Details

Time bar (total: 6.5s)

analyze326.0ms (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)

sample135.0ms (2.1%)

Algorithm
intervals
Results
15.0ms126×body256valid
10.0ms288×pre128true
7.0ms40×body512valid
7.0ms90×body128valid
2.0ms32×body128nan
Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify265.0ms (4.1%)

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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
52.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
52.9b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
52.9b
(*.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
0.1b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
0.1b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
29.6b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

series186.0ms (2.9%)

Counts
4 → 96
Calls

4 calls:

82.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
52.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
41.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
11.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite24.0ms (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:

8.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
7.0ms
(-.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))

simplify188.0ms (2.9%)

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

prune148.0ms (2.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2215226
Fresh101
Picked101
Done000
Total2235228
Error
0.0b
Counts
228 → 5
Alt Table
StatusErrorProgram
1.6b
(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))))))
1.9b
(*.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))
52.2b
(*.f64 (+.f64 (fma.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (neg.f64 b)) 0) (/.f64 1/2 a))
52.9b
(*.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (sqrt.f64 a))) (/.f64 (cbrt.f64 1/2) (sqrt.f64 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 6255 to 3656 computations (41.6% saved)

localize15.0ms (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
(/.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))
0.1b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.3b
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

series307.0ms (4.7%)

Counts
3 → 64
Calls

3 calls:

255.0ms
(/.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))
48.0ms
(+.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 (0.5%)

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)

simplify124.0ms (1.9%)

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

prune202.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2143217
Fresh224
Picked101
Done000
Total2175222
Error
0.0b
Counts
222 → 5
Alt Table
StatusErrorProgram
1.6b
(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))))))
1.9b
(*.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 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))))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.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)))
Compiler

Compiled 7274 to 4600 computations (36.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series326.0ms (5%)

Counts
2 → 72
Calls

2 calls:

226.0ms
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b))
99.0ms
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b)

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
associate-/l/_binary64
cbrt-undiv_binary64
div-exp_binary64
Counts
2 → 40
Calls

2 calls:

9.0ms
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b))
0.0ms
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b)

simplify159.0ms (2.5%)

Algorithm
egg-herbie
Rules
819×fma-def_binary64
640×times-frac_binary64
542×associate-/l*_binary64
173×*-commutative_binary64
163×fma-neg_binary64
Counts
112 → 177
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04937145
117296562
246746519
351736519

prune355.0ms (5.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2793282
Fresh314
Picked011
Done000
Total2825287
Error
0.0b
Counts
287 → 5
Alt Table
StatusErrorProgram
1.9b
(*.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 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 (*.f64 (*.f64 c a) -4) (/.f64 1/2 a))))
0.4b
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) 1/2) (*.f64 (-.f64 (*.f64 c (*.f64 a -4)) 0) a)) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b))
1.6b
(-.f64 (*.f64 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b))
Compiler

Compiled 15023 to 10188 computations (32.2% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series31.0ms (0.5%)

Counts
3 → 72
Calls

3 calls:

17.0ms
(*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4)))
10.0ms
(*.f64 (-.f64 (*.f64 c (*.f64 a -4)) 0) a)
4.0ms
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) 1/2) (*.f64 (-.f64 (*.f64 c (*.f64 a -4)) 0) a))

rewrite42.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
119×pow1_binary64
67×pow-prod-down_binary64
53×add-cbrt-cube_binary64
53×add-exp-log_binary64
32×cbrt-unprod_binary64
Counts
3 → 111
Calls

3 calls:

17.0ms
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) 1/2) (*.f64 (-.f64 (*.f64 c (*.f64 a -4)) 0) a))
8.0ms
(*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4)))
6.0ms
(*.f64 (-.f64 (*.f64 c (*.f64 a -4)) 0) a)

simplify108.0ms (1.7%)

Algorithm
egg-herbie
Rules
795×fma-def_binary64
662×fma-neg_binary64
340×associate-*l*_binary64
329×times-frac_binary64
322×distribute-rgt-in_binary64
Counts
183 → 132
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01552677
13982109
224561835
344971835
448451835

prune276.0ms (4.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1980198
Fresh033
Picked011
Done011
Total1985203
Error
0.0b
Counts
203 → 5
Alt Table
StatusErrorProgram
1.9b
(*.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 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 (*.f64 (*.f64 c a) -4) (/.f64 1/2 a))))
0.4b
(/.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) 1/2) (*.f64 (-.f64 (*.f64 c (*.f64 a -4)) 0) a)) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b))
1.6b
(-.f64 (*.f64 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b))
Compiler

Compiled 12050 to 8028 computations (33.4% saved)

regimes1.4s (21.4%)

Accuracy

Total 0.1b remaining (71.4%)

Threshold costs 0.1b (71.4%)

Counts
267 → 1
Compiler

Compiled 38208 to 25650 computations (32.9% saved)

simplify2.0ms (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)

sample1.8s (27.3%)

Algorithm
intervals
Results
467.0ms3735×body256valid
308.0ms8846×pre128true
275.0ms1476×body512valid
181.0ms2789×body128valid
53.0ms846×body128nan
Compiler

Compiled 279 to 197 computations (29.4% saved)

Profiling

Loading profile data...