Details

Time bar (total: 10.8s)

analyze3.2s (29.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
16.4%83.4%0.2%11
19.9%79.9%0.2%12
21.6%77.2%1.2%13
24.8%73.7%1.4%14
Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.9s (17.7%)

Symmetry

(sort x y)

(sort z t)

Results
1.2s8256×body128valid
540.0ms3165×body128invalid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify46.0ms (0.4%)

Algorithm
egg-herbie
Rules
828×fma-def_binary64
389×fma-neg_binary64
130×cancel-sign-sub-inv_binary64
113×distribute-rgt-in_binary64
103×associate-/l*_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
12113
24213
37313
414413
522313
631913
749513
867813
983313
1088913
1197613
1298213
1398713
1491413

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
8.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
8.4b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
Compiler

Compiled 42 to 27 computations (35.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.7b
(-.f64 (*.f64 x y) (*.f64 z t))
7.9b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

series37.0ms (0.3%)

Counts
2 → 108
Calls

2 calls:

28.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
8.0ms
(-.f64 (*.f64 x y) (*.f64 z t))

rewrite88.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
420×fma-def_binary64
226×egg-rr
220×fma-neg_binary64
214×expm1-udef_binary64
214×log1p-udef_binary64
Counts
2 → 226
Calls

2 calls:

83.0ms
(-.f64 (*.f64 x y) (*.f64 z t))
82.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01023
122323
2311223
3497323
000
100

simplify103.0ms (0.9%)

Algorithm
egg-herbie
Rules
1168×fma-def_binary64
351×fma-neg_binary64
125×cancel-sign-sub-inv_binary64
93×associate-/l*_binary64
92×unsub-neg_binary64
Counts
334 → 236
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0191140
1491140
2961140
32021140
43561140
55931140
68191140
79081140
89821140
99961140
1010011140
119281140

prune210.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New22610236
Fresh000
Picked101
Done000
Total22710237
Error
3.9b
Counts
237 → 10
Alt Table
StatusErrorProgram
9.3b
(/.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) 3) a)
34.0b
(pow.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) 2)
6.4b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 (*.f64 z t) a)))
8.5b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
8.0b
(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 (*.f64 z t) a)))
38.4b
(/.f64 (*.f64 y x) a)
38.7b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) 3))
33.6b
(*.f64 (/.f64 1 (cbrt.f64 (*.f64 a a))) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (cbrt.f64 a)))
9.4b
(*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (pow.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) 2))
8.5b
(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
Compiler

Compiled 4898 to 1240 computations (74.7% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
2.2b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 (*.f64 z t) a)))
4.9b
(/.f64 (*.f64 z t) a)

series45.0ms (0.4%)

Counts
2 → 96
Calls

2 calls:

30.0ms
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 (*.f64 z t) a)))
16.0ms
(/.f64 (*.f64 z t) a)

rewrite182.0ms (1.7%)

Algorithm
batch-egg-rewrite
Rules
623×prod-diff_binary64
366×egg-rr
209×expm1-udef_binary64
209×log1p-udef_binary64
188×log-pow_binary64
Counts
2 → 366
Calls

2 calls:

167.0ms
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 (*.f64 z t) a)))
167.0ms
(/.f64 (*.f64 z t) a)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01323
125421
2305421
3494221
4524821
000
100

simplify111.0ms (1%)

Algorithm
egg-herbie
Rules
1163×fma-def_binary64
349×fma-neg_binary64
125×cancel-sign-sub-inv_binary64
92×associate-/l*_binary64
92×unsub-neg_binary64
Counts
462 → 373
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
018972
146972
293972
3198972
4354972
5593972
6819972
7908972
8982972
9996972
101001972
11928972

prune330.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3694373
Fresh549
Picked101
Done000
Total3758383
Error
0.0b
Counts
383 → 8
Alt Table
StatusErrorProgram
38.7b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) 3))
7.1b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (*.f64 (/.f64 z a) t)))
9.8b
(+.f64 (fma.f64 (*.f64 y x) (/.f64 1 a) (neg.f64 (*.f64 (/.f64 t a) (/.f64 z 1)))) (fma.f64 (neg.f64 (/.f64 t a)) (/.f64 z 1) (*.f64 (/.f64 t a) (/.f64 z 1))))
17.9b
(+.f64 (fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (/.f64 x a)) (neg.f64 (*.f64 (/.f64 1 (/.f64 a t)) z))) (fma.f64 (neg.f64 (/.f64 1 (/.f64 a t))) z (*.f64 (/.f64 1 (/.f64 a t)) z)))
19.6b
(+.f64 (fma.f64 (cbrt.f64 (*.f64 y y)) (*.f64 (cbrt.f64 y) (/.f64 x a)) (neg.f64 (*.f64 t (/.f64 z a)))) (fma.f64 (neg.f64 t) (/.f64 z a) (*.f64 t (/.f64 z a))))
8.5b
(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
8.5b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
8.0b
(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 (*.f64 z t) a)))
Compiler

Compiled 15251 to 4270 computations (72% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
2.2b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (*.f64 (/.f64 z a) t)))
5.6b
(*.f64 (/.f64 z a) t)

series47.0ms (0.4%)

