Details

Time bar (total: 8.0s)

analyze414.0ms (5.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14
Compiler

Compiled 43 to 31 computations (27.9% saved)

sample1.6s (19.4%)

Results
1.2s7945×body128valid
143.0ms1016×body128invalid
93.0ms311×body256valid
Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify355.0ms (4.4%)

Algorithm
egg-herbie
Rules
1968×fma-neg_binary64
1363×fma-def_binary64
898×div-sub_binary64
743×associate-/l*_binary64
567×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01326
13022
26422
313522
420122
533522
655422
792922
8147722
9211522
10259922
11255422
12260222
13267122
14311722
15232722
16237522
17238322
18238922
19239522
20239722
21239722
22258522
23268522
24261922
25263122
26266122
27267722
28270722
29270722
30275122
31285122
32282722
33282722
34263822

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
28.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
28.3b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
28.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
Compiler

Compiled 111 to 74 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 a (*.f64 c -3) (*.f64 b b))
0.3b
(/.f64 1/3 a)
0.4b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
28.2b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)

series153.0ms (1.9%)

Counts
4 → 76
Calls

4 calls:

89.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
53.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
10.0ms
(fma.f64 a (*.f64 c -3) (*.f64 b b))
2.0ms
(/.f64 1/3 a)

rewrite43.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt_binary64
39×*-un-lft-identity_binary64
35×add-cube-cbrt_binary64
19×times-frac_binary64
18×prod-diff_binary64
Counts
4 → 123
Calls

4 calls:

8.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
4.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
2.0ms
(/.f64 1/3 a)
0.0ms
(fma.f64 a (*.f64 c -3) (*.f64 b b))

simplify113.0ms (1.4%)

Algorithm
egg-herbie
Rules
797×fma-def_binary64
340×distribute-rgt-in_binary64
235×cancel-sign-sub-inv_binary64
185×fma-neg_binary64
160×associate-*r*_binary64
Counts
199 → 221
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02835008
16614039
224643848
349113848

prune160.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2138221
Fresh101
Picked101
Done000
Total2158223
Error
0.1b
Counts
223 → 8
Alt Table
StatusErrorProgram
28.4b
(*.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (*.f64 b b)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (/.f64 1/3 a))
28.3b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (*.f64 1/3 (/.f64 1 a)))
5.9b
(neg.f64 (fma.f64 9/16 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (*.f64 3/8 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3)))))))
28.3b
(*.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (*.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/3 a)))) (cbrt.f64 (/.f64 1/3 a)))
28.3b
(/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) 1/3) a)
0.6b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
6.2b
(*.f64 (-.f64 (*.f64 -3/2 (/.f64 (*.f64 c a) b)) (fma.f64 9/8 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (*.f64 405/128 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (/.f64 1/3 a))
8.0b
(*.f64 (fma.f64 -3/2 (/.f64 (*.f64 c a) b) (fma.f64 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)) -9/8 (*.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16))) (/.f64 1/3 a))
Compiler

Compiled 6161 to 3595 computations (41.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
0.3b
(*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a))
0.3b
(fma.f64 a (*.f64 c -3) 0)
0.3b
(/.f64 1/3 a)

series328.0ms (4.1%)

Counts
3 → 68
Calls

3 calls:

311.0ms
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
11.0ms
(*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a))
5.0ms
(fma.f64 a (*.f64 c -3) 0)

rewrite24.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
17×*-un-lft-identity_binary64
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
14×times-frac_binary64
Counts
3 → 74
Calls

3 calls:

14.0ms
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
5.0ms
(*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a))
0.0ms
(fma.f64 a (*.f64 c -3) 0)

simplify98.0ms (1.2%)

