Details

Time bar (total: 8.9s)

analyze1.4s (16.2%)

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 (28.6%)

Results
762.0ms5404×body128valid
686.0ms1172×body2048valid
347.0ms740×body1024valid
261.0ms378×body4096valid
142.0ms1065×body128invalid
125.0ms376×body512valid
47.0ms186×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify140.0ms (1.6%)

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
34.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
34.8b
(*.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)

localize9.0ms (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)
1.5b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
23.4b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series120.0ms (1.4%)

Counts
4 → 96
Calls

4 calls:

46.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
32.0ms
(+.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)))
10.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite66.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
963×prod-diff_binary64
209×log1p-udef_binary64
119×egg-rr
118×add-sqr-sqrt_binary64
113×log1p-expm1-u_binary64
Counts
4 → 119
Calls

4 calls:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01159
123559
2294459
3502159

simplify75.0ms (0.8%)

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
215 → 190
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01072081
13511997
211691913
348961913
449931913

prune160.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New17614190
Fresh000
Picked101
Done000
Total17714191
Error
6.3b
Counts
191 → 14
Alt Table
StatusErrorProgram
35.7b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) 3))) a))
34.9b
(*.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) -1))
57.9b
(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
35.4b
(*.f64 -1/2 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 a) 2)) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (cbrt.f64 a))))
43.8b
(*.f64 -1/2 (/.f64 (-.f64 (/.f64 (*.f64 b b) (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (/.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) a))
53.6b
(*.f64 -1/2 (/.f64 (fma.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))) (*.f64 4 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))) a))
49.0b
(*.f64 -1/2 (fma.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)) (*.f64 4 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))))
39.3b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
47.2b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
35.3b
(*.f64 -1/2 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) 2) (pow.f64 (cbrt.f64 a) 2)) (cbrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))))
46.9b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
47.1b
(*.f64 -1/2 (/.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
34.9b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
55.6b
(*.f64 -1/2 (cbrt.f64 (/.f64 (pow.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) 3) (pow.f64 a 3))))
Compiler

Compiled 5191 to 3140 computations (39.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))
0.2b
(pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) -1)
1.5b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
23.4b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series720.0ms (8.1%)

Counts
2 → 40
Calls

2 calls:

608.0ms
(pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) -1)
112.0ms
(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))

rewrite64.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
963×prod-diff_binary64
136×add-sqr-sqrt_binary64
130×log1p-expm1-u_binary64
130×expm1-log1p-u_binary64
127×add-cbrt-cube_binary64
Counts
2 → 80
Calls

2 calls:

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01341
127638
2330538
3498138

simplify67.0ms (0.8%)

Algorithm
egg-herbie
Rules
860×times-frac_binary64
520×associate-/l*_binary64
485×associate-/r*_binary64
256×fma-def_binary64
233×fma-neg_binary64
Counts
120 → 124
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0951240
13181192
211131138
349051138
450471138

prune187.0ms (2.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New2196225
Fresh6713
Picked011
Done000
Total22514239
Error
6.3b
Counts
239 → 14
Alt Table
StatusErrorProgram
34.9b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
39.4b
(*.f64 -1/2 (pow.f64 (*.f64 1/2 (/.f64 b c)) -1))
35.7b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) 3))) a))
34.9b
(*.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) -1))
35.4b
(*.f64 -1/2 (/.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) 2) (/.f64 a (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))))
47.2b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
35.3b
(*.f64 -1/2 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) 3) -1))
42.2b
(*.f64 -1/2 (pow.f64 (*.f64 1/2 (-.f64 (/.f64 b c) (fma.f64 (/.f64 c (pow.f64 b 3)) (*.f64 a a) (/.f64 a b)))) -1))
34.9b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
49.0b
(*.f64 -1/2 (fma.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)) (*.f64 4 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))))
39.3b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
46.9b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
43.8b
(*.f64 -1/2 (/.f64 (-.f64 (/.f64 (*.f64 b b) (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (/.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) a))
38.8b
(*.f64 -1/2 (pow.f64 (*.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))) -1))
Compiler

Compiled 6426 to 3999 computations (37.8% 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))
0.2b
(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
1.5b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
23.4b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series47.0ms (0.5%)

