Details

Time bar (total: 5.2s)

analyze96.0ms (1.8%)

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)

sample822.0ms (15.7%)

Symmetry

(sort x y)

Results
769.0ms8256×body128valid
Compiler

Compiled 59 to 29 computations (50.8% saved)

simplify37.0ms (0.7%)

Algorithm
egg-herbie
Rules
356×fma-def_binary64
321×distribute-rgt-out_binary64
315×distribute-rgt-in_binary64
293×associate-/l/_binary64
285×distribute-lft-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01025
13925
217323
362323
4258823
5399323
6488523
7496423
Stop Event
node limit
Counts
1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
12.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
12.9b
(/.f64 x (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y))
21.8b
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
Compiler

Compiled 109 to 48 computations (56% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (+.f64 x y) 3)
0.0b
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
5.8b
(/.f64 x (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y))
9.2b
(/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y)

series73.0ms (1.4%)

Counts
4 → 96
Calls

4 calls:

43.0ms
(/.f64 x (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y))
12.0ms
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
11.0ms
(/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y)
7.0ms
(pow.f64 (+.f64 x y) 3)

rewrite61.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
604×prod-diff_binary64
209×fma-def_binary64
184×expm1-udef_binary64
184×log1p-udef_binary64
136×egg-rr
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0967
120764
2298464
Stop Event
node limit
Counts
4 → 136
Calls

4 calls:

58.0ms
(pow.f64 (+.f64 x y) 3)
58.0ms
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
58.0ms
(/.f64 x (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y))
58.0ms
(/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y)

simplify73.0ms (1.4%)

Algorithm
egg-herbie
Rules
386×associate-+r+_binary64
358×fma-def_binary64
269×associate-+l+_binary64
257×+-commutative_binary64
245×times-frac_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02874127
19333822
243013795
Stop Event
node limit
Counts
232 → 228

prune227.0ms (4.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2208228
Fresh011
Picked101
Done000
Total2219230
Error
2.6b
Counts
230 → 9
Alt Table
StatusErrorProgram
42.6b
(*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (/.f64 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)) (sqrt.f64 y))) (/.f64 (cbrt.f64 x) (/.f64 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)) (sqrt.f64 y))))
34.2b
(/.f64 x (fma.f64 3 (*.f64 y x) (fma.f64 y y y)))
21.8b
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
42.3b
(-.f64 (/.f64 y (*.f64 x x)) (fma.f64 3 (/.f64 y (/.f64 (pow.f64 x 3) y)) (/.f64 y (pow.f64 x 3))))
35.1b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)) (sqrt.f64 y))) (/.f64 x (/.f64 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)) (sqrt.f64 y))))
38.7b
(/.f64 x (/.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) 3)) y))
24.6b
(*.f64 y (/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))))
21.7b
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (/.f64 (pow.f64 x 3) y))) (fma.f64 3 (*.f64 y x) y)))
22.2b
(/.f64 x (+.f64 (*.f64 3 (*.f64 y x)) (+.f64 y (+.f64 (pow.f64 y 2) (+.f64 (/.f64 (pow.f64 x 2) y) (+.f64 (*.f64 3 (pow.f64 x 2)) (*.f64 2 x)))))))
Compiler

Compiled 7284 to 4011 computations (44.9% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
5.8b
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (/.f64 (pow.f64 x 3) y))) (fma.f64 3 (*.f64 y x) y)))
6.0b
(+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (/.f64 (pow.f64 x 3) y))
8.8b
(/.f64 (pow.f64 x 3) y)
13.5b
(+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (/.f64 (pow.f64 x 3) y)))

series84.0ms (1.6%)

Counts
4 → 72
Calls

4 calls:

45.0ms
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (/.f64 (pow.f64 x 3) y))) (fma.f64 3 (*.f64 y x) y)))
14.0ms
(/.f64 (pow.f64 x 3) y)
13.0ms
(+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (/.f64 (pow.f64 x 3) y)))
11.0ms
(+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (/.f64 (pow.f64 x 3) y))

rewrite44.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
218×add-sqr-sqrt_binary64
212×log1p-expm1-u_binary64
212×expm1-log1p-u_binary64
210×add-cbrt-cube_binary64
203×add-cube-cbrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
019106
1440106
Stop Event
node limit
Counts
4 → 107
Calls

4 calls:

41.0ms
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (/.f64 (pow.f64 x 3) y))) (fma.f64 3 (*.f64 y x) y)))
41.0ms
(+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (/.f64 (pow.f64 x 3) y))
41.0ms
(/.f64 (pow.f64 x 3) y)
41.0ms
(+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (/.f64 (pow.f64 x 3) y)))

simplify60.0ms (1.1%)

Algorithm
egg-herbie
Rules
239×times-frac_binary64
237×associate-+r+_binary64
229×cancel-sign-sub-inv_binary64
222×fma-def_binary64
201×sub-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02403112
17642936
235272839
Stop Event
node limit
Counts
179 → 164

prune213.0ms (4.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1595164
Fresh448
Picked101
Done000
Total1649173
Error
1.6b
Counts
173 → 9
Alt Table
StatusErrorProgram
24.5b
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (pow.f64 (pow.f64 (/.f64 (pow.f64 x 3) y) 3) 1/3))) (fma.f64 3 (*.f64 y x) y)))
35.1b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)) (sqrt.f64 y))) (/.f64 x (/.f64 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)) (sqrt.f64 y))))
21.8b
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
42.3b
(-.f64 (/.f64 y (*.f64 x x)) (fma.f64 3 (/.f64 y (/.f64 (pow.f64 x 3) y)) (/.f64 y (pow.f64 x 3))))
21.8b
(*.f64 x (/.f64 1 (+.f64 (fma.f64 y y (*.f64 (/.f64 x y) x)) (+.f64 (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 x 2)) (/.f64 (pow.f64 x 3) y)) (fma.f64 3 (*.f64 y x) y)))))
21.2b
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (*.f64 (/.f64 x 1) (/.f64 (*.f64 x x) y)))) (fma.f64 3 (*.f64 y x) y)))
41.6b
(/.f64 (/.f64 x y) y)
24.6b
(*.f64 y (/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))))
14.1b
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (*.f64 2 x)) (fma.f64 3 (*.f64 y x) y)))
Compiler

Compiled 7756 to 4072 computations (47.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 x (/.f64 y x))
0.2b
(fma.f64 y y (/.f64 x (/.f64 y x)))
4.1b
(+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (*.f64 2 x)) (fma.f64 3 (*.f64 y x) y))
10.9b
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (*.f64 2 x)) (fma.f64 3 (*.f64 y x) y)))

series53.0ms (1%)

Counts
4 → 96
Calls

4 calls:

27.0ms
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (*.f64 2 x)) (fma.f64 3 (*.f64 y x) y)))
9.0ms
(fma.f64 y y (/.f64 x (/.f64 y x)))
9.0ms
(/.f64 x (/.f64 y x))
8.0ms
(+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (*.f64 2 x)) (fma.f64 3 (*.f64 y x) y))

rewrite75.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
291×log1p-udef_binary64
161×add-sqr-sqrt_binary64
155×log1p-expm1-u_binary64
155×expm1-log1p-u_binary64
153×add-cbrt-cube_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01475
132071
2468271
Stop Event
node limit
Counts
4 → 139
Calls

4 calls:

72.0ms
(/.f64 x (/.f64 y x))
72.0ms
(fma.f64 y y (/.f64 x (/.f64 y x)))
72.0ms
(+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (*.f64 2 x)) (fma.f64 3 (*.f64 y x) y))
72.0ms
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (*.f64 2 x)) (fma.f64 3 (*.f64 y x) y)))

simplify50.0ms (0.9%)

Algorithm
egg-herbie
Rules
809×fma-def_binary64
748×associate-/l*_binary64
193×cancel-sign-sub-inv_binary64
170×sub-neg_binary64
164×associate-/r/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01692418
15352266
222332172
Stop Event
node limit
Counts
235 → 188

prune198.0ms (3.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1862188
Fresh178
Picked101
Done000
Total1889197
Error
1.6b
Counts
197 → 9
Alt Table
StatusErrorProgram
24.5b
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (pow.f64 (pow.f64 (/.f64 (pow.f64 x 3) y) 3) 1/3))) (fma.f64 3 (*.f64 y x) y)))
35.1b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)) (sqrt.f64 y))) (/.f64 x (/.f64 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)) (sqrt.f64 y))))
21.8b
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
42.3b
(-.f64 (/.f64 y (*.f64 x x)) (fma.f64 3 (/.f64 y (/.f64 (pow.f64 x 3) y)) (/.f64 y (pow.f64 x 3))))
14.2b
(*.f64 x (/.f64 1 (+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y)))))
21.2b
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (*.f64 (/.f64 x 1) (/.f64 (*.f64 x x) y)))) (fma.f64 3 (*.f64 y x) y)))
41.6b
(/.f64 (/.f64 x y) y)
24.6b
(*.f64 y (/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))))
14.6b
(pow.f64 (cbrt.f64 (/.f64 x (+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y))))) 3)
Compiler

