Details

Time bar (total: 9.6s)

analyze783.0ms (8.1%)

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 33 to 24 computations (27.3% saved)

sample48.0ms (0.5%)

Algorithm
intervals
Results
12.0ms169×body128valid
11.0ms87×body256valid
9.0ms283×pre128true
2.0ms27×body128nan
Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify367.0ms (3.8%)

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%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
43.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
43.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
43.9b
(/.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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 a (*.f64 c -3) (*.f64 b b))
0.3b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
0.3b
(/.f64 1/3 a)
38.6b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)

rewrite25.0ms (0.3%)

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:

10.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
5.0ms
(-.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))

series216.0ms (2.2%)

Counts
4 → 76
Calls

4 calls:

90.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
83.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
36.0ms
(fma.f64 a (*.f64 c -3) (*.f64 b b))
5.0ms
(/.f64 1/3 a)

simplify129.0ms (1.3%)

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 → 357
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02835008
16614039
224643848
349113848

prune166.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New3525357
Fresh101
Picked101
Done000
Total3545359
Error
0.1b
Counts
359 → 5
Alt Table
StatusErrorProgram
43.9b
(*.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)) (sqrt.f64 a))) (/.f64 (cbrt.f64 1/3) (sqrt.f64 a)))
3.0b
(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)))))))
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))
3.4b
(*.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))
4.6b
(*.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 5989 to 3489 computations (41.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.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)

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
15×*-un-lft-identity_binary64
13×associate-*r*_binary64
13×add-cube-cbrt_binary64
10×times-frac_binary64
Counts
3 → 64
Calls

3 calls:

5.0ms
(*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a))
3.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
0.0ms
(fma.f64 a (*.f64 c -3) 0)

series127.0ms (1.3%)

Counts
3 → 68
Calls

3 calls:

52.0ms
(*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a))
48.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
27.0ms
(fma.f64 a (*.f64 c -3) 0)

simplify90.0ms (0.9%)

Algorithm
egg-herbie
Rules
623×times-frac_binary64
538×associate-/l*_binary64
487×fma-def_binary64
394×associate-/r*_binary64
151×distribute-rgt-in_binary64
Counts
132 → 222
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01651963
14141772
213261748
348831748
449611748

prune212.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2527259
Fresh224
Picked101
Done000
Total2559264
Error
0.0b
Counts
264 → 9
Alt Table
StatusErrorProgram
3.1b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (-.f64 (*.f64 2 b) (fma.f64 3/2 (/.f64 (*.f64 c a) b) (fma.f64 9/8 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)) (*.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))))
3.0b
(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)))))))
1.3b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (*.f64 (*.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/3 a))) (cbrt.f64 (/.f64 1/3 a)))) (+.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))
3.4b
(*.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))
0.7b
(/.f64 (*.f64 (/.f64 (*.f64 -3 (*.f64 c a)) (sqrt.f64 a)) (/.f64 1/3 (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
0.8b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (cbrt.f64 (*.f64 (*.f64 (/.f64 1/3 a) (/.f64 1/3 a)) (/.f64 1/3 a)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
0.6b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (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))
0.7b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (*.f64 (sqrt.f64 (/.f64 1/3 a)) (sqrt.f64 (/.f64 1/3 a)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
Compiler

Compiled 5435 to 3376 computations (37.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity_binary64
40×times-frac_binary64
30×add-sqr-sqrt_binary64
29×add-cube-cbrt_binary64
15×distribute-lft-neg-in_binary64
Counts
2 → 87
Calls

2 calls:

8.0ms
(/.f64 (neg.f64 c) (+.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)))

series275.0ms (2.9%)

Counts
2 → 40
Calls

2 calls:

233.0ms
(/.f64 (neg.f64 c) (+.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)))

simplify141.0ms (1.5%)

Algorithm
egg-herbie
Rules
349×fma-def_binary64
320×associate-/r/_binary64
306×div-sub_binary64
243×associate-/l/_binary64
221×fma-neg_binary64
Counts
127 → 241
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02283973
15663858
218783711
346163705
451063705

prune223.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3926398
Fresh628
Picked101
Done000
Total3998407
Error
0b
Counts
407 → 8
Alt Table
StatusErrorProgram
2.8b
(/.f64 (neg.f64 c) (-.f64 (*.f64 2 b) (fma.f64 3/2 (/.f64 (*.f64 c a) b) (fma.f64 9/8 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)) (*.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))))
0.4b
(*.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))
3.0b
(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 (*.f64 c c) a) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c 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))
0.6b
(*.f64 (/.f64 -1 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (/.f64 c (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))))
1.3b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (*.f64 (*.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/3 a))) (cbrt.f64 (/.f64 1/3 a)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
0.6b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (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 6716 to 3639 computations (45.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
30×times-frac_binary64
25×*-un-lft-identity_binary64
25×add-sqr-sqrt_binary64
25×add-cube-cbrt_binary64
12×distribute-lft-neg-in_binary64
Counts
2 → 69
Calls

2 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))
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)

series350.0ms (3.6%)

Counts
2 → 72
Calls

2 calls:

251.0ms
(/.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))
99.0ms
(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)

simplify150.0ms (1.6%)

Algorithm
egg-herbie
Rules
680×times-frac_binary64
509×associate-/l*_binary64
206×fma-def_binary64
154×*-commutative_binary64
101×unswap-sqr_binary64
Counts
141 → 267
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05138031
116517737
249907737

prune336.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New8061807
Fresh257
Picked011
Done000
Total8087815
Error
0b
Counts
815 → 7
Alt Table
StatusErrorProgram
3.0b
(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 (*.f64 c c) a) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c 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))
0.6b
(*.f64 (/.f64 -1 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (/.f64 c (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))))
1.3b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (*.f64 (*.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/3 a))) (cbrt.f64 (/.f64 1/3 a)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
0.6b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (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))
2.8b
(/.f64 (neg.f64 c) (-.f64 (*.f64 2 b) (fma.f64 3/2 (/.f64 (*.f64 c a) b) (fma.f64 9/8 (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)) (*.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))))
0.6b
(*.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 (neg.f64 (sqrt.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 13016 to 8252 computations (36.6% saved)

regimes3.0s (30.9%)

Accuracy

Total 0.1b remaining (85.7%)

Threshold costs 0.1b (85.7%)

Compiler

Compiled 48118 to 31791 computations (33.9% 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
01323
12323
22723
33023
43123
53123

end1.0ms (0%)

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample2.9s (30.3%)

Algorithm
intervals
Results
706.0ms2873×body256valid
650.0ms5123×body128valid
514.0ms8888×pre128true
103.0ms888×body128nan
1.0msbody512valid
Compiler

Compiled 308 to 206 computations (33.1% saved)

Profiling

Loading profile data...