Details

Time bar (total: 11.4s)

analyze1.5s (12.9%)

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)

sample3.7s (32.1%)

Results
1.3s346×body4096valid
802.0ms5372×body128valid
705.0ms1168×body2048valid
367.0ms788×body1024valid
157.0ms1120×body128invalid
135.0ms399×body512valid
39.0ms183×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify192.0ms (1.7%)

Algorithm
egg-herbie
Rules
2079×fma-neg_binary64
1006×fma-def_binary64
919×div-sub_binary64
626×distribute-rgt-in_binary64
435×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01526
13824
29524
322722
435722
561422
6110322
7137322
8163622
9233022
10318722
11288022
12282722
13289622
14292222
15379722
16482422
17524022

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
36.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
36.2b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))
Compiler

Compiled 71 to 46 computations (35.2% 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 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
0.5b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
25.7b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series130.0ms (1.1%)

Counts
4 → 96
Calls

4 calls:

53.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
33.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
31.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
11.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite76.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
963×prod-diff_binary64
209×log1p-udef_binary64
123×egg-rr
118×add-sqr-sqrt_binary64
113×log1p-expm1-u_binary64
Counts
4 → 123
Calls

4 calls:

67.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))
67.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
67.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
67.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01159
123559
2294459
3502159
000
100

simplify81.0ms (0.7%)

Algorithm
egg-herbie
Rules
780×times-frac_binary64
480×associate-/l*_binary64
434×associate-/r*_binary64
344×fma-def_binary64
209×fma-neg_binary64
Counts
219 → 194
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01072081
13511997
211691913
348961913
449931913

prune180.0ms (1.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New18014194
Fresh000
Picked101
Done000
Total18114195
Error
6.6b
Counts
195 → 14
Alt Table
StatusErrorProgram
36.3b
(*.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) -1))
36.7b
(*.f64 -1/2 (/.f64 (*.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) 2)) a))
61.6b
(*.f64 -1/2 (/.f64 (log.f64 (exp.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) a))
41.0b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
43.4b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
46.6b
(*.f64 -1/2 (/.f64 (/.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))))) a))
46.6b
(*.f64 -1/2 (/.f64 (*.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) a))
49.1b
(*.f64 -1/2 (*.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 a))))
58.0b
(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
36.7b
(*.f64 -1/2 (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (/.f64 1 a))))
36.2b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
53.1b
(*.f64 -1/2 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))) 1))
37.1b
(*.f64 -1/2 (/.f64 (fma.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b) a))
43.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
Compiler

Compiled 5213 to 3140 computations (39.8% 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 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
0.5b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
25.7b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series59.0ms (0.5%)

Counts
1 → 20
Calls

1 calls:

59.0ms
(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))

rewrite60.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
954×prod-diff_binary64
227×log1p-udef_binary64
132×add-sqr-sqrt_binary64
125×log1p-expm1-u_binary64
125×expm1-log1p-u_binary64
Counts
1 → 42
Calls

1 calls:

59.0ms
(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01319
127119
2318119
3523219
000
100

simplify48.0ms (0.4%)

Algorithm
egg-herbie
Rules
751×cancel-sign-sub-inv_binary64
371×times-frac_binary64
351×unswap-sqr_binary64
285×fma-neg_binary64
236×associate-*r*_binary64
Counts
62 → 65
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
057567
1195555
2629529
33169529
45154529

prune191.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1994203
Fresh5813
Picked011
Done000
Total20413217
Error
6.6b
Counts
217 → 13
Alt Table
StatusErrorProgram
36.7b
(*.f64 -1/2 (/.f64 (*.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) 2)) a))
50.4b
(*.f64 -1/2 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (*.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
61.6b
(*.f64 -1/2 (/.f64 (log.f64 (exp.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) a))
41.0b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
46.6b
(*.f64 -1/2 (/.f64 (/.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))))) a))
36.2b
(*.f64 -1/2 (/.f64 (neg.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (neg.f64 a)))
36.6b
(*.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))))
58.0b
(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
43.5b
(*.f64 -1/2 (*.f64 (+.f64 b b) (/.f64 1 a)))
36.2b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
53.1b
(*.f64 -1/2 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))) 1))
37.1b
(*.f64 -1/2 (/.f64 (fma.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b) a))
43.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
Compiler

