Details

Time bar (total: 11.1s)

analyze654.0ms (5.9%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
12.5%87.4%0.1%5
18.7%81.1%0.1%6
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.5s (22.8%)

Results
813.0ms5377×body128valid
628.0ms1172×body2048valid
419.0ms735×body1024valid
258.0ms408×body4096valid
145.0ms1128×body128invalid
125.0ms367×body512valid
46.0ms197×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify257.0ms (2.3%)

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
33.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
33.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
33.1b
(/.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
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
1.2b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
1.2b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
22.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series310.0ms (2.8%)

Counts
4 → 96
Calls

4 calls:

167.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
86.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
46.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
10.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

rewrite121.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
278×expm1-udef_binary64
278×log1p-udef_binary64
166×add-sqr-sqrt_binary64
162×log1p-expm1-u_binary64
162×expm1-log1p-u_binary64
Counts
4 → 156
Calls

4 calls:

117.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
117.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
117.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
117.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01574
133762
2415862
3498762
4485062
000
100

simplify79.0ms (0.7%)

Algorithm
egg-herbie
Rules
742×times-frac_binary64
467×associate-/l*_binary64
436×fma-def_binary64
432×fma-neg_binary64
426×associate-/r*_binary64
Counts
252 → 229
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01212241
13982164
213272078
349542078
452182078

prune477.0ms (4.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New21910229
Fresh011
Picked101
Done000
Total22011231
Error
4.4b
Counts
231 → 11
Alt Table
StatusErrorProgram
45.6b
(pow.f64 (/.f64 (*.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) -1)
33.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
33.4b
(/.f64 (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) 1/4) 2)) (*.f64 2 a))
50.0b
(/.f64 (*.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
45.8b
(pow.f64 (cbrt.f64 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))) (/.f64 1/2 a))) 3)
44.3b
(-.f64 (/.f64 c b) (/.f64 b a))
44.1b
(/.f64 (neg.f64 b) a)
56.8b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
40.7b
(neg.f64 (/.f64 c b))
33.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (+.f64 (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)) (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a))
45.6b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) (/.f64 1/2 a)))
Compiler

Compiled 6129 to 3612 computations (41.1% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.2b
(+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (+.f64 (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)) (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c))))))
1.5b
(fma.f64 b b (*.f64 -4 (*.f64 a c)))
22.0b
(sqrt.f64 (+.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (+.f64 (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)) (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)))))
51.3b
(fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c))

series140.0ms (1.3%)

Counts
4 → 100
Calls

4 calls:

57.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (+.f64 (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)) (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c))))))
45.0ms
(sqrt.f64 (+.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (+.f64 (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)) (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)))))
25.0ms
(fma.f64 b b (*.f64 -4 (*.f64 a c)))
13.0ms
(fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c))

rewrite88.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
285×expm1-udef_binary64
285×log1p-udef_binary64
193×add-sqr-sqrt_binary64
186×log1p-expm1-u_binary64
186×expm1-log1p-u_binary64
Counts
4 → 106
Calls

4 calls:

85.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (+.f64 (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)) (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c))))))
85.0ms
(fma.f64 b b (*.f64 -4 (*.f64 a c)))
85.0ms
(sqrt.f64 (+.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (+.f64 (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)) (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)))))
85.0ms
(fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01894
139357
2425057
3484257
000
100

simplify72.0ms (0.7%)

Algorithm
egg-herbie
Rules
458×times-frac_binary64
447×unswap-sqr_binary64
283×associate-*r*_binary64
278×associate-/l*_binary64
270×fma-def_binary64
Counts
206 → 157
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0851653
12701579
28441517
342171517
450461517

prune215.0ms (1.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1810181
Fresh01010
Picked011
Done000
Total18111192
Error
4.4b
Counts
192 → 11
Alt Table
StatusErrorProgram
45.6b
(pow.f64 (/.f64 (*.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) -1)
33.1b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
33.4b
(/.f64 (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) 1/4) 2)) (*.f64 2 a))
50.0b
(/.f64 (*.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
45.8b
(pow.f64 (cbrt.f64 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))) (/.f64 1/2 a))) 3)
44.3b
(-.f64 (/.f64 c b) (/.f64 b a))
44.1b
(/.f64 (neg.f64 b) a)
56.8b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
40.7b
(neg.f64 (/.f64 c b))
33.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (+.f64 (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)) (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a))
45.6b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) (/.f64 1/2 a)))
Compiler