Compiled 6300 to 2913 computations (53.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 y y (*.f64 x (/.f64 x y)))
0.5b
(/.f64 1 (+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y))))
4.1b
(+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y)))
10.4b
(*.f64 x (/.f64 1 (+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y)))))

series70.0ms (1.3%)

Counts
4 → 96
Calls

4 calls:

26.0ms
(*.f64 x (/.f64 1 (+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y)))))
23.0ms
(/.f64 1 (+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y))))
10.0ms
(+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y)))
10.0ms
(fma.f64 y y (*.f64 x (/.f64 x y)))

rewrite74.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
867×prod-diff_binary64
156×add-sqr-sqrt_binary64
148×log1p-expm1-u_binary64
148×expm1-log1p-u_binary64
146×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01592
132192
2413992
Stop Event
node limit
Counts
4 → 113
Calls

4 calls:

72.0ms
(fma.f64 y y (*.f64 x (/.f64 x y)))
72.0ms
(/.f64 1 (+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y))))
72.0ms
(+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y)))
71.0ms
(*.f64 x (/.f64 1 (+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y)))))

simplify67.0ms (1.3%)

Algorithm
egg-herbie
Rules
481×cancel-sign-sub-inv_binary64
337×sub-neg_binary64
289×fma-def_binary64
264×associate-+r+_binary64
239×+-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02753756
19073532
238593466
Stop Event
node limit
Counts
209 → 192

prune222.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1920192
Fresh088
Picked011
Done000
Total1929201
Error
1.6b
Counts
201 → 9
Alt Table
StatusErrorProgram
24.5b
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (pow.f64 (pow.f64 (/.f64 (pow.f64 x 3) y) 3) 1/3))) (fma.f64 3 (*.f64 y x) y)))
35.1b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)) (sqrt.f64 y))) (/.f64 x (/.f64 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)) (sqrt.f64 y))))
21.8b
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
42.3b
(-.f64 (/.f64 y (*.f64 x x)) (fma.f64 3 (/.f64 y (/.f64 (pow.f64 x 3) y)) (/.f64 y (pow.f64 x 3))))
14.2b
(*.f64 x (/.f64 1 (+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y)))))
21.2b
(/.f64 x (+.f64 (+.f64 (fma.f64 y y (/.f64 x (/.f64 y x))) (+.f64 (fma.f64 3 (*.f64 x x) (*.f64 2 x)) (*.f64 (/.f64 x 1) (/.f64 (*.f64 x x) y)))) (fma.f64 3 (*.f64 y x) y)))
41.6b
(/.f64 (/.f64 x y) y)
24.6b
(*.f64 y (/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))))
14.6b
(pow.f64 (cbrt.f64 (/.f64 x (+.f64 (fma.f64 y y (*.f64 x (/.f64 x y))) (fma.f64 x 2 (fma.f64 3 (*.f64 x y) y))))) 3)
Compiler

Compiled 6939 to 3634 computations (47.6% saved)

regimes2.2s (42.6%)

Accuracy

Total 2.2b remaining (51.1%)

Threshold costs 0b (0%)

Counts
310 → 4
Compiler

Compiled 22949 to 13814 computations (39.8% saved)

bsearch57.0ms (1.1%)

Steps
ItersRangePoint
6
1.4012252044420972e-11
6.441951581647822e-11
6.342776204927889e-11
7
-1.3089406311694052e+34
-3.2875293245690826e+32
-5.005665752085898e+33
7
-3.104286440210014e+88
-3.393516016495352e+86
-2.325223106310958e+87
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
/-rgt-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040103
152103
Stop Event
saturated

end299.0ms (5.7%)

Compiler

Compiled 513 to 283 computations (44.8% saved)

Profiling

Loading profile data...