Algorithm
egg-herbie
Rules
561×associate-/l/_binary64
487×div-sub_binary64
483×fma-def_binary64
201×distribute-rgt-in_binary64
155×associate-/l*_binary64
Counts
142 → 149
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02023063
15292602
219782548
342892542
456312542

prune181.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1757182
Fresh617
Picked101
Done000
Total1828190
Error
0.0b
Counts
190 → 8
Alt Table
StatusErrorProgram
1.4b
(*.f64 (/.f64 (fma.f64 a (*.f64 c -3) 0) (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))) (/.f64 (/.f64 1/3 a) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))))
5.9b
(fma.f64 (/.f64 (*.f64 (pow.f64 c 3) (*.f64 a a)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b)))))
1.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (cbrt.f64 (/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))) (cbrt.f64 (/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))))
0.3b
(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
0.8b
(/.f64 (/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))
0.6b
(/.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a)))
0.6b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) 1/3) (*.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) a))
8.0b
(*.f64 (fma.f64 -3/2 (/.f64 (*.f64 c a) b) (fma.f64 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)) -9/8 (*.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16))) (/.f64 1/3 a))
Compiler

Compiled 6033 to 3669 computations (39.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))
0.2b
(fma.f64 a (*.f64 c -3) (*.f64 b b))
0.2b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
0.2b
(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))

series335.0ms (4.2%)

Counts
3 → 60
Calls

3 calls:

243.0ms
(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
50.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
42.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity_binary64
40×times-frac_binary64
33×add-sqr-sqrt_binary64
32×add-cube-cbrt_binary64
15×distribute-lft-neg-in_binary64
Counts
3 → 107
Calls

3 calls:

6.0ms
(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
3.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
1.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))

simplify159.0ms (2%)

Algorithm
egg-herbie
Rules
473×fma-def_binary64
278×div-sub_binary64
247×associate-/l/_binary64
187×cancel-sign-sub-inv_binary64
166×distribute-rgt-neg-out_binary64
Counts
167 → 223
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02534899
16384739
220584559
345284553
449834553
549034553

prune194.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2443247
Fresh437
Picked101
Done000
Total2496255
Error
0b
Counts
255 → 6
Alt Table
StatusErrorProgram
0.6b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) 1/3) (*.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) a))
0.9b
(/.f64 (neg.f64 c) (fma.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b))
5.9b
(fma.f64 (/.f64 (*.f64 (pow.f64 c 3) (*.f64 a a)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b)))))
0.4b
(*.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))
0.6b
(/.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a)))
0.3b
(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b))
Compiler

Compiled 6510 to 3527 computations (45.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))
0.2b
(fma.f64 a (*.f64 c -3) (*.f64 b b))
0.2b
(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b))
0.3b
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b)

series376.0ms (4.7%)

Counts
3 → 108
Calls

3 calls:

221.0ms
(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b))
101.0ms
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b)
53.0ms
(sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))

rewrite14.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
30×times-frac_binary64
30×add-sqr-sqrt_binary64
28×*-un-lft-identity_binary64
28×add-cube-cbrt_binary64
12×distribute-lft-neg-in_binary64
Counts
3 → 90
Calls

3 calls:

3.0ms
(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b))
1.0ms
(sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))
0.0ms
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b)

simplify198.0ms (2.5%)

Algorithm
egg-herbie
Rules
830×times-frac_binary64
291×fma-def_binary64
207×*-commutative_binary64
133×distribute-neg-in_binary64
131×sub-neg_binary64
Counts
198 → 304
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
067510375
1215910029
2497910029
3500010029

prune468.0ms (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New4271428
Fresh145
Picked011
Done000
Total4286434
Error
0b
Counts
434 → 6
Alt Table
StatusErrorProgram
0.5b
(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))))) b))
5.9b
(fma.f64 (/.f64 (*.f64 (pow.f64 c 3) (*.f64 a a)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b)))))
0.4b
(*.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))
0.6b
(/.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a)))
0.3b
(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b))
0.6b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) 1/3) (*.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) a))
Compiler

Compiled 20472 to 12886 computations (37.1% saved)

regimes2.6s (32.9%)

Accuracy

Total 0.2b remaining (86.7%)

Threshold costs 0.2b (86.7%)

Counts
322 → 1
Compiler

Compiled 47817 to 31168 computations (34.8% saved)

simplify3.0ms (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
01421
12421
22821
33121
43221
53121

end133.0ms (1.7%)

Compiler

Compiled 217 to 143 computations (34.1% saved)

Profiling

Loading profile data...