Details

Time bar (total: 4.4s)

analyze98.0ms (2.2%)

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)

sample913.0ms (20.8%)

Symmetry

(sort x y)

Results
789.0ms8256×body128valid
Compiler

Compiled 59 to 29 computations (50.8% saved)

simplify138.0ms (3.1%)

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 (0.1%)

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)

localize7.0ms (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)))

series89.0ms (2%)

Counts
3 → 72
Calls

3 calls:

68.0ms
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
12.0ms
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
8.0ms
(pow.f64 (+.f64 x y) 3)

rewrite148.0ms (3.4%)

Algorithm
batch-egg-rewrite
Rules
705×prod-diff_binary64
539×fma-udef_binary64
264×fma-def_binary64
214×fma-neg_binary64
176×expm1-udef_binary64
Counts
3 → 103
Calls

3 calls:

145.0ms
(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
145.0ms
(pow.f64 (+.f64 x y) 3)
145.0ms
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0947
120045
2262345
3475445
4473845
5496845
000
100

simplify85.0ms (1.9%)

Algorithm
egg-herbie
Rules
308×fma-def_binary64
297×associate-+r+_binary64
242×times-frac_binary64
212×+-commutative_binary64
210×associate-+l+_binary64
Counts
175 → 169
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02563481
18283208
238133181
351423181

prune174.0ms (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1618169
Fresh101
Picked011
Done000
Total1629171
Error
5.1b
Counts
171 → 9
Alt Table
StatusErrorProgram
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (/.f64 y (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))))
40.3b
(/.f64 x (pow.f64 y 2))
28.7b
(*.f64 (cbrt.f64 (/.f64 (*.f64 x y) (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)))) (pow.f64 (cbrt.f64 (/.f64 (*.f64 x y) (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)))) 2))
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))))
19.1b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
38.2b
(*.f64 (/.f64 1 (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (/.f64 (*.f64 x y) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))))
24.2b
(*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))) y)
28.7b
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) (/.f64 1 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)))))
25.6b
(*.f64 x (/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) y)))
Compiler

Compiled 6025 to 3324 computations (44.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (+.f64 x y) 3)
5.2b
(*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))) y)
8.3b
(/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)))
14.0b
(+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))

series158.0ms (3.6%)

Counts
3 → 72
Calls

3 calls:

74.0ms
(*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))) y)
67.0ms
(/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)))
16.0ms
(+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))

rewrite72.0ms (1.6%)

Algorithm
batch-egg-rewrite
Rules
417×fma-def_binary64
220×fma-neg_binary64
210×expm1-udef_binary64
210×log1p-udef_binary64
183×log-pow_binary64
Counts
3 → 121
Calls

3 calls:

70.0ms
(*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))) y)
70.0ms
(/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)))
70.0ms
(+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01157
125357
2313157
3502757
000
100

simplify82.0ms (1.9%)

Algorithm
egg-herbie
Rules
471×fma-def_binary64
365×times-frac_binary64
350×associate-+l+_binary64
293×associate-/l*_binary64
271×associate-/r*_binary64
Counts
193 → 208
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03955271
113304911
253344911

prune270.0ms (6.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2514255
Fresh437
Picked101
Done011
Total2568264
Error
5.0b
Counts
264 → 8
Alt Table
StatusErrorProgram
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (/.f64 y (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))))
40.3b
(/.f64 x (pow.f64 y 2))
38.2b
(/.f64 (/.f64 (*.f64 x y) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)))
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))))
25.6b
(/.f64 x (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) y))
24.3b
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) x) -1) y)
19.1b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
35.4b
(log.f64 (pow.f64 (exp.f64 y) (/.f64 x (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)))))
Compiler

Compiled 9542 to 5813 computations (39.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) x) -1)
5.2b
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) x) -1) y)
7.9b
(/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) x)
14.0b
(+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2))

series161.0ms (3.7%)

Counts
3 → 72
Calls

3 calls:

74.0ms
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) x) -1) y)
68.0ms
(pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) x) -1)
18.0ms
(/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) x)

rewrite98.0ms (2.2%)

Algorithm
batch-egg-rewrite
Rules
424×fma-def_binary64
236×expm1-udef_binary64
236×log1p-udef_binary64
226×fma-neg_binary64
137×add-sqr-sqrt_binary64
Counts
3 → 94
Calls

3 calls:

