Details

Time bar (total: 7.5s)

analyze1.4s (18.2%)

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
9.4%90.4%0.2%11
9.4%90.4%0.2%12
10.1%89.6%0.2%13
20.8%78.9%0.2%14
Compiler

Compiled 19 to 14 computations (26.3% saved)

sample94.0ms (1.2%)

Algorithm
intervals
Symmetry

(sort x y)

(sort z t)

Results
12.0ms256×body128valid
4.0ms90×body128invalid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify191.0ms (2.5%)

Algorithm
egg-herbie
Rules
2966×fma-def_binary64
757×fma-neg_binary64
541×cancel-sign-sub-inv_binary64
473×associate-/l/_binary64
472×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01419
13117
210317
331817
479417
5152617
6205417
7228117
8297517
9354017
10395417
11415817
12409717
13410817
14411817
15446217
16453117
17453617
18453617
19647417

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
6.6b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
6.8b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
Compiler

Compiled 100 to 69 computations (31% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
6.2b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series52.0ms (0.7%)

Counts
2 → 108
Calls

2 calls:

40.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
12.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
2 → 44
Calls

2 calls:

5.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
0.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

simplify104.0ms (1.4%)

Algorithm
egg-herbie
Rules
937×fma-def_binary64
487×associate-*l*_binary64
418×associate-*r*_binary64
225×associate-*r/_binary64
211×associate-*l/_binary64
Counts
152 → 88
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01082547
12482243
28122243
332062242
449372242
550192242

prune89.0ms (1.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New781088
Fresh011
Picked011
Done000
Total781290
Error
6.1b
Counts
90 → 12
Alt Table
StatusErrorProgram
31.3b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
7.4b
(*.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
7.4b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)))) (*.f64 (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (/.f64 1/2 a)))
7.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)) (/.f64 (cbrt.f64 1/2) a))
6.6b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
36.1b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
7.4b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a)))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
7.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/2 (cbrt.f64 a)))
32.4b
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) 3)) (/.f64 1/2 a))
36.2b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1 (sqrt.f64 a))) (/.f64 1/2 (sqrt.f64 a)))
34.4b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
6.8b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
Compiler

Compiled 2227 to 1220 computations (45.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
0.4b
(*.f64 (*.f64 z 9) t)
6.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))

series52.0ms (0.7%)

Counts
3 → 132
Calls

3 calls:

37.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
11.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
4.0ms
(*.f64 (*.f64 z 9) t)

rewrite22.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
3 → 62
Calls

3 calls:

13.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
4.0ms
(*.f64 (*.f64 z 9) t)
3.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

simplify91.0ms (1.2%)

Algorithm
egg-herbie
Rules
470×fma-def_binary64
445×*-commutative_binary64
325×div-sub_binary64
307×associate-/l*_binary64
287×fma-neg_binary64
Counts
194 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01482790
13962561
215062551
341282551
452472551

prune123.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1123115
Fresh4610
Picked101
Done011
Total11710127
Error
6.1b
Counts
127 → 10
Alt Table
StatusErrorProgram
31.3b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
7.4b
(*.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
7.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)) (/.f64 (cbrt.f64 1/2) a))
6.6b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
36.1b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
7.4b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a)))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
35.4b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
6.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
34.4b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
6.8b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
Compiler

Compiled 2702 to 1553 computations (42.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
0.2b
(*.f64 z (*.f64 9 t))
6.2b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))

series58.0ms (0.8%)

Counts
3 → 132
Calls

3 calls:

41.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
11.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
6.0ms
(*.f64 z (*.f64 9 t))

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
3 → 62
Calls

3 calls:

5.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
5.0ms
(*.f64 z (*.f64 9 t))
3.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))

simplify88.0ms (1.2%)

Algorithm
egg-herbie
Rules
423×fma-def_binary64
421×*-commutative_binary64
320×div-sub_binary64
286×associate-/l*_binary64
251×fma-neg_binary64
Counts
194 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01462786
13882556
213912549
338852549
449522549

prune92.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1150115
Fresh088
Picked011
Done011
Total11510125
Error
6.1b
Counts
125 → 10
Alt Table
StatusErrorProgram
31.3b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
7.4b
(*.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
7.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)) (/.f64 (cbrt.f64 1/2) a))
6.6b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
36.1b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
7.4b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a)))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
35.4b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
6.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
34.4b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
6.8b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
Compiler

Compiled 2695 to 1541 computations (42.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)
0.3b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
0.3b
(fma.f64 t (*.f64 z -9) (*.f64 y x))
6.1b
(/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2))

series153.0ms (2%)

Counts
4 → 216
Calls

4 calls:

84.0ms
(/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2))
41.0ms
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
17.0ms
(/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)
11.0ms
(fma.f64 t (*.f64 z -9) (*.f64 y x))

rewrite62.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
480×times-frac_binary64
239×*-un-lft-identity_binary64
239×add-sqr-sqrt_binary64
239×add-cube-cbrt_binary64
60×associate-/r*_binary64
Counts
4 → 317
Calls

4 calls:

10.0ms
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
4.0ms
(/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2))
2.0ms
(/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)
0.0ms
(fma.f64 t (*.f64 z -9) (*.f64 y x))

simplify351.0ms (4.7%)

Algorithm
egg-herbie
Rules
410×fma-def_binary64
376×fma-neg_binary64
307×associate-/r/_binary64
236×times-frac_binary64
226×*-commutative_binary64
Counts
533 → 537
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
038815766
195514652
2336514501
3469614489
4495714489

prune500.0ms (6.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New5343537
Fresh167
Picked011
Done022
Total53512547
Error
6.1b
Counts
547 → 12
Alt Table
StatusErrorProgram
31.3b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
7.4b
(*.f64 (/.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
6.8b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
7.7b
(/.f64 (/.f64 1 (/.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 1 (sqrt.f64 2)))) (/.f64 (cbrt.f64 a) (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (sqrt.f64 2))))
34.5b
(/.f64 1 (*.f64 -2/9 (/.f64 a (*.f64 t z))))
6.6b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
36.1b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
7.4b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a)))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
35.4b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
6.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
34.4b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
35.9b
(/.f64 1 (fma.f64 2 (/.f64 a (*.f64 y x)) (*.f64 18 (/.f64 (*.f64 a (*.f64 t z)) (*.f64 (*.f64 y x) (*.f64 y x))))))
Compiler

Compiled 16013 to 9500 computations (40.7% saved)

regimes2.7s (35.2%)

Accuracy

Total 0.4b remaining (6.1%)

Threshold costs 0.4b (6.1%)

Counts
179 → 1
Compiler

Compiled 48678 to 34498 computations (29.1% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
distribute-lft-neg-in_binary64
distribute-rgt-neg-in_binary64
sub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01419
12517
24017
34717
45117
55217
65117

end25.0ms (0.3%)

Remove

(sort x y)

Compiler

Compiled 119 to 84 computations (29.4% saved)

sample1.3s (17.2%)

Algorithm
intervals
Results
396.0ms8000×body128valid
166.0ms3113×body128invalid
Compiler

Compiled 315 to 216 computations (31.4% saved)

Profiling

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