Counts
2 → 96
Calls

2 calls:

33.0ms
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (*.f64 (/.f64 z a) t)))
13.0ms
(*.f64 (/.f64 z a) t)

rewrite131.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
494×prod-diff_binary64
398×fma-udef_binary64
221×fma-def_binary64
213×expm1-udef_binary64
213×log1p-udef_binary64
Counts
2 → 95
Calls

2 calls:

126.0ms
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (*.f64 (/.f64 z a) t)))
126.0ms
(*.f64 (/.f64 z a) t)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01323
125721
2307921
3484721
4475421
5503521
000
100

simplify165.0ms (1.5%)

Algorithm
egg-herbie
Rules
1163×fma-def_binary64
349×fma-neg_binary64
125×cancel-sign-sub-inv_binary64
92×associate-/l*_binary64
92×unsub-neg_binary64
Counts
191 → 102
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
018972
146972
293972
3198972
4354972
5593972
6819972
7908972
8982972
9996972
101001972
11928972

prune87.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1002102
Fresh167
Picked101
Done000
Total1028110
Error
0.0b
Counts
110 → 8
Alt Table
StatusErrorProgram
38.7b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) 3))
7.1b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 t (/.f64 a z))))
7.2b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 z (/.f64 a t))))
17.9b
(+.f64 (fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (/.f64 x a)) (neg.f64 (*.f64 (/.f64 1 (/.f64 a t)) z))) (fma.f64 (neg.f64 (/.f64 1 (/.f64 a t))) z (*.f64 (/.f64 1 (/.f64 a t)) z)))
19.6b
(+.f64 (fma.f64 (cbrt.f64 (*.f64 y y)) (*.f64 (cbrt.f64 y) (/.f64 x a)) (neg.f64 (*.f64 t (/.f64 z a)))) (fma.f64 (neg.f64 t) (/.f64 z a) (*.f64 t (/.f64 z a))))
8.5b
(/.f64 (fma.f64 x y (fma.f64 z (neg.f64 t) (fma.f64 z (neg.f64 t) (*.f64 z t)))) a)
8.5b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
8.0b
(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 (*.f64 z t) a)))
Compiler

Compiled 2618 to 866 computations (66.9% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
2.2b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 t (/.f64 a z))))
5.6b
(/.f64 t (/.f64 a z))

series45.0ms (0.4%)

Counts
2 → 96
Calls

2 calls:

28.0ms
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 t (/.f64 a z))))
17.0ms
(/.f64 t (/.f64 a z))

rewrite190.0ms (1.8%)

Algorithm
batch-egg-rewrite
Rules
553×prod-diff_binary64
550×egg-rr
217×expm1-udef_binary64
217×log1p-udef_binary64
131×add-sqr-sqrt_binary64
Counts
2 → 550
Calls

2 calls:

151.0ms
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 t (/.f64 a z))))
151.0ms
(/.f64 t (/.f64 a z))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01323
126121
2324621
3502621
000
100

simplify117.0ms (1.1%)

Algorithm
egg-herbie
Rules
1163×fma-def_binary64
349×fma-neg_binary64
125×cancel-sign-sub-inv_binary64
92×associate-/l*_binary64
92×unsub-neg_binary64
Counts
646 → 557
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
018972
146972
293972
3198972
4354972
5593972
6819972
7908972
8982972
9996972
101001972
11928972

prune393.0ms (3.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New5561557
Fresh167
Picked011
Done000
Total5578565
Error
0.0b
Counts
565 → 8
Alt Table
StatusErrorProgram
38.7b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) 3))
7.0b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (*.f64 z (/.f64 t a))))
7.1b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 t (/.f64 a z))))
7.2b
(fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (/.f64 z (/.f64 a t))))
17.9b
(+.f64 (fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (/.f64 x a)) (neg.f64 (*.f64 (/.f64 1 (/.f64 a t)) z))) (fma.f64 (neg.f64 (/.f64 1 (/.f64 a t))) z (*.f64 (/.f64 1 (/.f64 a t)) z)))
19.6b
(+.f64 (fma.f64 (cbrt.f64 (*.f64 y y)) (*.f64 (cbrt.f64 y) (/.f64 x a)) (neg.f64 (*.f64 t (/.f64 z a)))) (fma.f64 (neg.f64 t) (/.f64 z a) (*.f64 t (/.f64 z a))))
8.5b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
8.0b
(fma.f64 (/.f64 x 1) (/.f64 y a) (neg.f64 (/.f64 (*.f64 z t) a)))
Compiler

Compiled 20976 to 4370 computations (79.2% saved)

regimes3.0s (28.1%)

Accuracy

Total 0.7b remaining (96.2%)

Threshold costs 0.7b (96.2%)

Counts
159 → 3
Compiler

Compiled 34400 to 20168 computations (41.4% saved)

bsearch5.0ms (0%)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify7.0ms (0.1%)

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

Useful iterations: 2 (0.0ms)

IterNodesCost
03381
15481
28279
39979
410779
510879
610679

end301.0ms (2.8%)

Remove

(sort x y)

Compiler

Compiled 649 to 326 computations (49.8% saved)

Profiling

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