Compiled 5687 to 3499 computations (38.5% saved)

localize14.0ms (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 (neg.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (neg.f64 a))
0.5b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
25.7b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series52.0ms (0.5%)

Counts
1 → 20
Calls

1 calls:

52.0ms
(/.f64 (neg.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (neg.f64 a))

rewrite66.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
593×log-prod_binary64
321×fma-def_binary64
218×fma-neg_binary64
215×expm1-udef_binary64
215×log1p-udef_binary64
Counts
1 → 44
Calls

1 calls:

65.0ms
(/.f64 (neg.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (neg.f64 a))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01323
128419
2310218
3567118
000
100

simplify46.0ms (0.4%)

Algorithm
egg-herbie
Rules
751×cancel-sign-sub-inv_binary64
371×times-frac_binary64
351×unswap-sqr_binary64
285×fma-neg_binary64
236×associate-*r*_binary64
Counts
64 → 67
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
057567
1195555
2629529
33169529
45154529

prune179.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2023205
Fresh3811
Picked101
Done011
Total20612218
Error
6.6b
Counts
218 → 12
Alt Table
StatusErrorProgram
36.7b
(*.f64 -1/2 (/.f64 (*.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) 2)) a))
50.4b
(*.f64 -1/2 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (*.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
58.0b
(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
43.4b
(*.f64 -1/2 (/.f64 (neg.f64 (+.f64 b b)) (neg.f64 a)))
61.6b
(*.f64 -1/2 (/.f64 (log.f64 (exp.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) a))
41.0b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
46.6b
(*.f64 -1/2 (/.f64 (/.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))))) a))
36.6b
(*.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))))
36.2b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
52.6b
(*.f64 -1/2 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a))) 1))
43.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
37.4b
(*.f64 -1/2 (pow.f64 (cbrt.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a)) 3))
Compiler

Compiled 5572 to 3416 computations (38.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))
0.2b
(/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
0.5b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
25.7b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series385.0ms (3.4%)

Counts
2 → 32
Calls

2 calls:

322.0ms
(/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))
63.0ms
(/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))

rewrite96.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
329×fma-def_binary64
243×expm1-udef_binary64
243×log1p-udef_binary64
205×fma-neg_binary64
138×add-sqr-sqrt_binary64
Counts
2 → 76
Calls

2 calls:

94.0ms
(/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))
94.0ms
(/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01362
127940
2353238
3498238
4490738
000
100

simplify124.0ms (1.1%)

Algorithm
egg-herbie
Rules
717×times-frac_binary64
642×associate-/l*_binary64
498×fma-def_binary64
188×cancel-sign-sub-inv_binary64
162×fma-neg_binary64
Counts
108 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01381512
14291482
214851403
349651403
450071403

prune265.0ms (2.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New3210321
Fresh01010
Picked011
Done011
Total32112333
Error
6.6b
Counts
333 → 12
Alt Table
StatusErrorProgram
36.7b
(*.f64 -1/2 (/.f64 (*.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) 2)) a))
50.4b
(*.f64 -1/2 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (*.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
58.0b
(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
43.4b
(*.f64 -1/2 (/.f64 (neg.f64 (+.f64 b b)) (neg.f64 a)))
61.6b
(*.f64 -1/2 (/.f64 (log.f64 (exp.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) a))
41.0b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
46.6b
(*.f64 -1/2 (/.f64 (/.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))))) a))
36.6b
(*.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))))
36.2b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
52.6b
(*.f64 -1/2 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a))) 1))
43.5b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
37.4b
(*.f64 -1/2 (pow.f64 (cbrt.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a)) 3))
Compiler

Compiled 12164 to 7458 computations (38.7% saved)

regimes3.7s (32.5%)

Accuracy

Total 4.7b remaining (44.2%)

Threshold costs 0b (0%)

Counts
165 → 3
Compiler

Compiled 14968 to 10482 computations (30% saved)

bsearch88.0ms (0.8%)

Steps
ItersRangePoint
8
1.1610024044160129e+50
1.326598259492515e+53
1.30762203111794e+53
10
-1.2061160045863032e-102
-2.0413542939239333e-119
-8.430934381176968e-103
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
16×*-commutative_binary64
10×+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03064
15164
27262
39062
49862
510062
69962

end195.0ms (1.7%)

Compiler

Compiled 348 to 232 computations (33.3% saved)

Profiling

Loading profile data...