Details

Time bar (total: 7.4s)

analyze1.2s (16.8%)

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)

sample1.6s (21.2%)

Symmetry

(sort x y)

(sort z t)

Results
1.1s8256×body128valid
387.0ms3178×body128invalid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify45.0ms (0.6%)

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
7.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
7.0b
(/.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 1 expressions with local error:

NewErrorProgram
6.6b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

series25.0ms (0.3%)

Counts
1 → 60
Calls

1 calls:

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

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
times-frac_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
associate-/r*_binary64
Counts
1 → 32
Calls

1 calls:

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

simplify77.0ms (1%)

Algorithm
egg-herbie
Rules
742×fma-def_binary64
440×distribute-rgt-in_binary64
432×distribute-lft-in_binary64
335×associate-/l/_binary64
300×neg-mul-1_binary64
Counts
92 → 61
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0801433
12041377
25521377
316691377
446351377
551531377

prune49.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New511061
Fresh000
Picked101
Done000
Total521062
Error
6.6b
Counts
62 → 10
Alt Table
StatusErrorProgram
34.5b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
33.2b
(/.f64 (*.f64 y x) a)
7.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (cbrt.f64 a)))
32.8b
(neg.f64 (/.f64 (*.f64 t z) a))
33.5b
(/.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))
30.4b
(/.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))))
7.9b
(*.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))
7.1b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
30.2b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
7.9b
(*.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)))
Compiler

Compiled 1577 to 423 computations (73.2% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
6.7b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

series25.0ms (0.3%)

Counts
1 → 60
Calls

1 calls:

25.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

rewrite11.0ms (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))

simplify87.0ms (1.2%)

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

prune60.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New71273
Fresh189
Picked011
Done000
Total721183
Error
6.6b
Counts
83 → 11
Alt Table
StatusErrorProgram
34.5b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
33.2b
(/.f64 (*.f64 y x) a)
7.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (cbrt.f64 a)))
32.8b
(neg.f64 (/.f64 (*.f64 t z) a))
7.9b
(*.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)))
7.9b
(*.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)))
30.4b
(/.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))))
33.5b
(/.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))
7.9b
(*.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))
7.1b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
30.2b
(*.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 1899 to 677 computations (64.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a)
0.5b
(*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))))
0.6b
(*.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))
7.9b
(cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z)))

series797.0ms (10.8%)

Counts
4 → 216
Calls

4 calls:

528.0ms
(/.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a)
119.0ms
(*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))))
103.0ms
(cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z)))
47.0ms
(*.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))

rewrite64.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt_binary64
41×*-un-lft-identity_binary64
41×cbrt-prod_binary64
41×add-cube-cbrt_binary64
40×cbrt-div_binary64
Counts
4 → 171
Calls

4 calls:

22.0ms
(*.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))
8.0ms
(*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))))
4.0ms
(/.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a)
3.0ms
(cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z)))

simplify334.0ms (4.5%)

Algorithm
egg-herbie
Rules
717×fma-def_binary64
344×*-commutative_binary64
211×cancel-sign-sub-inv_binary64
208×sub-neg_binary64
183×fma-neg_binary64
Counts
387 → 483
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
086717300
1300815800
2483615800
3521915800

prune526.0ms (7.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New6721673
Fresh099
Picked011
Done011
Total67212684
Error
6.6b
Counts
684 → 12
Alt Table
StatusErrorProgram
34.5b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
33.2b
(/.f64 (*.f64 y x) a)
7.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (cbrt.f64 a)))
32.8b
(neg.f64 (/.f64 (*.f64 t z) a))
7.9b
(*.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)))
7.9b
(*.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)))
30.4b
(/.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))))
33.5b
(/.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))
7.9b
(*.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))
7.9b
(*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a)))
7.1b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
30.2b
(*.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 37717 to 13736 computations (63.6% saved)

localize11.0ms (0.1%)

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))
1.0b
(*.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)))
5.9b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a))))

series552.0ms (7.5%)

Counts
4 → 144
Calls

4 calls:

444.0ms
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a))))
39.0ms
(*.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)))
38.0ms
(*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))
30.0ms
(cbrt.f64 (/.f64 1 a))

rewrite59.0ms (0.8%)

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:

15.0ms
(*.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)))
12.0ms
(*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))
9.0ms
(*.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))

simplify179.0ms (2.4%)

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

prune293.0ms (4%)

Pruning

18 alts after pruning (15 fresh and 3 done)

PrunedKeptTotal
New3596365
Fresh099
Picked011
Done022
Total35918377
Error
6.6b
Counts
377 → 18
Alt Table
StatusErrorProgram
34.5b
(*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
33.2b
(/.f64 (*.f64 y x) a)
7.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (cbrt.f64 a)))
32.8b
(neg.f64 (/.f64 (*.f64 t z) a))
7.9b
(*.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))
34.9b
(*.f64 (*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (sqrt.f64 (/.f64 1 a)))) (cbrt.f64 (sqrt.f64 (/.f64 1 a))))
7.9b
(*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (*.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y x) (*.f64 t z))) a)))
49.9b
(*.f64 (*.f64 (pow.f64 (/.f64 1 a) 2/3) (*.f64 y x)) (cbrt.f64 (/.f64 1 a)))
7.1b
(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))
43.8b
(*.f64 (*.f64 (*.f64 y x) (pow.f64 (/.f64 1 (pow.f64 a 2)) 1/3)) (cbrt.f64 (/.f64 1 a)))
30.2b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)))
48.4b
(*.f64 (*.f64 (pow.f64 (/.f64 1 a) 2/3) (neg.f64 (*.f64 t z))) (cbrt.f64 (/.f64 1 a)))
7.9b
(*.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)))
7.9b
(*.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)))
8.3b
(*.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a))))) (cbrt.f64 (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))))) (cbrt.f64 (/.f64 1 a)))
30.4b
(/.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))))
33.5b
(/.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))
43.2b
(*.f64 (*.f64 -1 (*.f64 (pow.f64 (/.f64 1 (pow.f64 a 2)) 1/3) (*.f64 t z))) (cbrt.f64 (/.f64 1 a)))
Compiler

Compiled 11251 to 5968 computations (47% saved)

regimes1.1s (14.7%)

Accuracy

Total 0.3b remaining (4.6%)

Threshold costs 0.3b (4.6%)

Counts
104 → 1
Compiler

Compiled 23898 to 14576 computations (39% saved)

simplify2.0ms (0%)

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
01213
12113
23013
33613
44013
54113
64013

end258.0ms (3.5%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 539 to 329 computations (39% saved)

Profiling

Loading profile data...