Details

Time bar (total: 9.6s)

analyze2.1s (21.5%)

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
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)

sample53.0ms (0.6%)

Algorithm
intervals
Results
13.0ms256×body128valid
5.0ms111×body128invalid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify208.0ms (2.2%)

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%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
5.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
5.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
5.8b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
Compiler

Compiled 100 to 69 computations (31% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
0.2b
(*.f64 (*.f64 z 9) t)
5.3b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))

series56.0ms (0.6%)

Counts
3 → 132
Calls

3 calls:

39.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
12.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
4.0ms
(*.f64 (*.f64 z 9) t)

rewrite14.0ms (0.1%)

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 (*.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))

simplify127.0ms (1.3%)

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

prune117.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10411115
Fresh011
Picked101
Done000
Total10512117
Error
5.3b
Counts
117 → 12
Alt Table
StatusErrorProgram
31.9b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
6.1b
(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) 2)))
28.3b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (+.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))
5.8b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
34.1b
(/.f64 (*.f64 y x) (*.f64 a 2))
5.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
37.0b
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 3) (pow.f64 (*.f64 (*.f64 z 9) t) 3)) (*.f64 (*.f64 a 2) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (+.f64 (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t)) (*.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))))
6.6b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) a) (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
31.9b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
6.6b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
37.1b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2)) (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))) (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))))
36.2b
(exp.f64 (log.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
Compiler

Compiled 2933 to 1693 computations (42.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
0.2b
(*.f64 z (*.f64 9 t))
5.3b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))

series60.0ms (0.6%)

Counts
3 → 132
Calls

3 calls:

41.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
15.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
5.0ms
(*.f64 z (*.f64 9 t))

rewrite15.0ms (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))
4.0ms
(*.f64 z (*.f64 9 t))
3.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))

simplify96.0ms (1%)

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

prune105.0ms (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1132115
Fresh3811
Picked011
Done000
Total11611127
Error
5.3b
Counts
127 → 11
Alt Table
StatusErrorProgram
34.1b
(/.f64 (*.f64 y x) (*.f64 a 2))
33.7b
(/.f64 (/.f64 (fma.f64 y (*.f64 y (*.f64 x x)) (*.f64 (*.f64 (*.f64 t z) (*.f64 t z)) -81)) (fma.f64 z (*.f64 t 9) (*.f64 y x))) (*.f64 a 2))
6.6b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) a) (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
28.3b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z (*.f64 9 t)) (*.f64 z (*.f64 9 t)))) (*.f64 (*.f64 a 2) (fma.f64 z (*.f64 t 9) (*.f64 y x))))
31.9b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
5.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
37.0b
(/.f64 (-.f64 (pow.f64 (*.f64 x y) 3) (pow.f64 (*.f64 (*.f64 z 9) t) 3)) (*.f64 (*.f64 a 2) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (+.f64 (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t)) (*.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))))))
31.9b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
6.6b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
36.2b
(exp.f64 (log.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
5.8b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
Compiler

Compiled 2860 to 1633 computations (42.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
5.4b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series54.0ms (0.6%)

Counts
2 → 108
Calls

2 calls:

41.0ms
(*.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))

simplify107.0ms (1.1%)

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

prune85.0ms (0.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New84488
Fresh189
Picked011
Done011
Total851499
Error
5.3b
Counts
99 → 14
Alt Table
StatusErrorProgram
34.1b
(/.f64 (*.f64 y x) (*.f64 a 2))
33.7b
(/.f64 (/.f64 (fma.f64 y (*.f64 y (*.f64 x x)) (*.f64 (*.f64 (*.f64 t z) (*.f64 t z)) -81)) (fma.f64 z (*.f64 t 9) (*.f64 y x))) (*.f64 a 2))
31.9b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
34.8b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
6.6b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) a) (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
28.3b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z (*.f64 9 t)) (*.f64 z (*.f64 9 t)))) (*.f64 (*.f64 a 2) (fma.f64 z (*.f64 t 9) (*.f64 y x))))
36.2b
(exp.f64 (log.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
6.6b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))) (/.f64 (cbrt.f64 1/2) a))
6.6b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))
5.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
31.9b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
6.6b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
6.1b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
5.8b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
Compiler

Compiled 2325 to 1295 computations (44.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 y x (*.f64 (*.f64 t z) -9))
0.4b
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2))
0.5b
(/.f64 (sqrt.f64 1/2) a)
5.4b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))

series150.0ms (1.6%)

Counts
4 → 156
Calls

4 calls:

112.0ms
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
22.0ms
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2))
12.0ms
(fma.f64 y x (*.f64 (*.f64 t z) -9))
3.0ms
(/.f64 (sqrt.f64 1/2) a)

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt_binary64
36×times-frac_binary64
35×*-un-lft-identity_binary64
35×add-cube-cbrt_binary64
28×associate-*r*_binary64
Counts
4 → 119
Calls

4 calls:

7.0ms
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
4.0ms
(*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2))
3.0ms
(/.f64 (sqrt.f64 1/2) a)
0.0ms
(fma.f64 y x (*.f64 (*.f64 t z) -9))

simplify212.0ms (2.2%)

Algorithm
egg-herbie
Rules
683×fma-def_binary64
567×associate-/l*_binary64
434×associate-*l/_binary64
262×distribute-rgt-in_binary64
261×distribute-lft-in_binary64
Counts
275 → 178
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01634876
13904209
213664209
347404209
453014209

prune398.0ms (4.1%)

Pruning

16 alts after pruning (13 fresh and 3 done)

PrunedKeptTotal
New1744178
Fresh2911
Picked011
Done022
Total17616192
Error
5.0b
Counts
192 → 16
Alt Table
StatusErrorProgram
34.1b
(/.f64 (*.f64 y x) (*.f64 a 2))
33.7b
(/.f64 (/.f64 (fma.f64 y (*.f64 y (*.f64 x x)) (*.f64 (*.f64 (*.f64 t z) (*.f64 t z)) -81)) (fma.f64 z (*.f64 t 9) (*.f64 y x))) (*.f64 a 2))
5.5b
(neg.f64 (/.f64 (fma.f64 x (*.f64 y -1/2) (*.f64 (*.f64 t z) 9/2)) a))
34.8b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
34.5b
(/.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 y x)) a)
5.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
6.6b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)))) a) (/.f64 (cbrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
28.3b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 z (*.f64 9 t)) (*.f64 z (*.f64 9 t)))) (*.f64 (*.f64 a 2) (fma.f64 z (*.f64 t 9) (*.f64 y x))))
36.2b
(exp.f64 (log.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
6.6b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))) (/.f64 (cbrt.f64 1/2) a))
6.6b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))
31.9b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
31.9b
(*.f64 (/.f64 -9/2 a) (*.f64 t z))
32.3b
(*.f64 -9 (/.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 t z)) a))
6.1b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
5.8b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
Compiler

Compiled 4437 to 2832 computations (36.2% saved)

regimes3.0s (31.5%)

Accuracy

Total 0.4b remaining (5.5%)

Threshold costs 0.4b (5.5%)

Counts
109 → 1
Compiler

Compiled 36498 to 25172 computations (31% saved)

simplify7.0ms (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
01419
12319
22719
33019
43119
53119

end51.0ms (0.5%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 90 to 65 computations (27.8% saved)

sample2.5s (26.4%)

Algorithm
intervals
Results
888.0ms8000×body128valid
362.0ms3215×body128invalid
Compiler

Compiled 387 to 276 computations (28.7% saved)

Profiling

Loading profile data...