Details

Time bar (total: 11.4s)

analyze2.6s (23.2%)

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
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)

sample212.0ms (1.9%)

Algorithm
intervals
Results
57.0ms66×body1024valid
26.0ms50×body512valid
20.0ms123×body128valid
5.0ms16×body256valid
3.0ms21×body128invalid
2.0msbody2048valid
1.0msbody128nan
Compiler

Compiled 64 to 50 computations (21.9% saved)

simplify53.0ms (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

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
13.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
13.4b
(+.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)))))
13.3b
(-.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
0.2b
(/.f64 F (sin.f64 B))
0.2b
(/.f64 x (tan.f64 B))
7.5b
(*.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)

series329.0ms (2.9%)

Counts
4 → 80
Calls

4 calls:

145.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
92.0ms
(/.f64 x (tan.f64 B))
73.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
17.0ms
(/.f64 F (sin.f64 B))

rewrite22.0ms (0.2%)

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:

8.0ms
(*.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)

simplify172.0ms (1.5%)

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

prune461.0ms (4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New26011271
Fresh101
Picked101
Done000
Total26211273
Error
0.0b
Counts
273 → 11
Alt Table
StatusErrorProgram
32.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
13.4b
(-.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 (/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B))))
32.4b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
33.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
26.7b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.3b
(-.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)))
9.6b
(-.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)))
13.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
13.4b
(-.f64 (*.f64 (*.f64 (/.f64 F (sin.f64 B)) (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 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
Compiler

Compiled 10343 to 5790 computations (44% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 x (tan.f64 B))
0.2b
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
1.2b
(/.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)

series223.0ms (2%)

Counts
2 → 44
Calls

2 calls:

149.0ms
(/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B))
74.0ms
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

rewrite12.0ms (0.1%)

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:

5.0ms
(/.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))

simplify128.0ms (1.1%)

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

prune453.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2682270
Fresh2810
Picked101
Done000
Total27110281
Error
0.0b
Counts
281 → 10
Alt Table
StatusErrorProgram
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 (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B))))
32.4b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
33.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
26.7b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.4b
(-.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))))
13.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
13.4b
(-.f64 (*.f64 (*.f64 (/.f64 F (sin.f64 B)) (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 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
9.6b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
26.7b
(-.f64 (/.f64 (*.f64 F (/.f64 1 F)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10594 to 6439 computations (39.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
0.2b
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
1.2b
(/.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)

series22.0ms (0.2%)

Counts
1 → 4
Calls

1 calls:

22.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

rewrite5.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
associate-/r*_binary64
*-un-lft-identity_binary64
times-frac_binary64
Counts
1 → 23
Calls

1 calls:

4.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

simplify90.0ms (0.8%)

Algorithm
egg-herbie
Rules
486×fma-def_binary64
400×*-commutative_binary64
387×associate-/l*_binary64
366×distribute-rgt-neg-in_binary64
328×cancel-sign-sub-inv_binary64
Counts
27 → 35
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
072458
1182387
2593380
32237378
43591378
54379378
64991378
74921378

prune365.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2613264
Fresh279
Picked101
Done000
Total26410274
Error
0.0b
Counts
274 → 10
Alt Table
StatusErrorProgram
9.6b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (/.f64 (sin.f64 B) (cos.f64 B))))
13.4b
(-.f64 (*.f64 (*.f64 (/.f64 F (sin.f64 B)) (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)))
39.9b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (*.f64 (/.f64 x (sqrt.f64 (sin.f64 B))) (/.f64 (cos.f64 B) (sqrt.f64 (sin.f64 B)))))
32.4b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
33.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
26.7b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.4b
(-.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))))
13.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.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 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
26.7b
(-.f64 (/.f64 (*.f64 F (/.f64 1 F)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 11207 to 6362 computations (43.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (sin.f64 B) (cos.f64 B))
0.2b
(*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
1.2b
(/.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)

series9.0ms (0.1%)

Counts
1 → 4
Calls

1 calls:

9.0ms
(/.f64 (sin.f64 B) (cos.f64 B))

rewrite4.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
times-frac_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
associate-/r*_binary64
Counts
1 → 30
Calls

1 calls:

3.0ms
(/.f64 (sin.f64 B) (cos.f64 B))

simplify115.0ms (1%)

Algorithm
egg-herbie
Rules
953×fma-def_binary64
718×unswap-sqr_binary64
714×fma-neg_binary64
389×associate-/l/_binary64
350×times-frac_binary64
Counts
34 → 40
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
068499
1134465
2280465
3519465
4905465
51582465
62822465
74271465
84410465
94953465
104961465
114831465

prune393.0ms (3.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2690269
Fresh099
Picked011
Done000
Total26910279
Error
0.0b
Counts
279 → 10
Alt Table
StatusErrorProgram
9.6b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (/.f64 x (/.f64 (sin.f64 B) (cos.f64 B))))
13.4b
(-.f64 (*.f64 (*.f64 (/.f64 F (sin.f64 B)) (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)))
39.9b
(-.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sin.f64 B)) (*.f64 (/.f64 x (sqrt.f64 (sin.f64 B))) (/.f64 (cos.f64 B) (sqrt.f64 (sin.f64 B)))))
32.4b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
33.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
26.7b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
13.4b
(-.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))))
13.4b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 2 x (fma.f64 F F 2)) -1/4))) (/.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 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
26.7b
(-.f64 (/.f64 (*.f64 F (/.f64 1 F)) (sin.f64 B)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 11122 to 6300 computations (43.4% saved)

regimes1.7s (14.5%)

Accuracy

Total 0.2b remaining (77.7%)

Threshold costs 0.2b (77.7%)

Counts
235 → 3
Compiler

Compiled 24808 to 16848 computations (32.1% saved)

bsearch134.0ms (1.2%)

Steps
ItersRangePoint
9
211.5461137538968
134987166.6714017
92747884.29196976
4
-1.0289009727507371e+65
-5.347402030770609e+64
-7.972631119662014e+64
Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03997
15297
27097
39497
410797
511397
611497
711297

end1.0ms (0%)

Compiler

Compiled 67 to 41 computations (38.8% saved)

sample3.8s (33.6%)

Algorithm
intervals
Results
1.7s2235×body1024valid
672.0ms4104×body128valid
562.0ms1118×body512valid
179.0ms538×body256valid
110.0ms660×body128invalid
15.0ms112×body128nan
7.0msbody2048valid
1.0msbody1024invalid
0.0msbody512invalid
Compiler

Compiled 344 to 230 computations (33.1% saved)

Profiling

Loading profile data...