Details

Time bar (total: 5.4s)

analyze1.1s (20.6%)

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)

sample102.0ms (1.9%)

Algorithm
intervals
Symmetry

(sort x y)

(sort z t)

Results
11.0ms256×body128valid
3.0ms73×body128invalid
Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify47.0ms (0.9%)

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
9.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
9.0b
(/.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
0.2b
(-.f64 (*.f64 x y) (*.f64 z t))
8.4b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

series35.0ms (0.7%)

Counts
2 → 108
Calls

2 calls:

27.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
8.0ms
(-.f64 (*.f64 x y) (*.f64 z t))

rewrite9.0ms (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:

4.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)
3.0ms
(-.f64 (*.f64 x y) (*.f64 z t))

simplify118.0ms (2.2%)

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

prune222.0ms (4.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New811293
Fresh000
Picked101
Done000
Total821294
Error
8.5b
Counts
94 → 12
Alt Table
StatusErrorProgram
35.1b
(/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) a)
41.2b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) a) 3))
35.1b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
35.3b
(neg.f64 (/.f64 (*.f64 t z) a))
9.1b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
36.3b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
33.1b
(/.f64 (*.f64 y x) a)
9.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (cbrt.f64 a)))
37.1b
(/.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
9.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
32.0b
(/.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))))
10.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 a)))
Compiler

Compiled 2134 to 563 computations (73.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 x y) (*.f64 z t))
8.5b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

series33.0ms (0.6%)

Counts
1 → 60
Calls

1 calls:

33.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

rewrite10.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64
13×associate-*r*_binary64
11×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-exp-log_binary64
Counts
1 → 42
Calls

1 calls:

7.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

simplify90.0ms (1.7%)

Algorithm
egg-herbie
Rules
493×associate-*l*_binary64
488×fma-neg_binary64
416×associate-*r*_binary64
344×distribute-lft-neg-out_binary64
344×distribute-rgt-neg-out_binary64
Counts
102 → 73
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0921553
12431454
27771454
327121454
449761454
552171454

prune133.0ms (2.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1014105
Fresh11011
Picked101
Done000
Total10314117
Error
8.5b
Counts
117 → 14
Alt Table
StatusErrorProgram
35.1b
(/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) a)
41.2b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) a) 3))
9.9b
(*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
9.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (cbrt.f64 a)))
32.0b
(/.f64 (*.f64 (-.f64 (*.f64 y x) (*.f64 t z)) (fma.f64 t z (*.f64 y x))) (*.f64 a (fma.f64 t z (*.f64 y x))))
35.1b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
35.3b
(*.f64 (neg.f64 (*.f64 t z)) (/.f64 1 a))
35.3b
(neg.f64 (/.f64 (*.f64 t z) a))
33.1b
(*.f64 (*.f64 y x) (/.f64 1 a))
37.1b
(/.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
33.1b
(/.f64 (*.f64 y x) a)
9.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
10.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 a)))
36.3b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
Compiler

Compiled 2554 to 910 computations (64.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))
0.6b
(cbrt.f64 (/.f64 1 a))
1.7b
(*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
6.9b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a))))

series591.0ms (10.9%)

Counts
4 → 144
Calls

4 calls:

481.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a))))
43.0ms
(*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
37.0ms
(*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))
30.0ms
(cbrt.f64 (/.f64 1 a))

rewrite58.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
106×cbrt-prod_binary64
93×add-sqr-sqrt_binary64
70×times-frac_binary64
62×*-un-lft-identity_binary64
53×cbrt-div_binary64
Counts
4 → 204
Calls

4 calls:

16.0ms
(*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
10.0ms
(*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))
10.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a))))
2.0ms
(cbrt.f64 (/.f64 1 a))

simplify195.0ms (3.6%)

Algorithm
egg-herbie
Rules
461×times-frac_binary64
404×distribute-rgt-in_binary64
390×distribute-lft-in_binary64
336×associate-*l*_binary64
284×associate-*r*_binary64
Counts
348 → 307
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02096998
14466303
217006063
345726042
449716042

