Details

Time bar (total: 9.6s)

analyze426.0ms (4.5%)

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)

sample54.0ms (0.6%)

Algorithm
intervals
Results
15.0ms127×body256valid
10.0ms278×pre128true
8.0ms47×body512valid
5.0ms82×body128valid
1.0ms22×body128nan
Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify263.0ms (2.7%)

Algorithm
egg-herbie
Rules
1743×fma-neg_binary64
1393×fma-def_binary64
800×div-sub_binary64
619×times-frac_binary64
473×associate-/r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13322
26722
313822
420422
533822
655822
792422
8138822
9160422
10237522
11274222
12253322
13262122
14317122
15331322
16387322
17367922
18402922
19431722
20448522
21456122
22480522
23479322
24479722
25479722
26494822

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
54.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
54.0b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
54.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
0.0b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
27.6b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

series186.0ms (1.9%)

Counts
4 → 96
Calls

4 calls:

81.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
51.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
42.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
11.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64
32×*-un-lft-identity_binary64
28×add-cube-cbrt_binary64
18×prod-diff_binary64
17×sqrt-prod_binary64
Counts
4 → 109
Calls

4 calls:

8.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
1.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
0.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

simplify195.0ms (2%)

Algorithm
egg-herbie
Rules
527×fma-neg_binary64
338×distribute-rgt-in_binary64
273×cancel-sign-sub-inv_binary64
155×associate-*l*_binary64
153×associate-*r*_binary64
Counts
205 → 226
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02675424
16734468
225244293
345504293
449914293
549944293
648844293

prune143.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2224226
Fresh101
Picked101
Done000
Total2244228
Error
0.0b
Counts
228 → 4
Alt Table
StatusErrorProgram
1.7b
(*.f64 (neg.f64 (+.f64 (*.f64 2 (/.f64 (*.f64 c a) b)) (+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (*.f64 10 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (*.f64 4 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/2 a))
0.3b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
54.0b
(*.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (*.f64 b b)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) (/.f64 1/2 a))
1.4b
(neg.f64 (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))))
Compiler

Compiled 6217 to 3618 computations (41.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
0.0b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
0.0b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.3b
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

series283.0ms (3%)

Counts
2 → 44
Calls

2 calls:

280.0ms
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
3.0ms
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

rewrite25.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
14×times-frac_binary64
Counts
2 → 72
Calls

2 calls:

11.0ms
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
9.0ms
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

simplify99.0ms (1%)

Algorithm
egg-herbie
Rules
618×fma-neg_binary64
365×distribute-rgt-in_binary64
288×distribute-lft-in_binary64
237×associate-*l*_binary64
199×associate-*r*_binary64
Counts
116 → 146
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02092891
15772397
226732333
345512333
449042333

prune204.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2054209
Fresh123
Picked101
Done000
Total2076213
Error
0b
Counts
213 → 6
Alt Table
StatusErrorProgram
0.4b
(*.f64 (/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) 1) (/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
0.7b
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1 (sqrt.f64 a))) (/.f64 1/2 (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
1.7b
(*.f64 (neg.f64 (+.f64 (*.f64 2 (/.f64 (*.f64 c a) b)) (+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (*.f64 10 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (*.f64 4 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/2 a))
0.5b
(/.f64 (/.f64 (*.f64 (/.f64 1/2 a) (*.f64 (pow.f64 (*.f64 c a) 3) -64)) (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
1.4b
(neg.f64 (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))))
0.7b
(/.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (+.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (*.f64 c (*.f64 a -4)) 0)) (/.f64 (*.f64 (*.f64 1/2 1/2) 1/2) (*.f64 (*.f64 a a) a)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
Compiler

Compiled 7094 to 4507 computations (36.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
0.0b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.3b
(/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
0.3b
(*.f64 (/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) 1) (/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))

series511.0ms (5.3%)

Counts
2 → 40
Calls

2 calls:

259.0ms
(*.f64 (/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) 1) (/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
251.0ms
(/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

rewrite68.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
209×times-frac_binary64
157×*-un-lft-identity_binary64
130×add-sqr-sqrt_binary64
100×add-cube-cbrt_binary64
58×associate-*r*_binary64
Counts
2 → 197
Calls

2 calls:

25.0ms
(*.f64 (/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) 1) (/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
9.0ms
(/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

simplify261.0ms (2.7%)

