Details

Time bar (total: 5.9s)

analyze1.2s (19.8%)

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)

sample112.0ms (1.9%)

Algorithm
intervals
Symmetry

(sort x y)

(sort z t)

Results
15.0ms256×body128valid
4.0ms104×body128invalid
Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify43.0ms (0.7%)

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

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
5.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
5.9b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
Compiler

Compiled 42 to 27 computations (35.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 z t))
5.6b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

series57.0ms (1%)

Counts
2 → 108
Calls

2 calls:

47.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
9.0ms
(-.f64 (*.f64 x y) (*.f64 z t))

rewrite10.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
2 → 48
Calls

2 calls:

5.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
2.0ms
(-.f64 (*.f64 x y) (*.f64 z t))

simplify126.0ms (2.1%)

Algorithm
egg-herbie
Rules
644×distribute-rgt-in_binary64
301×fma-neg_binary64
270×associate-*l*_binary64
223×fma-def_binary64
213×associate-*r*_binary64
Counts
156 → 93
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0992115
12512035
27432029
323552029
445902029
549962029
649232029

prune85.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New811293
Fresh000
Picked101
Done000
Total821294
Error
5.6b
Counts
94 → 12
Alt Table
StatusErrorProgram
28.8b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z t) (*.f64 z t))) (*.f64 a (fma.f64 t z (*.f64 y x))))
27.6b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
6.0b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
32.7b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) a) 3))
6.8b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) a)
6.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (cbrt.f64 a)))
31.8b
(/.f64 (*.f64 y x) a)
34.7b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (sqrt.f64 a)) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (sqrt.f64 a)))
6.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
6.1b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
5.9b
(-.f64 (/.f64 (*.f64 y x) a) (/.f64 (*.f64 t z) a))
29.6b
(neg.f64 (/.f64 (*.f64 t z) a))
Compiler

Compiled 2134 to 561 computations (73.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 (*.f64 y x) a) (/.f64 (*.f64 t z) a))
4.1b
(/.f64 (*.f64 t z) a)
6.2b
(/.f64 (*.f64 y x) a)

series56.0ms (0.9%)

Counts
3 → 24
Calls

3 calls:

30.0ms
(-.f64 (/.f64 (*.f64 y x) a) (/.f64 (*.f64 t z) a))
14.0ms
(/.f64 (*.f64 y x) a)
12.0ms
(/.f64 (*.f64 t z) a)

rewrite31.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
54×times-frac_binary64
49×prod-diff_binary64
41×*-un-lft-identity_binary64
41×add-sqr-sqrt_binary64
39×add-cube-cbrt_binary64
Counts
3 → 127
Calls

3 calls:

8.0ms
(/.f64 (*.f64 y x) a)
8.0ms
(-.f64 (/.f64 (*.f64 y x) a) (/.f64 (*.f64 t z) a))
4.0ms
(/.f64 (*.f64 t z) a)

simplify156.0ms (2.7%)

Algorithm
egg-herbie
Rules
943×times-frac_binary64
526×fma-def_binary64
355×fma-neg_binary64
145×cancel-sign-sub-inv_binary64
145×exp-prod_binary64
Counts
151 → 162
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02113243
14832673
216752230
342002230
449002230
549992230
648542230

prune151.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1566162
Fresh7411
Picked101
Done000
Total16410174
Error
0.0b
Counts
174 → 10
Alt Table
StatusErrorProgram
7.1b
(-.f64 (/.f64 (*.f64 y x) a) (*.f64 t (/.f64 z a)))
6.0b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
32.7b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) a) 3))
6.6b
(-.f64 (/.f64 (*.f64 y x) a) (*.f64 (/.f64 t (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 z (cbrt.f64 a))))
6.8b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) a)
5.9b
(-.f64 (*.f64 y (/.f64 x a)) (/.f64 (*.f64 t z) a))
28.9b
(/.f64 (*.f64 a (-.f64 (*.f64 y x) (*.f64 t z))) (*.f64 a a))
6.9b
(-.f64 (/.f64 (*.f64 y x) a) (/.f64 t (/.f64 a z)))
6.1b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
5.9b
(-.f64 (/.f64 y (/.f64 a x)) (/.f64 (*.f64 t z) a))
Compiler

Compiled 4537 to 934 computations (79.4% saved)

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 y (/.f64 x a)) (/.f64 (*.f64 t z) a))
4.1b
(/.f64 (*.f64 t z) a)
4.9b
(*.f64 y (/.f64 x a))

series42.0ms (0.7%)

Counts
2 → 96
Calls

2 calls:

30.0ms
(-.f64 (*.f64 y (/.f64 x a)) (/.f64 (*.f64 t z) a))
12.0ms
(*.f64 y (/.f64 x a))

rewrite18.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64
16×times-frac_binary64
14×*-un-lft-identity_binary64
14×add-cube-cbrt_binary64
13×associate-*r*_binary64
Counts
2 → 64
Calls