Counts
1 → 20
Calls

1 calls:

47.0ms
(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))

rewrite54.0ms (0.6%)

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:

53.0ms
(*.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

simplify43.0ms (0.5%)

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

prune152.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1991200
Fresh11112
Picked101
Done011
Total20113214
Error
6.3b
Counts
214 → 13
Alt Table
StatusErrorProgram
34.9b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
39.4b
(*.f64 -1/2 (pow.f64 (*.f64 1/2 (/.f64 b c)) -1))
35.4b
(*.f64 -1/2 (/.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) 2) (/.f64 a (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))))
47.2b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
35.3b
(*.f64 -1/2 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) 3) -1))
42.2b
(*.f64 -1/2 (pow.f64 (*.f64 1/2 (-.f64 (/.f64 b c) (fma.f64 (/.f64 c (pow.f64 b 3)) (*.f64 a a) (/.f64 a b)))) -1))
35.7b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) 3))) (/.f64 1 a)))
34.9b
(*.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) -1))
49.0b
(*.f64 -1/2 (fma.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)) (*.f64 4 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))))
39.3b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
46.9b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
43.8b
(*.f64 -1/2 (/.f64 (-.f64 (/.f64 (*.f64 b b) (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (/.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)) (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) a))
38.8b
(*.f64 -1/2 (pow.f64 (*.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))) -1))
Compiler

Compiled 5630 to 3483 computations (38.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))
0.3b
(/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))
1.5b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
23.4b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series157.0ms (1.8%)

Counts
2 → 40
Calls

2 calls:

109.0ms
(/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))
48.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))

rewrite66.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
977×prod-diff_binary64
148×add-sqr-sqrt_binary64
141×log1p-expm1-u_binary64
141×expm1-log1p-u_binary64
138×add-cbrt-cube_binary64
Counts
2 → 65
Calls

2 calls:

64.0ms
(/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))
64.0ms
(/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01444
130238
2361938
3532738

simplify42.0ms (0.5%)

Algorithm
egg-herbie
Rules
642×times-frac_binary64
414×associate-/r*_binary64
398×associate-/l*_binary64
341×associate-*r*_binary64
283×associate-*l*_binary64
Counts
105 → 110
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0911163
12971130
210071088
351211088

prune151.0ms (1.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New2083211
Fresh3811
Picked011
Done011
Total21113224
Error
6.2b
Counts
224 → 13
Alt Table
StatusErrorProgram
34.9b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
39.4b
(*.f64 -1/2 (pow.f64 (*.f64 1/2 (/.f64 b c)) -1))
47.2b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
35.3b
(*.f64 -1/2 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) 3) -1))
34.9b
(*.f64 -1/2 (pow.f64 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) -1))
49.0b
(*.f64 -1/2 (fma.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)) (*.f64 4 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)))))
39.3b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
46.9b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
44.1b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (*.f64 1/2 (-.f64 (/.f64 b (*.f64 a c)) (fma.f64 (/.f64 c (pow.f64 b 3)) a (/.f64 1 b))))))
44.2b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (fma.f64 1/2 (/.f64 b (*.f64 a c)) (/.f64 -1/2 b))))
35.7b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) 3))) (/.f64 1 a)))
43.8b
(*.f64 -1/2 (/.f64 (/.f64 1 a) (*.f64 (/.f64 1 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
38.8b
(*.f64 -1/2 (pow.f64 (*.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b))) -1))
Compiler

Compiled 5946 to 3846 computations (35.3% saved)

regimes2.3s (25.5%)

Accuracy

Total 4.4b remaining (44.7%)

Threshold costs 0b (0%)

Counts
185 → 3
Compiler

Compiled 18456 to 12542 computations (32% saved)

bsearch84.0ms (0.9%)

Steps
ItersRangePoint
7
1.9254665904238227e+139
6.252983785752134e+140
1.3933076843620099e+140
8
-1.3460450616846217e-65
-4.173266225943494e-70
-6.828974244409841e-68
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 4 (0.0ms)

IterNodesCost
03674
15173
26373
37773
49471
510671
611171
711271
811171

end185.0ms (2.1%)

Compiler

Compiled 365 to 257 computations (29.6% saved)

Profiling

Loading profile data...