Details

Time bar (total: 13.7s)

analyze2.1s (15.4%)

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
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%93.6%6.4%8
9.4%84.3%6.4%9
14.8%75.7%9.5%10
16%71.4%12.6%11
20.9%65.7%13.4%12
24.2%60.5%15.3%13
24.8%58.6%16.6%14
Compiler

Compiled 31 to 24 computations (22.6% saved)

sample5.5s (40%)

Results
2.7s2291×body1024valid
1.2s4190×body128valid
939.0ms1208×body512valid
275.0ms778×body128invalid
272.0ms562×body256valid
8.0msbody2048valid
Compiler

Compiled 92 to 71 computations (22.8% saved)

simplify63.0ms (0.5%)

Algorithm
egg-herbie
Rules
640×distribute-rgt-neg-in_binary64
474×fma-neg_binary64
418×distribute-lft-neg-in_binary64
379×div-sub_binary64
378×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02335
14928
210028
319528
439128
5107528
6254328
7420028
8495528

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
10.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
10.9b
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (*.f64 F F) 2) (*.f64 2 x)) (neg.f64 (/.f64 1 2)))))
10.9b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 153 to 108 computations (29.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 F (sin.f64 B))
0.2b
(/.f64 x (tan.f64 B))
6.0b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
15.8b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series223.0ms (1.6%)

Counts
4 → 80
Calls

4 calls:

129.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
41.0ms
(/.f64 x (tan.f64 B))
37.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
15.0ms
(/.f64 F (sin.f64 B))

rewrite201.0ms (1.5%)

Algorithm
egg-rewrite
Rules
78×egg
76×egg
47×egg
25×egg
Counts
4 → 226
Calls

4 calls:

56.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
49.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
47.0ms
(/.f64 F (sin.f64 B))
44.0ms
(/.f64 x (tan.f64 B))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
116612
2174912
3525112
01220
125220
2295120
3515020
056
11066
213716
353426
056
11036
213186
351406

simplify107.0ms (0.8%)

Algorithm
egg-herbie
Rules
965×times-frac_binary64
300×fma-def_binary64
196×+-commutative_binary64
187×fma-neg_binary64
166×*-commutative_binary64
Counts
306 → 325
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03333644
110303471
235483471
350223471

prune400.0ms (2.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New31114325
Fresh101
Picked101
Done000
Total31314327
Error
0.0b
Counts
327 → 14
Alt Table
StatusErrorProgram
11.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (cbrt.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (cbrt.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1)))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
10.9b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
11.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 3))
35.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 -1 F)) (/.f64 x (tan.f64 B)))
10.8b
(-.f64 (*.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))
8.2b
(-.f64 (*.f64 (/.f64 F 1) (/.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2) (sin.f64 B))) (/.f64 x (tan.f64 B)))
37.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (pow.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) 2))
31.9b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
11.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (/.f64 x (cbrt.f64 (tan.f64 B)))))
8.2b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
10.9b
(-.f64 (*.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/4) (*.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/4) (/.f64 F (sin.f64 B)))) (/.f64 x (tan.f64 B)))
10.9b
(-.f64 (*.f64 (*.f64 F (/.f64 1 (sin.f64 B))) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))
11.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (tan.f64 B)) (pow.f64 (/.f64 1 x) -1)))
Compiler

Compiled 11651 to 6595 computations (43.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 x (tan.f64 B))
0.2b
(*.f64 (/.f64 F 1) (/.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2) (sin.f64 B)))
0.4b
(/.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2) (sin.f64 B))
15.8b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series254.0ms (1.8%)

Counts
2 → 56
Calls

2 calls:

128.0ms
(*.f64 (/.f64 F 1) (/.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2) (sin.f64 B)))
126.0ms
(/.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2) (sin.f64 B))

rewrite122.0ms (0.9%)

Algorithm
egg-rewrite
Rules
68×egg
48×egg
Counts
2 → 116
Calls

2 calls:

66.0ms
(*.f64 (/.f64 F 1) (/.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2) (sin.f64 B)))
53.0ms
(/.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2) (sin.f64 B))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01117
123017
2262917
3494917
01420
127720
2316720
3554020

simplify114.0ms (0.8%)

Algorithm
egg-herbie
Rules
497×times-frac_binary64
431×fma-neg_binary64
291×cancel-sign-sub-inv_binary64
240×sub-neg_binary64
214×fma-def_binary64
Counts
172 → 197
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02423054
17502832
224182698
348322696
450642696

prune689.0ms (5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New3484352
Fresh31013
Picked101
Done000
Total35214366
Error
0.0b
Counts
366 → 14
Alt Table
StatusErrorProgram
11.1b
(-.f64 (*.f64 (/.f64 F 1) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2) 3)) (sin.f64 B))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
10.9b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
11.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 3))
37.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (pow.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) 2))
10.8b
(-.f64 (*.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))
31.7b
(-.f64 (*.f64 (/.f64 F 1) (/.f64 -1 (*.f64 (sin.f64 B) F))) (/.f64 x (tan.f64 B)))
32.1b
(-.f64 (*.f64 (/.f64 F 1) (/.f64 1 (*.f64 (sin.f64 B) F))) (/.f64 x (tan.f64 B)))
31.9b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
11.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (/.f64 x (cbrt.f64 (tan.f64 B)))))
8.2b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
10.9b
(-.f64 (*.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/4) (*.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/4) (/.f64 F (sin.f64 B)))) (/.f64 x (tan.f64 B)))
11.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (tan.f64 B)) (pow.f64 (/.f64 1 x) -1)))
8.3b
(-.f64 (*.f64 (/.f64 F 1) (/.f64 (pow.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/4) 2) (sin.f64 B))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 13582 to 8357 computations (38.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 x (tan.f64 B))
0.3b
(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
0.4b
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
15.8b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series188.0ms (1.4%)