2 calls:

5.0ms
(-.f64 (*.f64 y (/.f64 x a)) (/.f64 (*.f64 t z) a))
5.0ms
(*.f64 y (/.f64 x a))

simplify101.0ms (1.7%)

Algorithm
egg-herbie
Rules
485×associate-/l*_binary64
456×fma-def_binary64
432×fma-neg_binary64
336×*-commutative_binary64
246×div-sub_binary64
Counts
160 → 93
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01651930
14111858
214701793
337771793
443941793
548361793

prune92.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1210121
Fresh099
Picked011
Done000
Total12110131
Error
0.0b
Counts
131 → 10
Alt Table
StatusErrorProgram
7.1b
(-.f64 (/.f64 (*.f64 y x) a) (*.f64 t (/.f64 z a)))
6.0b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
32.7b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) a) 3))
6.6b
(-.f64 (/.f64 (*.f64 y x) a) (*.f64 (/.f64 t (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 z (cbrt.f64 a))))
6.8b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) a)
5.9b
(-.f64 (*.f64 y (/.f64 x a)) (/.f64 (*.f64 t z) a))
28.9b
(/.f64 (*.f64 a (-.f64 (*.f64 y x) (*.f64 t z))) (*.f64 a a))
6.9b
(-.f64 (/.f64 (*.f64 y x) a) (/.f64 t (/.f64 a z)))
6.1b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
5.9b
(-.f64 (/.f64 y (/.f64 a x)) (/.f64 (*.f64 t z) a))
Compiler

Compiled 2579 to 680 computations (73.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 y (/.f64 a x)) (/.f64 (*.f64 t z) a))
4.1b
(/.f64 (*.f64 t z) a)
5.0b
(/.f64 y (/.f64 a x))

series41.0ms (0.7%)

Counts
2 → 96
Calls

2 calls:

30.0ms
(-.f64 (/.f64 y (/.f64 a x)) (/.f64 (*.f64 t z) a))
11.0ms
(/.f64 y (/.f64 a x))

rewrite115.0ms (2%)

Algorithm
rewrite-expression-head
Rules
741×times-frac_binary64
423×add-sqr-sqrt_binary64
416×*-un-lft-identity_binary64
414×add-cube-cbrt_binary64
308×prod-diff_binary64
Counts
2 → 449
Calls

2 calls:

25.0ms
(-.f64 (/.f64 y (/.f64 a x)) (/.f64 (*.f64 t z) a))
4.0ms
(/.f64 y (/.f64 a x))

simplify530.0ms (9%)

Algorithm
egg-herbie
Rules
658×fma-neg_binary64
437×times-frac_binary64
309×fma-udef_binary64
191×associate-*l/_binary64
163×unsub-neg_binary64
Counts
545 → 604
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
052218928
191716349
2278813040
3422313040
4492612893
5499012893
6486412893

prune390.0ms (6.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New6311632
Fresh178
Picked011
Done011
Total63210642
Error
0.0b
Counts
642 → 10
Alt Table
StatusErrorProgram
7.1b
(-.f64 (/.f64 (*.f64 y x) a) (*.f64 t (/.f64 z a)))
6.0b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
32.7b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) a) 3))
5.9b
(-.f64 (*.f64 y (/.f64 x a)) (/.f64 (*.f64 t z) a))
28.9b
(/.f64 (*.f64 a (-.f64 (*.f64 y x) (*.f64 t z))) (*.f64 a a))
31.8b
(/.f64 (-.f64 (*.f64 y a) (*.f64 (/.f64 a x) (*.f64 t z))) (*.f64 (/.f64 a x) a))
6.9b
(-.f64 (/.f64 (*.f64 y x) a) (/.f64 t (/.f64 a z)))
6.1b
(/.f64 1 (/.f64 a (-.f64 (*.f64 x y) (*.f64 z t))))
6.6b
(-.f64 (/.f64 (*.f64 y x) a) (*.f64 (/.f64 t (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 z (cbrt.f64 a))))
5.9b
(-.f64 (/.f64 y (/.f64 a x)) (/.f64 (*.f64 t z) a))
Compiler

Compiled 22974 to 3704 computations (83.9% saved)

regimes1.0s (17.6%)

Accuracy

Total 3.8b remaining (88.1%)

Threshold costs 0b (0%)

Counts
64 → 3
Compiler

Compiled 14944 to 7781 computations (47.9% saved)

bsearch2.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02566
13166
24066
35066
45766
56266
66466
76466

end28.0ms (0.5%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 250 to 110 computations (56% saved)

sample1.4s (24.5%)

Algorithm
intervals
Results
484.0ms2990×body128invalid
408.0ms8000×body128valid
Compiler

Compiled 246 to 147 computations (40.2% saved)

Profiling

Loading profile data...