Details

Time bar (total: 13.3s)

analyze2.6s (19.6%)

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)

sample249.0ms (1.9%)

Algorithm
intervals
Results
83.0ms69×body1024valid
24.0ms44×body512valid
22.0ms133×body128valid
4.0ms25×body128invalid
3.0ms10×body256valid
1.0msbody128nan
Compiler

Compiled 64 to 50 computations (21.9% saved)

simplify51.0ms (0.4%)

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
13.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
13.8b
(+.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)))))
13.8b
(-.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))
0.1b
(/.f64 x (tan.f64 B))
5.9b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
16.1b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series237.0ms (1.8%)

Counts
4 → 80
Calls

4 calls:

136.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
42.0ms
(/.f64 x (tan.f64 B))
42.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
16.0ms
(/.f64 F (sin.f64 B))

rewrite53.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt_binary64
31×*-un-lft-identity_binary64
31×add-cube-cbrt_binary64
30×times-frac_binary64
22×add-exp-log_binary64
Counts
4 → 123
Calls

4 calls:

40.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
3.0ms
(/.f64 x (tan.f64 B))
2.0ms
(/.f64 F (sin.f64 B))
2.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

simplify165.0ms (1.2%)

Algorithm
egg-herbie
Rules
302×fma-def_binary64
223×*-commutative_binary64
221×associate-*r*_binary64
218×fma-neg_binary64
202×+-commutative_binary64
Counts
203 → 271
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05005883
113605603
245185575
349845575
449325575

prune351.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New26110271
Fresh101
Picked101
Done000
Total26310273
Error
0.0b
Counts
273 → 10
Alt Table
StatusErrorProgram
32.8b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
14.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
13.8b
(-.f64 (*.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)) (sqrt.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
11.4b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (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)))
39.2b
(-.f64 (-.f64 (/.f64 1 (sin.f64 B)) (+.f64 (/.f64 x (*.f64 (sin.f64 B) (pow.f64 F 2))) (/.f64 1 (*.f64 (sin.f64 B) (pow.f64 F 2))))) (/.f64 x (tan.f64 B)))
34.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10315 to 5778 computations (44% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 x (tan.f64 B))
0.3b
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
0.8b
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
16.1b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series312.0ms (2.3%)

Counts
2 → 44
Calls

2 calls:

169.0ms
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
143.0ms
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))

rewrite60.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
17×add-exp-log_binary64
12×add-sqr-sqrt_binary64
add-cbrt-cube_binary64
associate-*r*_binary64
*-un-lft-identity_binary64
Counts
2 → 52
Calls

2 calls:

53.0ms
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
4.0ms
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

simplify131.0ms (1%)

Algorithm
egg-herbie
Rules
829×fma-def_binary64
324×cancel-sign-sub-inv_binary64
258×sub-neg_binary64
210×fma-neg_binary64
171×associate-*r*_binary64
Counts
96 → 153
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02983456
18193211
228793191
348063191
449733191
549423191

prune364.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2691270
Fresh189
Picked011
Done000
Total27010280
Error
0.0b
Counts
280 → 10
Alt Table
StatusErrorProgram
32.8b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
39.2b
(-.f64 (/.f64 (-.f64 1 (+.f64 (/.f64 x (pow.f64 F 2)) (/.f64 1 (pow.f64 F 2)))) (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
14.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
13.8b
(-.f64 (*.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)) (sqrt.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
11.4b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (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)))
34.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10576 to 6438 computations (39.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
3.1b
(*.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)) (sqrt.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
3.1b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))
16.1b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
16.6b
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)

series1.8s (13.4%)

Counts
3 → 96
Calls

3 calls:

1.2s
(*.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)) (sqrt.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
571.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))
43.0ms
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)

rewrite25.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
38×add-exp-log_binary64
30×add-sqr-sqrt_binary64
19×prod-exp_binary64
17×associate-*r*_binary64
17×add-cbrt-cube_binary64
Counts
3 → 97
Calls

3 calls:

9.0ms
(*.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)) (sqrt.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
7.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))
1.0ms
(pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)

simplify208.0ms (1.6%)

Algorithm
egg-herbie
Rules
465×*-commutative_binary64
461×times-frac_binary64
298×+-commutative_binary64
260×fma-def_binary64
219×associate-+r+_binary64
Counts
193 → 288
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0124915031
1413214756
2505514756

prune686.0ms (5.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3640364
Fresh088
Picked011
Done011
Total36410374
Error
0.0b
Counts
374 → 10
Alt Table
StatusErrorProgram
32.8b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
39.2b
(-.f64 (/.f64 (-.f64 1 (+.f64 (/.f64 x (pow.f64 F 2)) (/.f64 1 (pow.f64 F 2)))) (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
14.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
13.8b
(-.f64 (*.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)) (sqrt.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
11.4b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (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)))
34.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 28154 to 18824 computations (33.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 1 (tan.f64 B))
0.3b
(*.f64 x (/.f64 1 (tan.f64 B)))
5.9b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
16.1b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series61.0ms (0.5%)

Counts
2 → 36
Calls

2 calls:

45.0ms
(*.f64 x (/.f64 1 (tan.f64 B)))
15.0ms
(/.f64 1 (tan.f64 B))

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×times-frac_binary64
19×*-un-lft-identity_binary64
18×add-cube-cbrt_binary64
15×add-exp-log_binary64
Counts
2 → 73
Calls

2 calls:

8.0ms
(*.f64 x (/.f64 1 (tan.f64 B)))
3.0ms
(/.f64 1 (tan.f64 B))

simplify114.0ms (0.9%)

Algorithm
egg-herbie
Rules
649×sub-neg_binary64
486×cancel-sign-sub-inv_binary64
450×associate-/l*_binary64
409×distribute-rgt-neg-in_binary64
376×fma-neg_binary64
Counts
109 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01021140
12281053
26061044
313571044
427051044
541781044
645431044
748811044

prune348.0ms (2.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New2991300
Fresh167
Picked011
Done022
Total30010310
Error
0.0b
Counts
310 → 10
Alt Table
StatusErrorProgram
32.8b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 1 (/.f64 (tan.f64 B) x)))
14.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
13.8b
(-.f64 (*.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4)) (sqrt.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
11.4b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))) -1/2))) (/.f64 x (tan.f64 B)))
13.8b
(-.f64 (*.f64 (/.f64 F (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)))
30.9b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
34.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 11268 to 6808 computations (39.6% saved)

regimes1.3s (9.4%)

Accuracy

Total 0.2b remaining (77.3%)

Threshold costs 0.2b (77.3%)

Counts
187 → 3
Compiler

Compiled 19832 to 13580 computations (31.5% saved)

bsearch187.0ms (1.4%)

Steps
ItersRangePoint
8
9.425039105731514
203025.05433430706
199346.12227644376
11
-68169152033962250.0
-2.034986824905378e-18
-84561923.8329791
Compiler

Compiled 4 to 3 computations (25% saved)

simplify13.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
039112
151112
265112
380112
488112
591112
689112

end1.0ms (0%)

Compiler

Compiled 77 to 46 computations (40.3% saved)

sample3.9s (29.7%)

Algorithm
intervals
Results
1.8s2243×body1024valid
690.0ms4084×body128valid
563.0ms1130×body512valid
183.0ms538×body256valid
111.0ms656×body128invalid
18.0ms130×body128nan
7.0msbody2048valid
0.0msbody256invalid
Compiler

Compiled 344 to 234 computations (32% saved)

Profiling

Loading profile data...