Details

Time bar (total: 7.5s)

analyze103.0ms (1.4%)

Algorithm
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
12.5%87.4%0.1%5
46.8%53.1%0.1%6
70.2%29.7%0.1%7
76.5%23.4%0.1%8
83.5%16.4%0.1%9
87%12.9%0.1%10
91.1%8.8%0.1%11
93.2%6.7%0.1%12
95.4%4.5%0.1%13
96.5%3.4%0.1%14
Compiler

Compiled 20 to 10 computations (50% saved)

sample971.0ms (13%)

Symmetry

(sort x y)

Results
848.0ms8256×body128valid
Compiler

Compiled 59 to 29 computations (50.8% saved)

simplify138.0ms (1.8%)

Algorithm
egg-herbie
Rules
985×associate-/l*_binary64
659×distribute-lft-out_binary64
601×*-commutative_binary64
469×distribute-rgt-out_binary64
356×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01025
13925
213523
347423
4153623
5212223
6258923
7256723
8262023
9267723
10277023
11395623
12408823
13445423
14498323
15496823
16496123

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
19.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
19.1b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
19.2b
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
Compiler

Compiled 109 to 47 computations (56.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
0.0b
(pow.f64 (+.f64 x y) 3)
19.0b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series65.0ms (0.9%)

Counts
3 → 72
Calls

3 calls:

47.0ms
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
11.0ms
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
7.0ms
(pow.f64 (+.f64 x y) 3)

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
3 → 62
Calls

3 calls:

3.0ms
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
3.0ms
(pow.f64 (+.f64 x y) 3)
0.0ms
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))

simplify154.0ms (2.1%)

Algorithm
egg-herbie
Rules
326×fma-def_binary64
301×times-frac_binary64
297×associate-+r+_binary64
257×associate-/l*_binary64
223×+-commutative_binary64
Counts
134 → 162
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03474819
110474272
247024260
349814260
449964260
549814260

prune178.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1557162
Fresh101
Picked011
Done000
Total1568164
Error
5.1b
Counts
164 → 8
Alt Table
StatusErrorProgram
13.2b
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
40.3b
(/.f64 x (pow.f64 y 2))
13.6b
(/.f64 x (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y))
33.2b
(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
19.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
19.1b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
41.6b
(-.f64 (/.f64 y (*.f64 x x)) (fma.f64 3 (/.f64 (*.f64 y y) (pow.f64 x 3)) (/.f64 y (pow.f64 x 3))))
Compiler

Compiled 6031 to 3174 computations (47.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
0.0b
(pow.f64 (+.f64 x y) 3)
6.3b
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
9.2b
(/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series89.0ms (1.2%)

Counts
2 → 48
Calls

2 calls:

48.0ms
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
40.0ms
(/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64
34×times-frac_binary64
26×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
21×add-exp-log_binary64
Counts
2 → 85
Calls

2 calls:

9.0ms
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
2.0ms
(/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

simplify106.0ms (1.4%)

Algorithm
egg-herbie
Rules
428×times-frac_binary64
391×associate-/l*_binary64
391×fma-def_binary64
316×associate-/r*_binary64
246×associate-*r*_binary64
Counts
133 → 207
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04867311
114736634
249816634

prune370.0ms (5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2952297
Fresh156
Picked011
Done011
Total2969305
Error
5.1b
Counts
305 → 9
Alt Table
StatusErrorProgram
13.2b
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
40.3b
(/.f64 x (pow.f64 y 2))
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
40.4b
(*.f64 (/.f64 x 1) (/.f64 1 (pow.f64 y 2)))
32.8b
(*.f64 (/.f64 x 1) (*.f64 (/.f64 1 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))))
33.2b
(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
19.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
19.1b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
41.6b
(-.f64 (/.f64 y (*.f64 x x)) (fma.f64 3 (/.f64 (*.f64 y y) (pow.f64 x 3)) (/.f64 y (pow.f64 x 3))))
Compiler

Compiled 12080 to 6655 computations (44.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
0.3b
(*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
19.0b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
29.7b
(cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))

series926.0ms (12.4%)