Compiled 6373 to 4075 computations (36.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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))
1.2b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
22.0b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series194.0ms (1.7%)

Counts
4 → 96
Calls

4 calls:

83.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
56.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
45.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
10.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite102.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
781×prod-diff_binary64
244×log1p-udef_binary64
165×egg-rr
138×add-sqr-sqrt_binary64
132×log1p-expm1-u_binary64
Counts
4 → 165
Calls

4 calls:

77.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))
77.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
77.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
77.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01362
127962
2338562
3510262
000
100

simplify96.0ms (0.9%)

Algorithm
egg-herbie
Rules
742×times-frac_binary64
467×associate-/l*_binary64
436×fma-def_binary64
432×fma-neg_binary64
426×associate-/r*_binary64
Counts
261 → 238
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01212241
13982164
213272078
349542078
452182078

prune267.0ms (2.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New2317238
Fresh369
Picked101
Done011
Total23514249
Error
4.4b
Counts
249 → 14
Alt Table
StatusErrorProgram
33.4b
(/.f64 (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) 1/4) 2)) (*.f64 2 a))
33.6b
(/.f64 (/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a))
56.8b
(*.f64 (-.f64 b b) (/.f64 1/2 a))
33.1b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2)))
50.0b
(/.f64 (*.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
33.4b
(*.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 1/4) 2) b) (/.f64 1/2 a))
45.6b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) (/.f64 1/2 a)))
33.6b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) 2)) (/.f64 1/2 a))
33.1b
(/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2) a)
44.3b
(-.f64 (/.f64 c b) (/.f64 b a))
44.1b
(/.f64 (neg.f64 b) a)
40.7b
(neg.f64 (/.f64 c b))
33.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (+.f64 (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)) (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a))
36.0b
(*.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a))
Compiler

Compiled 6663 to 3906 computations (41.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.1b
(/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2) a)
1.2b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
22.0b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series194.0ms (1.8%)

Counts
1 → 20
Calls

1 calls:

194.0ms
(/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2) a)

rewrite64.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
790×prod-diff_binary64
245×log1p-udef_binary64
138×add-sqr-sqrt_binary64
132×log1p-expm1-u_binary64
132×expm1-log1p-u_binary64
Counts
1 → 44
Calls

1 calls:

62.0ms
(/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2) a)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01322
127822
2345422
3522122
000
100

simplify61.0ms (0.5%)

Algorithm
egg-herbie
Rules
794×fma-neg_binary64
351×unswap-sqr_binary64
333×distribute-neg-frac_binary64
328×times-frac_binary64
221×associate-*r*_binary64
Counts
64 → 67
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
064612
1210609
2666585
33266585
44979585
55005585

prune233.0ms (2.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2382240
Fresh21012
Picked101
Done011
Total24113254
Error
4.4b
Counts
254 → 13
Alt Table
StatusErrorProgram
33.6b
(/.f64 (/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 a))
56.8b
(*.f64 (-.f64 b b) (/.f64 1/2 a))
33.1b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2)))
50.0b
(/.f64 (*.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
33.4b
(*.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 1/4) 2) b) (/.f64 1/2 a))
33.4b
(/.f64 (*.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) 1/4) 2) b) 1/2) a)
40.7b
(neg.f64 (/.f64 c b))
36.0b
(/.f64 (*.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b) 1/2) a)
33.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (+.f64 (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)) (fma.f64 (*.f64 a -4) c (*.f64 (*.f64 4 a) c)))))) (*.f64 2 a))
45.6b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) (/.f64 1/2 a)))
33.6b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) 2)) (/.f64 1/2 a))
44.3b
(-.f64 (/.f64 c b) (/.f64 b a))
44.1b
(/.f64 (neg.f64 b) a)
Compiler

Compiled 6333 to 3736 computations (41% saved)

regimes4.6s (41.3%)

Accuracy

Total 4.3b remaining (43.2%)

Threshold costs 0b (0%)

Counts
283 → 3
Compiler

Compiled 29504 to 19818 computations (32.8% saved)

bsearch91.0ms (0.8%)

Steps
ItersRangePoint
10
1.901565658296121e-67
1.68094319869498e-53
2.7919095286000728e-58
6
-4.337663542347003e+121
-2.705837089243012e+119
-3.996635431194612e+121
Compiler

Compiled 4 to 3 computations (25% 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
02550
13950
24950
35550
45750
55750

end184.0ms (1.7%)

Compiler

Compiled 346 to 225 computations (35% saved)

Profiling

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