Details

Time bar (total: 12.5s)

analyze906.0ms (7.3%)

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)

sample212.0ms (1.7%)

Algorithm
intervals
Results
30.0ms117×body256valid
18.0ms284×pre128true
18.0ms51×body512valid
11.0ms88×body128valid
3.0ms28×body128nan
Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify281.0ms (2.2%)

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

prune8.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
52.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
52.3b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
52.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
Compiler

Compiled 111 to 74 computations (33.3% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
0.1b
(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))
25.6b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

series396.0ms (3.2%)

Counts
4 → 96
Calls

4 calls:

161.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
133.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
82.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
20.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite44.0ms (0.4%)

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:

17.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
9.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
2.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))
2.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

simplify379.0ms (3%)

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

prune282.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2215226
Fresh101
Picked011
Done000
Total2226228
Error
0.0b
Counts
228 → 6
Alt Table
StatusErrorProgram
52.3b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
1.6b
(*.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))
1.3b
(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))))))
52.3b
(*.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
52.3b
(*.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
0.4b
(/.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))
Compiler

Compiled 6257 to 3656 computations (41.6% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
0.1b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.1b
(/.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))
0.4b
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

series322.0ms (2.6%)

Counts
3 → 64
Calls

3 calls:

269.0ms
(/.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))
49.0ms
(+.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))

rewrite31.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
15×add-cube-cbrt_binary64
Counts
3 → 92
Calls

3 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))
3.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

simplify115.0ms (0.9%)

Algorithm
egg-herbie
Rules
616×fma-neg_binary64
248×associate-*l*_binary64
225×associate-/l*_binary64
220×associate-*r*_binary64
176×div-sub_binary64
Counts
156 → 198
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02503787
17083244
231323157
346133157
449323157

prune206.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2134217
Fresh224
Picked101
Done101
Total2176223
Error
0b
Counts
223 → 6
Alt Table
StatusErrorProgram
0.5b
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))))
1.3b
(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))))))
0.6b
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 c (*.f64 a -4)) 3) (pow.f64 0 3)) 1/2) (*.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0))) a)))
52.3b
(*.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
0.4b
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
0.7b
(cbrt.f64 (*.f64 (*.f64 (/.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)) (/.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))) (/.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))))
Compiler

Compiled 7378 to 4660 computations (36.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
0.3b
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) (-.f64 (*.f64 c (*.f64 a -4)) 0))
0.3b
(*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a))
0.5b
(*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4)))

series407.0ms (3.3%)

Counts
4 → 92
Calls

4 calls:

354.0ms
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
36.0ms
(*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4)))
11.0ms
(*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a))
5.0ms
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) (-.f64 (*.f64 c (*.f64 a -4)) 0))

rewrite148.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
120×pow1_binary64
68×add-cbrt-cube_binary64
68×add-exp-log_binary64
67×pow-prod-down_binary64
64×times-frac_binary64
Counts
4 → 205
Calls

4 calls:

36.0ms
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
28.0ms
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) (-.f64 (*.f64 c (*.f64 a -4)) 0))
24.0ms
(*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a))
14.0ms
(*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4)))

simplify312.0ms (2.5%)

Algorithm
egg-herbie
Rules
453×associate-*l*_binary64
435×times-frac_binary64
426×fma-neg_binary64
380×associate-/l*_binary64
245×associate-/l/_binary64
Counts
297 → 315
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03628697
19257788
244597685
350287685

prune883.0ms (7.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3141315
Fresh235
Picked011
Done000
Total3165321
Error
0b
Counts
321 → 5
Alt Table
StatusErrorProgram
0.6b
(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) 1) (/.f64 (/.f64 1 (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
0.6b
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 c (*.f64 a -4)) 3) (pow.f64 0 3)) 1/2) (*.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0))) a)))
1.3b
(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))))))
52.3b
(*.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
0.4b
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
Compiler

Compiled 16226 to 10494 computations (35.3% saved)

localize46.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (-.f64 (*.f64 c (*.f64 a -4)) 0))
0.3b
(*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a))
0.3b
(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) 1) (/.f64 (/.f64 1 (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
0.5b
(*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4)))

series472.0ms (3.8%)

Counts
2 → 44
Calls

2 calls:

455.0ms
(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) 1) (/.f64 (/.f64 1 (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
17.0ms
(/.f64 1 (-.f64 (*.f64 c (*.f64 a -4)) 0))

rewrite154.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
156×add-exp-log_binary64
113×times-frac_binary64
87×*-un-lft-identity_binary64
84×div-exp_binary64
68×add-sqr-sqrt_binary64
Counts
2 → 173
Calls

2 calls:

60.0ms
(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) 1) (/.f64 (/.f64 1 (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
10.0ms
(/.f64 1 (-.f64 (*.f64 c (*.f64 a -4)) 0))

simplify381.0ms (3%)

Algorithm
egg-herbie
Rules
767×fma-def_binary64
352×associate-*l*_binary64
311×associate-*r*_binary64
262×associate-*l/_binary64
230×associate-/l*_binary64
Counts
217 → 259
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02749815
17377918
233677771
348397771
449847771

prune1.0s (8.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New3762378
Fresh213
Picked101
Done011
Total3794383
Error
0b
Counts
383 → 4
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 (*.f64 8 (*.f64 (*.f64 c c) a)) 1) (/.f64 (/.f64 1 (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
1.3b
(-.f64 (*.f64 (/.f64 (*.f64 (pow.f64 c 3) (*.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
0.6b
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 c (*.f64 a -4)) 3) (pow.f64 0 3)) 1/2) (*.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0))) a)))
0.4b
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) (-.f64 (*.f64 c (*.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
Compiler

Compiled 21273 to 14432 computations (32.2% saved)

regimes2.8s (22.7%)

Accuracy

Total 0.1b remaining (73.1%)

Threshold costs 0.1b (73.1%)

Counts
280 → 1
Compiler

Compiled 43732 to 30594 computations (30% saved)

simplify3.0ms (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)

sample2.6s (20.7%)

Algorithm
intervals
Results
689.0ms3778×body256valid
452.0ms8867×pre128true
417.0ms1486×body512valid
274.0ms2736×body128valid
83.0ms867×body128nan
Compiler

Compiled 236 to 169 computations (28.4% saved)

Profiling

Loading profile data...