Counts
3 → 72
Calls

3 calls:

635.0ms
(*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
236.0ms
(cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
53.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))

rewrite37.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
47×cbrt-prod_binary64
30×add-sqr-sqrt_binary64
29×pow1_binary64
20×associate-*r*_binary64
20×*-un-lft-identity_binary64
Counts
3 → 124
Calls

3 calls:

11.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
7.0ms
(*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
2.0ms
(cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))

simplify305.0ms (4.1%)

Algorithm
egg-herbie
Rules
618×*-commutative_binary64
414×fma-def_binary64
398×associate-+r+_binary64
313×associate-/l*_binary64
311×associate-*r/_binary64
Counts
196 → 315
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0181532802
1543632802

prune2.0s (26.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New6890689
Fresh066
Picked011
Done022
Total6899698
Error
5.1b
Counts
698 → 9
Alt Table
StatusErrorProgram
13.2b
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
40.3b
(/.f64 x (pow.f64 y 2))
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
40.4b
(*.f64 (/.f64 x 1) (/.f64 1 (pow.f64 y 2)))
32.8b
(*.f64 (/.f64 x 1) (*.f64 (/.f64 1 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))))
33.2b
(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
19.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
19.1b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
41.6b
(-.f64 (/.f64 y (*.f64 x x)) (fma.f64 3 (/.f64 (*.f64 y y) (pow.f64 x 3)) (/.f64 y (pow.f64 x 3))))
Compiler

Compiled 99675 to 57995 computations (41.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))
0.1b
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
2.6b
(/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))
10.8b
(/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))

series227.0ms (3%)

Counts
4 → 96
Calls

4 calls:

77.0ms
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
62.0ms
(/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))
56.0ms
(/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))
32.0ms
(hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt_binary64
40×times-frac_binary64
34×*-un-lft-identity_binary64
34×add-cube-cbrt_binary64
20×add-cbrt-cube_binary64
Counts
4 → 120
Calls

4 calls:

9.0ms
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
2.0ms
(/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))
2.0ms
(/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))
0.0ms
(hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))

simplify171.0ms (2.3%)

Algorithm
egg-herbie
Rules
973×fma-def_binary64
306×times-frac_binary64
267×*-commutative_binary64
233×+-commutative_binary64
200×sub-neg_binary64
Counts
216 → 329
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
080012208
1265810448
2498410448

prune484.0ms (6.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New3775382
Fresh325
Picked101
Done033
Total38110391
Error
3.1b
Counts
391 → 10
Alt Table
StatusErrorProgram
32.3b
(/.f64 (*.f64 x (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))) (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))
50.8b
(-.f64 (/.f64 y x) (*.f64 2 (*.f64 (/.f64 y x) (/.f64 y x))))
32.8b
(*.f64 x (*.f64 (/.f64 1 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))))
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (*.f64 y (/.f64 1 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))))
39.5b
(*.f64 (-.f64 (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
13.2b
(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
40.4b
(*.f64 (/.f64 x 1) (/.f64 1 (pow.f64 y 2)))
19.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))) (cbrt.f64 (/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
19.1b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
41.6b
(-.f64 (/.f64 y (*.f64 x x)) (fma.f64 3 (/.f64 (*.f64 y y) (pow.f64 x 3)) (/.f64 y (pow.f64 x 3))))
Compiler

Compiled 20995 to 12452 computations (40.7% saved)

regimes721.0ms (9.7%)

Accuracy

Total 4.1b remaining (58%)

Threshold costs 0b (0%)

Counts
128 → 3
Compiler

Compiled 9608 to 5027 computations (47.7% saved)

bsearch39.0ms (0.5%)

Steps
ItersRangePoint
8
-5.590189577891837e-143
-5.586811506282266e-146
-5.664768576413203e-146
6
-9.785478050113318e+112
-1.6984622260640051e+112
-1.754960936749458e+112
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028120
130120
230120

end295.0ms (4%)

Compiler

Compiled 577 to 264 computations (54.2% saved)

Profiling

Loading profile data...