prune305.0ms (5.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New3596365
Fresh21113
Picked011
Done000
Total36118379
Error
8.5b
Counts
379 → 18
Alt Table
StatusErrorProgram
9.9b
(*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
9.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (cbrt.f64 a)))
32.0b
(/.f64 (*.f64 (-.f64 (*.f64 y x) (*.f64 t z)) (fma.f64 t z (*.f64 y x))) (*.f64 a (fma.f64 t z (*.f64 y x))))
35.1b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
35.3b
(*.f64 (neg.f64 (*.f64 t z)) (/.f64 1 a))
35.3b
(neg.f64 (/.f64 (*.f64 t z) a))
9.0b
(neg.f64 (/.f64 (-.f64 (*.f64 t z) (*.f64 y x)) a))
33.1b
(*.f64 (*.f64 y x) (/.f64 1 a))
37.1b
(/.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
45.5b
(*.f64 (*.f64 (*.f64 y x) (pow.f64 (/.f64 1 (pow.f64 a 2)) 1/3)) (cbrt.f64 (/.f64 1 a)))
9.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
50.8b
(*.f64 (*.f64 (pow.f64 (/.f64 1 a) 2/3) (neg.f64 (*.f64 t z))) (cbrt.f64 (/.f64 1 a)))
9.7b
(*.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (/.f64 1 a)))
41.2b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) a) 3))
50.1b
(*.f64 (*.f64 (pow.f64 (/.f64 1 a) 2/3) (*.f64 y x)) (cbrt.f64 (/.f64 1 a)))
47.2b
(*.f64 (*.f64 -1 (*.f64 (pow.f64 (/.f64 1 (pow.f64 a 2)) 1/3) (*.f64 t z))) (cbrt.f64 (/.f64 1 a)))
10.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (cbrt.f64 a)))
36.3b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
Compiler

Compiled 11555 to 6147 computations (46.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.3b
(-.f64 (*.f64 t z) (*.f64 y x))
8.4b
(/.f64 (-.f64 (*.f64 t z) (*.f64 y x)) a)

series36.0ms (0.7%)

Counts
2 → 64
Calls

2 calls:

25.0ms
(/.f64 (-.f64 (*.f64 t z) (*.f64 y x)) a)
11.0ms
(-.f64 (*.f64 t z) (*.f64 y x))

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

simplify107.0ms (2%)

Algorithm
egg-herbie
Rules
643×distribute-rgt-in_binary64
297×fma-neg_binary64
267×associate-*l*_binary64
223×fma-def_binary64
209×associate-*r*_binary64
Counts
112 → 65
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0941651
12431571
27391565
323311565
445511565
549701565
649121565

prune58.0ms (1.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New63265
Fresh21416
Picked101
Done011
Total661783
Error
8.5b
Counts
83 → 17
Alt Table
StatusErrorProgram
9.9b
(*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
9.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (cbrt.f64 a)))
32.0b
(/.f64 (*.f64 (-.f64 (*.f64 y x) (*.f64 t z)) (fma.f64 t z (*.f64 y x))) (*.f64 a (fma.f64 t z (*.f64 y x))))
35.1b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
35.3b
(neg.f64 (/.f64 (*.f64 t z) a))
33.1b
(*.f64 (*.f64 y x) (/.f64 1 a))
37.1b
(/.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
45.5b
(*.f64 (*.f64 (*.f64 y x) (pow.f64 (/.f64 1 (pow.f64 a 2)) 1/3)) (cbrt.f64 (/.f64 1 a)))
9.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a))
50.8b
(*.f64 (*.f64 (pow.f64 (/.f64 1 a) 2/3) (neg.f64 (*.f64 t z))) (cbrt.f64 (/.f64 1 a)))
9.7b
(*.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (/.f64 1 a)))
41.2b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y x) (*.f64 t z)) a) 3))
50.1b
(*.f64 (*.f64 (pow.f64 (/.f64 1 a) 2/3) (*.f64 y x)) (cbrt.f64 (/.f64 1 a)))
47.2b
(*.f64 (*.f64 -1 (*.f64 (pow.f64 (/.f64 1 (pow.f64 a 2)) 1/3) (*.f64 t z))) (cbrt.f64 (/.f64 1 a)))
36.3b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
9.6b
(neg.f64 (/.f64 1 (/.f64 a (-.f64 (*.f64 t z) (*.f64 y x)))))
37.6b
(neg.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 t z) (*.f64 y x))) (/.f64 (sqrt.f64 (-.f64 (*.f64 t z) (*.f64 y x))) a)))
Compiler

Compiled 1550 to 505 computations (67.4% saved)

regimes1.0s (19.1%)

Accuracy

Total 0.4b remaining (4.7%)

Threshold costs 0.4b (4.7%)

Counts
102 → 1
Compiler

Compiled 23184 to 14171 computations (38.9% saved)

simplify3.0ms (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
01325
12425
23225
33625
43725
53725

end23.0ms (0.4%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 110 to 60 computations (45.5% saved)

sample1.0s (19.3%)

Algorithm
intervals
Results
315.0ms8000×body128valid
123.0ms2972×body128invalid
Compiler

Compiled 409 to 253 computations (38.1% saved)

Profiling

Loading profile data...