Counts
2 → 56
Calls

2 calls:

130.0ms
(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
58.0ms
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

rewrite120.0ms (0.9%)

Algorithm
egg-rewrite
Rules
60×egg
49×egg
Counts
2 → 109
Calls

2 calls:

64.0ms
(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
53.0ms
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01117
123016
2261216
3491216
01220
125819
2315419
3562019

simplify110.0ms (0.8%)

Algorithm
egg-herbie
Rules
559×fma-neg_binary64
528×times-frac_binary64
474×cancel-sign-sub-inv_binary64
273×neg-mul-1_binary64
230×sub-neg_binary64
Counts
165 → 189
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02342803
17372637
225022493
345872489
451092489

prune454.0ms (3.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New3395344
Fresh5813
Picked101
Done000
Total34513358
Error
0.0b
Counts
358 → 13
Alt Table
StatusErrorProgram
11.1b
(-.f64 (*.f64 (/.f64 F 1) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2) 3)) (sin.f64 B))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
36.6b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 (/.f64 x (sqrt.f64 (tan.f64 B))) (sqrt.f64 (tan.f64 B))))
31.9b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
8.2b
(-.f64 (/.f64 1 (/.f64 (sin.f64 B) (/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))))) (/.f64 x (tan.f64 B)))
11.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 3))
8.2b
(-.f64 (/.f64 F (*.f64 (sin.f64 B) (sqrt.f64 (fma.f64 F F 2)))) (/.f64 x (tan.f64 B)))
10.8b
(-.f64 (*.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))
31.7b
(-.f64 (*.f64 (/.f64 F 1) (/.f64 -1 (*.f64 (sin.f64 B) F))) (/.f64 x (tan.f64 B)))
11.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (/.f64 x (cbrt.f64 (tan.f64 B)))))
8.2b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
11.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (tan.f64 B)) (pow.f64 (/.f64 1 x) -1)))
32.1b
(-.f64 (/.f64 F (*.f64 (sin.f64 B) F)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 12483 to 7290 computations (41.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
0.3b
(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
0.4b
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
15.8b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series21.0ms (0.2%)

Counts
1 → 4
Calls

1 calls:

21.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

rewrite51.0ms (0.4%)

Algorithm
egg-rewrite
Rules
59×egg
Counts
1 → 59
Calls

1 calls:

50.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0711
11446
219106
351336

simplify201.0ms (1.5%)

Algorithm
egg-herbie
Rules
824×unswap-sqr_binary64
470×distribute-rgt-neg-in_binary64
466×fma-def_binary64
422×sub-neg_binary64
384×distribute-lft-neg-in_binary64
Counts
63 → 65
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02373
16771
219264
358462
4189862
5271362
6372162
7395062
8478662
9476762
10493962
11497062
12500062
13475562

prune417.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New3203323
Fresh4812
Picked101
Done000
Total32511336
Error
0.0b
Counts
336 → 11
Alt Table
StatusErrorProgram
31.7b
(-.f64 (*.f64 (/.f64 F 1) (/.f64 -1 (*.f64 (sin.f64 B) F))) (/.f64 x (tan.f64 B)))
8.2b
(-.f64 (/.f64 F (*.f64 (sin.f64 B) (sqrt.f64 (fma.f64 F F 2)))) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
11.1b
(-.f64 (*.f64 (/.f64 F 1) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2) 3)) (sin.f64 B))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
31.9b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
8.2b
(-.f64 (/.f64 1 (/.f64 (sin.f64 B) (/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))))) (/.f64 x (tan.f64 B)))
8.2b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
8.3b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (*.f64 (/.f64 x 1) (/.f64 (cos.f64 B) (sin.f64 B))))
11.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (tan.f64 B)) (pow.f64 (/.f64 1 x) -1)))
32.1b
(-.f64 (/.f64 F (*.f64 (sin.f64 B) F)) (/.f64 x (tan.f64 B)))
10.8b
(-.f64 (*.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 12299 to 6688 computations (45.6% saved)

regimes2.0s (14.7%)

Accuracy

Total 0.2b remaining (85.1%)

Threshold costs 0.2b (85.1%)

Counts
251 → 3
Compiler

Compiled 25080 to 17556 computations (30% saved)

bsearch104.0ms (0.8%)

Steps
ItersRangePoint
5
1.2093724008996791e+61
2.3622688567421822e+80
4.846391617640927e+61
4
-4.8179249921160045e+44
-2.311468214312411e+43
-2.912720275885683e+43
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03178
14078
25178
36478
47278
57678
67778
77678

end192.0ms (1.4%)

Compiler

Compiled 339 to 221 computations (34.8% saved)

Profiling

Loading profile data...