f64 y x))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(*.f64 -1 (*.f64 y x))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(*.f64 -1 (*.f64 y x))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
Outputs
(*.f64 -1 (*.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 x (neg.f64 y))
(*.f64 y (neg.f64 x))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(*.f64 -1 (*.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 x (neg.f64 y))
(*.f64 y (neg.f64 x))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(*.f64 -1 (*.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 x (neg.f64 y))
(*.f64 y (neg.f64 x))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (*.f64 -1 (*.f64 y x)))
(+.f64 (neg.f64 (*.f64 y x)) (*.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))

localize9.0ms (0.4%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (*.f64 2 x) (-.f64 x y))
Compiler

Compiled 18 to 9 computations (50% saved)

series5.0ms (0.2%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
y
@0
(*.f64 (*.f64 2 x) (-.f64 x y))
1.0ms
x
@0
(*.f64 (*.f64 2 x) (-.f64 x y))
1.0ms
x
@inf
(*.f64 (*.f64 2 x) (-.f64 x y))
1.0ms
y
@inf
(*.f64 (*.f64 2 x) (-.f64 x y))
1.0ms
x
@-inf
(*.f64 (*.f64 2 x) (-.f64 x y))

rewrite69.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
824×pow1_binary64
767×add-log-exp_binary64
766×log1p-expm1-u_binary64
766×expm1-log1p-u_binary64
751×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
115310
2204910
Stop Event
1×node limit
Counts
1 → 19
Calls
Call 1
Inputs
(*.f64 (*.f64 2 x) (-.f64 x y))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 2 x)) (*.f64 (neg.f64 y) (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 2 x) x) (*.f64 (*.f64 2 x) (neg.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (*.f64 2 (-.f64 x y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (*.f64 2 x)) (fma.f64 x x (*.f64 y (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 y y)) (*.f64 2 x)) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 x) (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (*.f64 y (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 x) (-.f64 (*.f64 x x) (*.f64 y y))) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 2 (-.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 2 (-.f64 x y))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 2 (-.f64 x y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (*.f64 2 (-.f64 x y)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 2 (-.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (-.f64 x y)) (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 2 (-.f64 x y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 2 x) 3) (pow.f64 (-.f64 x y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (-.f64 x y) 3) (pow.f64 (*.f64 2 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 2 (-.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 2 (-.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 2 (-.f64 x y)))))))))

simplify179.0ms (8.2%)

Algorithm
1×egg-herbie
Rules
2020×unswap-sqr_binary64
1080×sqr-pow_binary64
633×fabs-mul_binary64
612×pow-sqr_binary64
610×cube-prod_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
010294
122294
244276
394240
4226240
5669240
61002240
71441240
81545240
91678240
101847240
112092240
122405240
132777240
143234240
153825240
164531240
175389240
185815240
196127240
206435240
216511240
226545240
Stop Event
1×node limit
Counts
43 → 24
Calls
Call 1
Inputs
(*.f64 -2 (*.f64 y x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(*.f64 -2 (*.f64 y x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(*.f64 -2 (*.f64 y x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
Outputs
(*.f64 -2 (*.f64 y x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 x (*.f64 x 2))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 x (*.f64 x 2))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 x x))
(*.f64 x (*.f64 x 2))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(*.f64 -2 (*.f64 y x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(*.f64 -2 (*.f64 y x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 -2 (*.f64 y x)))
(fma.f64 2 (*.f64 x x) (*.f64 -2 (*.f64 y x)))
(fma.f64 -2 (*.f64 y x) (*.f64 x (*.f64 x 2)))
(*.f64 x (+.f64 (*.f64 -2 y) (*.f64 x 2)))
(*.f64 x (fma.f64 -2 y (*.f64 x 2)))

eval25.0ms (1.2%)

Compiler

Compiled 1153 to 480 computations (58.4% saved)

prune11.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New78280
Fresh000
Picked011
Done011
Total78482
Error
0b
Counts
82 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶32.2b
(*.f64 x (*.f64 x 2))
▶22.8b
(*.f64 -2 (*.f64 y x))
✓0.0b
(*.f64 2 (-.f64 (*.f64 x x) (*.f64 x y)))
✓0.0b
(*.f64 (*.f64 2 x) (-.f64 x y))
Compiler

Compiled 34 to 23 computations (32.4% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 -2 (*.f64 y x))
Compiler

Compiled 13 to 6 computations (53.8% saved)

series3.0ms (0.1%)

Counts
1 → 0
Calls

6 calls:

TimeVariablePointExpression
1.0ms
y
@0
(*.f64 -2 (*.f64 y x))
1.0ms
x
@inf
(*.f64 -2 (*.f64 y x))
1.0ms
x
@0
(*.f64 -2 (*.f64 y x))
0.0ms
y
@inf
(*.f64 -2 (*.f64 y x))
0.0ms
y
@-inf
(*.f64 -2 (*.f64 y x))

rewrite48.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
555×pow1_binary64
512×add-log-exp_binary64
512×log1p-expm1-u_binary64
512×expm1-log1p-u_binary64
502×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11217
213957
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 -2 (*.f64 y x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 -2 (*.f64 y x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -2 (*.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -2 (*.f64 y x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -2 (*.f64 y x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 -2 (*.f64 y x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 y x) 2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -2) (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 y x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -2 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -2 (*.f64 y x))))))))

simplify8.0ms (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
11 → 11
Calls
Call 1
Inputs
Outputs

localize5.0ms (0.2%)

Compiler

Compiled 12 to 8 computations (33.3% saved)

eval4.0ms (0.2%)

Compiler

Compiled 87 to 55 computations (36.8% saved)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New11011
Fresh000
Picked011
Done033
Total11415
Error
0b
Counts
15 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓32.2b
(*.f64 x (*.f64 x 2))
✓22.8b
(*.f64 -2 (*.f64 y x))
✓0.0b
(*.f64 2 (-.f64 (*.f64 x x) (*.f64 x y)))
✓0.0b
(*.f64 (*.f64 2 x) (-.f64 x y))
Compiler

Compiled 34 to 23 computations (32.4% saved)

regimes25.0ms (1.1%)

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

4 calls:

10.0ms
y
5.0ms
x
4.0ms
(-.f64 (*.f64 x x) (*.f64 x y))
4.0ms
(*.f64 2 (-.f64 (*.f64 x x) (*.f64 x y)))
Results
ErrorSegmentsBranch
0.0b1x
0.0b1y
0.0b1(*.f64 2 (-.f64 (*.f64 x x) (*.f64 x y)))
0.0b1(-.f64 (*.f64 x x) (*.f64 x y))
Compiler

Compiled 54 to 33 computations (38.9% saved)

regimes36.0ms (1.6%)

Accuracy

Total -46.9b remaining (-716.7%)

Threshold costs -46.9b (-716.7%)

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

2 calls:

19.0ms
x
16.0ms
y
Results
ErrorSegmentsBranch
9.7b5x
6.5b3y
Compiler

Compiled 18 to 12 computations (33.3% saved)

bsearch36.0ms (1.6%)

Algorithm
2×binary-search
Steps
TimeLeftRight
17.0ms
9.232376549514604e-48
2.371634316245209e-42
19.0ms
-2.3833745838419967e-56
-1.3305288491337478e-73
Compiler

Compiled 16 to 11 computations (31.3% saved)

simplify5.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01950
12650
23150
33350
43450
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 2 x) (-.f64 x y))
(if (<=.f64 y -2631911492330397/110427941548649020598956093796432407239217743554726184882600387580788736) (*.f64 -2 (*.f64 y x)) (if (<=.f64 y 237373713861433/25711008708143844408671393477458601640355247900524685364822016) (*.f64 x (*.f64 x 2)) (*.f64 -2 (*.f64 y x))))
(*.f64 x (*.f64 x 2))
Outputs
(*.f64 (*.f64 2 x) (-.f64 x y))
(*.f64 (-.f64 x y) (*.f64 2 x))
(if (<=.f64 y -2631911492330397/110427941548649020598956093796432407239217743554726184882600387580788736) (*.f64 -2 (*.f64 y x)) (if (<=.f64 y 237373713861433/25711008708143844408671393477458601640355247900524685364822016) (*.f64 x (*.f64 x 2)) (*.f64 -2 (*.f64 y x))))
(if (<=.f64 y -2631911492330397/110427941548649020598956093796432407239217743554726184882600387580788736) (*.f64 -2 (*.f64 x y)) (if (<=.f64 y 237373713861433/25711008708143844408671393477458601640355247900524685364822016) (*.f64 x (*.f64 2 x)) (*.f64 -2 (*.f64 x y))))
(*.f64 x (*.f64 x 2))
(*.f64 x (*.f64 2 x))
Compiler

Compiled 41 to 27 computations (34.1% saved)

soundness126.0ms (5.8%)

Algorithm
1×egg-herbie
Rules
388×fma-def_binary64
286×fma-neg_binary64
70×distribute-rgt-in_binary64
68×cancel-sign-sub-inv_binary64
67×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11810
24310
310210
420710
529410
650110
787110
8125410
9145110
10150110
Stop Event
1×saturated
Compiler

Compiled 29 to 19 computations (34.5% saved)

end27.0ms (1.3%)

Compiler

Compiled 37 to 23 computations (37.8% saved)

Profiling

Loading profile data...