96.0ms
(pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) x) -1)
96.0ms
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) x) -1) y)
96.0ms
(/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) x)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01366
129360
2346760
3497860
4487360
000
100

simplify81.0ms (1.8%)

Algorithm
egg-herbie
Rules
469×fma-def_binary64
371×associate-+l+_binary64
368×times-frac_binary64
298×associate-/l*_binary64
271×associate-/r*_binary64
Counts
166 → 184
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04115179
113814879
253344879

prune275.0ms (6.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2681269
Fresh156
Picked101
Done011
Total2707277
Error
3.0b
Counts
277 → 7
Alt Table
StatusErrorProgram
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (/.f64 y (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))))
40.3b
(/.f64 x (pow.f64 y 2))
38.2b
(/.f64 (/.f64 (*.f64 x y) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)))
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))))
25.6b
(/.f64 x (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) y))
19.1b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
24.8b
(*.f64 (pow.f64 (fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x)))) -1) y)
Compiler

Compiled 10104 to 6147 computations (39.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 3 (*.f64 y y) (fma.f64 x x x))
0.5b
(pow.f64 (fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x)))) -1)
3.6b
(fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x))))
14.8b
(*.f64 (pow.f64 (fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x)))) -1) y)

series107.0ms (2.4%)

Counts
4 → 96
Calls

4 calls:

46.0ms
(*.f64 (pow.f64 (fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x)))) -1) y)
43.0ms
(pow.f64 (fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x)))) -1)
10.0ms
(fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x))))
7.0ms
(fma.f64 3 (*.f64 y y) (fma.f64 x x x))

rewrite75.0ms (1.7%)

Algorithm
batch-egg-rewrite
Rules
601×log-prod_binary64
269×prod-diff_binary64
237×expm1-udef_binary64
237×log1p-udef_binary64
214×log-pow_binary64
Counts
4 → 103
Calls

4 calls:

72.0ms
(fma.f64 3 (*.f64 y y) (fma.f64 x x x))
72.0ms
(pow.f64 (fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x)))) -1)
72.0ms
(fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x))))
72.0ms
(*.f64 (pow.f64 (fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x)))) -1) y)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01490
128387
2303587
3548987
000
100

simplify100.0ms (2.3%)

Algorithm
egg-herbie
Rules
390×fma-def_binary64
362×associate-+r+_binary64
313×+-commutative_binary64
289×times-frac_binary64
273×associate-+l+_binary64
Counts
199 → 188
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03434383
111294164
247154128
350324128

prune195.0ms (4.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1853188
Fresh145
Picked011
Done011
Total1869195
Error
3.0b
Counts
195 → 9
Alt Table
StatusErrorProgram
32.3b
(*.f64 (/.f64 x (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (/.f64 y (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))))
40.3b
(/.f64 x (pow.f64 y 2))
38.2b
(/.f64 (/.f64 (*.f64 x y) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)))
19.1b
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
61.9b
(-.f64 (*.f64 1/3 (/.f64 1 y)) (+.f64 (*.f64 2/9 (/.f64 1 (pow.f64 y 2))) (*.f64 1/3 (/.f64 x (pow.f64 y 2)))))
33.6b
(/.f64 y (fma.f64 x x x))
24.8b
(*.f64 (pow.f64 (fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x)))) -1) y)
25.0b
(pow.f64 (cbrt.f64 (/.f64 y (fma.f64 3 (*.f64 y x) (fma.f64 y 2 (fma.f64 3 (*.f64 y y) (fma.f64 x x x)))))) 3)
25.6b
(/.f64 x (/.f64 (+.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (+.f64 x y) 2)) y))
Compiler

Compiled 7558 to 4444 computations (41.2% saved)

regimes739.0ms (16.8%)

Accuracy

Total 4.3b remaining (59.3%)

Threshold costs 0b (0%)

Counts
163 → 3
Compiler

Compiled 9074 to 5720 computations (37% saved)

bsearch37.0ms (0.8%)

Steps
ItersRangePoint
8
-5.590189577891837e-143
-5.586811506282266e-146
-5.664768576413203e-146
6
-9.785478050113318e+112
-1.6984622260640051e+112
-1.7172951296258227e+112
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02676
12976
22976

end259.0ms (5.9%)

Compiler

Compiled 386 to 207 computations (46.4% saved)

Profiling

Loading profile data...