Details

Time bar (total: 7.1s)

analyze332.0ms (4.7%)

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)

sample131.0ms (1.9%)

Algorithm
intervals
Results
13.0ms96×body256valid
11.0ms289×pre128true
10.0ms160×body128valid
2.0ms33×body128nan
Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify359.0ms (5.1%)

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
43.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
43.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))
43.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 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 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
0.3b
(/.f64 1/3 a)
38.0b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)

series165.0ms (2.3%)

Counts
4 → 76
Calls

4 calls:

93.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
61.0ms
(-.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)

rewrite24.0ms (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:

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

simplify109.0ms (1.5%)

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

prune164.0ms (2.3%)

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
42.7b
(*.f64 (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)))) (neg.f64 b)) (/.f64 1/3 a))
43.0b
(*.f64 (+.f64 (fma.f64 (fabs.f64 (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)))) (neg.f64 b)) 0) (/.f64 1/3 a))
4.6b
(*.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))
43.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (exp.f64 (log.f64 (/.f64 1/3 a))))
43.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b) (expm1.f64 (log1p.f64 (/.f64 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))
4.2b
(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)))))))
43.2b
(*.f64 (-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))) b) (/.f64 1/3 a))
Compiler

Compiled 6109 to 3569 computations (41.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series14.0ms (0.2%)

Counts
2 → 48
Calls

2 calls:

9.0ms
(*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a))
5.0ms
(fma.f64 a (*.f64 c -3) 0)

rewrite10.0ms (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:

8.0ms
(*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a))
0.0ms
(fma.f64 a (*.f64 c -3) 0)

simplify98.0ms (1.4%)

Algorithm
egg-herbie
Rules
517×distribute-rgt-in_binary64
506×associate-/l/_binary64
492×associate-*l*_binary64
430×associate-/r/_binary64
383×associate-*r*_binary64
Counts
92 → 79
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0851049
1175901
2597847
32395797
44205797
54724797
65000797
74845797

prune148.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1306136
Fresh437
Picked101
Done000
Total1359144
Error
0.0b
Counts
144 → 9
Alt Table
StatusErrorProgram
0.3b
(/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
4.2b
(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)))))))
1.1b
(/.f64 (*.f64 (*.f64 (*.f64 -3 (*.f64 c a)) (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))) (/.f64 (cbrt.f64 1/3) a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
0.7b
(/.f64 (cbrt.f64 (*.f64 1/27 (*.f64 -27 (pow.f64 c 3)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
43.0b
(*.f64 (+.f64 (fma.f64 (fabs.f64 (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)))) (neg.f64 b)) 0) (/.f64 1/3 a))
0.6b
(/.f64 (*.f64 (*.f64 -3 (*.f64 c a)) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
4.6b
(*.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))
0.6b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))) b))
0.7b
(/.f64 (*.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b))) (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)))) (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b))))) b))
Compiler

Compiled 4329 to 2701 computations (37.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series315.0ms (4.5%)

Counts
3 → 64
Calls

3 calls:

258.0ms
(/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
51.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)
3.0ms
(/.f64 (*.f64 a (neg.f64 c)) a)

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
46×times-frac_binary64
43×*-un-lft-identity_binary64
25×add-sqr-sqrt_binary64
25×add-cube-cbrt_binary64
17×add-cbrt-cube_binary64
Counts
3 → 105
Calls

3 calls:

8.0ms
(/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
4.0ms
(/.f64 (*.f64 a (neg.f64 c)) a)
3.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)

simplify172.0ms (2.4%)

Algorithm
egg-herbie
Rules
546×fma-def_binary64
380×distribute-frac-neg_binary64
255×div-sub_binary64
198×associate-/l*_binary64
191×times-frac_binary64
Counts
169 → 206
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02544591
17043837
225923703
347473703
449753703
549983703
649253703

prune195.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2264230
Fresh448
Picked101
Done000
Total2318239
Error
0b
Counts
239 → 8
Alt Table
StatusErrorProgram
0.3b
(/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))) b))
0.6b
(/.f64 (*.f64 (*.f64 -3 (*.f64 c a)) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
4.2b
(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)))))))
1.1b
(/.f64 (*.f64 (*.f64 (*.f64 -3 (*.f64 c a)) (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))) (/.f64 (cbrt.f64 1/3) a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))))
0.4b
(*.f64 (/.f64 (/.f64 a 1) 1) (/.f64 (/.f64 (neg.f64 c) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))
0.3b
(/.f64 (/.f64 1 (/.f64 -1 c)) (+.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 1/3 a)) (+.f64 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b))) (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)))) (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b))))) b))
Compiler

Compiled 6847 to 3252 computations (52.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))) b)
0.2b
(fma.f64 c (*.f64 a -3) (*.f64 b b))
0.6b
(cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))
0.7b
(pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3)

series113.0ms (1.6%)

Counts
4 → 128
Calls

4 calls:

57.0ms
(+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))) b)
33.0ms
(pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3)
13.0ms
(fma.f64 c (*.f64 a -3) (*.f64 b b))
10.0ms
(cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))

rewrite19.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod_binary64
18×fma-def_binary64
17×*-un-lft-identity_binary64
15×sqrt-prod_binary64
15×add-sqr-sqrt_binary64
Counts
4 → 90
Calls

4 calls:

7.0ms
(+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))) b)
2.0ms
(pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3)
2.0ms
(cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))
0.0ms
(fma.f64 c (*.f64 a -3) (*.f64 b b))

simplify115.0ms (1.6%)

Algorithm
egg-herbie
Rules
452×fma-def_binary64
422×times-frac_binary64
278×unswap-sqr_binary64
247×associate-/l*_binary64
237×associate-/r*_binary64
Counts
218 → 153
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01584004
13923668
212543533
345073533
449643533

prune187.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1512153
Fresh257
Picked101
Done000
Total1547161
Error
0b
Counts
161 → 7
Alt Table
StatusErrorProgram
4.2b
(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 (*.f64 a (neg.f64 c)) a) (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))) b)) (sqrt.f64 (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3))) b))))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)) (/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))) (/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))))
0.3b
(/.f64 (/.f64 (*.f64 a (neg.f64 c)) a) (fma.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)) 3)))) b))
0.4b
(*.f64 (/.f64 (/.f64 a 1) 1) (/.f64 (/.f64 (neg.f64 c) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)))
0.3b
(/.f64 (/.f64 1 (/.f64 -1 c)) (+.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 1/3 a)) (+.f64 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b))) (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b)))) (cbrt.f64 (fma.f64 c (*.f64 a -3) (*.f64 b b))))) b))
Compiler

Compiled 4747 to 2359 computations (50.3% saved)

regimes2.7s (37.8%)

Accuracy

Total 0.1b remaining (89.4%)

Threshold costs 0.1b (89.4%)

Counts
314 → 1
Compiler

Compiled 47071 to 30926 computations (34.3% 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
01221
12021
22421
32721
42821
52821

end1.0ms (0%)

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.6s (23.1%)

Algorithm
intervals
Results
386.0ms2982×body256valid
333.0ms5015×body128valid
305.0ms8871×pre128true
57.0ms871×body128nan
1.0msbody512valid
Compiler

Compiled 339 to 217 computations (36% saved)

Profiling

Loading profile data...