Algorithm
egg-herbie
Rules
345×associate-*l*_binary64
326×associate-*r*_binary64
299×associate-/l*_binary64
280×associate-*l/_binary64
257×*-commutative_binary64
Counts
237 → 345
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03679096
19878324
241498076
346018076
449778076
548308076

prune434.0ms (4.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New4080408
Fresh055
Picked011
Done000
Total4086414
Error
0b
Counts
414 → 6
Alt Table
StatusErrorProgram
0.4b
(*.f64 (/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) 1) (/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
0.7b
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1 (sqrt.f64 a))) (/.f64 1/2 (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
1.7b
(*.f64 (neg.f64 (+.f64 (*.f64 2 (/.f64 (*.f64 c a) b)) (+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (*.f64 10 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (*.f64 4 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/2 a))
0.5b
(/.f64 (/.f64 (*.f64 (/.f64 1/2 a) (*.f64 (pow.f64 (*.f64 c a) 3) -64)) (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
1.4b
(neg.f64 (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))))
0.7b
(/.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (+.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (*.f64 c (*.f64 a -4)) 0)) (/.f64 (*.f64 (*.f64 1/2 1/2) 1/2) (*.f64 (*.f64 a a) a)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
Compiler

Compiled 16302 to 10678 computations (34.5% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (*.f64 (/.f64 1/2 a) (*.f64 (pow.f64 (*.f64 c a) 3) -64)) (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0))))
0.3b
(*.f64 (/.f64 1/2 a) (*.f64 (pow.f64 (*.f64 c a) 3) -64))
0.5b
(*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4)))
0.7b
(pow.f64 (*.f64 c a) 3)

series54.0ms (0.6%)

Counts
4 → 96
Calls

4 calls:

20.0ms
(*.f64 (/.f64 1/2 a) (*.f64 (pow.f64 (*.f64 c a) 3) -64))
16.0ms
(*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4)))
14.0ms
(pow.f64 (*.f64 c a) 3)
4.0ms
(/.f64 (*.f64 (/.f64 1/2 a) (*.f64 (pow.f64 (*.f64 c a) 3) -64)) (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0))))

rewrite56.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
123×pow1_binary64
121×add-exp-log_binary64
73×add-cbrt-cube_binary64
68×prod-exp_binary64
68×pow-prod-down_binary64
Counts
4 → 164
Calls

4 calls:

18.0ms
(/.f64 (*.f64 (/.f64 1/2 a) (*.f64 (pow.f64 (*.f64 c a) 3) -64)) (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0))))
9.0ms
(*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4)))
6.0ms
(*.f64 (/.f64 1/2 a) (*.f64 (pow.f64 (*.f64 c a) 3) -64))
3.0ms
(pow.f64 (*.f64 c a) 3)

simplify134.0ms (1.4%)

Algorithm
egg-herbie
Rules
505×log-prod_binary64
494×associate-*r*_binary64
406×associate-*l*_binary64
244×fma-def_binary64
229×unswap-sqr_binary64
Counts
260 → 192
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02334312
15763138
228443057
346733057
452213057

prune270.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1920192
Fresh044
Picked011
Done011
Total1926198
Error
0b
Counts
198 → 6
Alt Table
StatusErrorProgram
0.4b
(*.f64 (/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) 1) (/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
0.7b
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1 (sqrt.f64 a))) (/.f64 1/2 (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
1.7b
(*.f64 (neg.f64 (+.f64 (*.f64 2 (/.f64 (*.f64 c a) b)) (+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (*.f64 10 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (*.f64 4 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/2 a))
0.5b
(/.f64 (/.f64 (*.f64 (/.f64 1/2 a) (*.f64 (pow.f64 (*.f64 c a) 3) -64)) (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
1.4b
(neg.f64 (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))))
0.7b
(/.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (+.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (*.f64 c (*.f64 a -4)) 0)) (/.f64 (*.f64 (*.f64 1/2 1/2) 1/2) (*.f64 (*.f64 a a) a)))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
Compiler

Compiled 10912 to 7246 computations (33.6% saved)

regimes2.3s (24%)

Accuracy

Total 0.1b remaining (79.8%)

Threshold costs 0.1b (79.8%)

Counts
274 → 1
Compiler

Compiled 40764 to 28298 computations (30.6% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01322
11622
21622

end1.0ms (0%)

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample3.5s (36.8%)

Algorithm
intervals
Results
955.0ms3797×body256valid
572.0ms8846×pre128true
532.0ms1452×body512valid
356.0ms2751×body128valid
104.0ms846×body128nan
Compiler

Compiled 325 to 235 computations (27.7% saved)

Profiling

Loading profile data...