Details

Time bar (total: 7.4s)

analyze361.0ms (4.9%)

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)

sample2.6s (35%)

Results
1.1s3906×body256valid
811.0ms1499×body512valid
438.0ms2851×body128valid
123.0ms832×body128invalid
Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify256.0ms (3.4%)

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 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
52.9b
(/.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)

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)))
0.1b
(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))
24.9b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

series209.0ms (2.8%)

Counts
4 → 96
Calls

4 calls:

85.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
71.0ms
(-.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)))
10.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite24.0ms (0.3%)

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))

simplify187.0ms (2.5%)

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

prune152.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2206226
Fresh101
Picked101
Done000
Total2226228
Error
0.0b
Counts
228 → 6
Alt Table
StatusErrorProgram
2.3b
(*.f64 (fma.f64 -2 (+.f64 (/.f64 (*.f64 c a) b) (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))) (*.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -4)) (/.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)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
1.5b
(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))))))
53.2b
(*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 b)) (*.f64 (-.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 b)) (/.f64 1/2 a)))
52.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))) (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) (/.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))
Compiler

Compiled 6319 to 3674 computations (41.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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))
0.1b
(+.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))

series328.0ms (4.4%)

Counts
3 → 64
Calls

3 calls:

271.0ms
(/.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))
53.0ms
(+.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))

rewrite30.0ms (0.4%)

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:

12.0ms
(/.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))
8.0ms
(*.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)

simplify112.0ms (1.5%)

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 → 196
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02503787
17083244
231323157
346133157
449323157

prune203.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2114215
Fresh325
Picked101
Done000
Total2156221
Error
0b
Counts
221 → 6
Alt Table
StatusErrorProgram
1.4b
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
2.3b
(*.f64 (fma.f64 -2 (+.f64 (/.f64 (*.f64 c a) b) (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))) (*.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -4)) (/.f64 1/2 a))
0.6b
(*.f64 (/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))) (/.f64 (/.f64 1/2 a) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3))) b))
0.3b
(/.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))
1.5b
(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 7252 to 4566 computations (37% saved)

localize27.0ms (0.4%)

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))

series333.0ms (4.5%)

Counts
2 → 72
Calls

2 calls:

229.0ms
(/.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))
104.0ms
(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)

rewrite14.0ms (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:

10.0ms
(/.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)

simplify141.0ms (1.9%)

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

prune368.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2802282
Fresh235
Picked011
Done000
Total2826288
Error
0b
Counts
288 → 6
Alt Table
StatusErrorProgram
1.4b
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
2.3b
(*.f64 (fma.f64 -2 (+.f64 (/.f64 (*.f64 c a) b) (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))) (*.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -4)) (/.f64 1/2 a))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3))) b))
0.3b
(/.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))
1.5b
(-.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))))
0.6b
(*.f64 (/.f64 (*.f64 (*.f64 c a) -4) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))) (/.f64 (/.f64 1/2 a) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))))
Compiler

Compiled 15037 to 10186 computations (32.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3))) b)
0.3b
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))
0.5b
(cbrt.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3))
0.6b
(pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3)

series94.0ms (1.3%)

Counts
3 → 92
Calls

3 calls:

52.0ms
(+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3))) b)
32.0ms
(pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3)
10.0ms
(cbrt.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3))

rewrite18.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod_binary64
18×fma-def_binary64
16×*-un-lft-identity_binary64
15×sqrt-prod_binary64
14×add-sqr-sqrt_binary64
Counts
3 → 80
Calls

3 calls:

10.0ms
(+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3))) b)
2.0ms
(pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3)
2.0ms
(cbrt.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3))

simplify101.0ms (1.4%)

Algorithm
egg-herbie
Rules
463×fma-def_binary64
436×times-frac_binary64
278×unswap-sqr_binary64
249×associate-/r*_binary64
247×associate-/l*_binary64
Counts
172 → 142
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01523473
13933197
212533088
345523074
449823074

prune252.0ms (3.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2090209
Fresh044
Picked011
Done011
Total2096215
Error
0b
Counts
215 → 6
Alt Table
StatusErrorProgram
1.4b
(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
2.3b
(*.f64 (fma.f64 -2 (+.f64 (/.f64 (*.f64 c a) b) (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))) (*.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -4)) (/.f64 1/2 a))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 3))) b))
0.3b
(/.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))
1.5b
(-.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))))
0.6b
(*.f64 (/.f64 (*.f64 (*.f64 c a) -4) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))) (/.f64 (/.f64 1/2 a) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))))
Compiler

Compiled 7381 to 4844 computations (34.4% saved)

regimes1.4s (19.1%)

Accuracy

Total 0.1b remaining (71.9%)

Threshold costs 0.1b (71.9%)

Counts
271 → 1
Compiler

Compiled 34632 to 23658 computations (31.7% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01322
11622
21622

end149.0ms (2%)

Compiler

Compiled 258 to 174 computations (32.6% saved)

Profiling

Loading profile data...