Details

Time bar (total: 7.8s)

analyze1.0s (12.8%)

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
12.5%87.4%0.1%6
18.7%81.2%0.1%7
25%73.4%1.7%8
28.1%68.7%3.2%9
31.2%62.8%6%10
32.8%60.1%7.1%11
34.3%56.7%9%12
35.1%55.2%9.7%13
35.9%53.4%10.7%14
Compiler

Compiled 15 to 12 computations (20% saved)

sample236.0ms (3%)

Algorithm
intervals
Results
125.0ms72×body1024valid
13.0ms133×body128valid
9.0ms36×body512valid
2.0ms14×body256valid
1.0ms12×body128invalid
1.0msbody2048valid
Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify14.0ms (0.2%)

Algorithm
egg-herbie
Rules
105×fma-def_binary64
66×fma-neg_binary64
27×cancel-sign-sub-inv_binary64
19×sub-neg_binary64
11×associate-/l*_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01119
12414
24814
38114
412214
516814
618714
722914
822614
924414
1024114
1121614

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.2b
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
Compiler

Compiled 73 to 53 computations (27.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.1b
(/.f64 1 (sin.f64 B))
0.2b
(/.f64 x (tan.f64 B))

series86.0ms (1.1%)

Counts
3 → 52
Calls

3 calls:

41.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
38.0ms
(/.f64 x (tan.f64 B))
6.0ms
(/.f64 1 (sin.f64 B))

rewrite90.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
288×times-frac_binary64
239×add-sqr-sqrt_binary64
231×*-un-lft-identity_binary64
222×add-cube-cbrt_binary64
182×prod-diff_binary64
Counts
3 → 295
Calls

3 calls:

45.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
3.0ms
(/.f64 x (tan.f64 B))
2.0ms
(/.f64 1 (sin.f64 B))

simplify307.0ms (3.9%)

Algorithm
egg-herbie
Rules
908×fma-def_binary64
453×times-frac_binary64
255×fma-neg_binary64
182×associate-/l/_binary64
153×cancel-sign-sub-inv_binary64
Counts
347 → 340
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
031211199
17497806
217756080
343566080
448286080
549966080
647886080

prune565.0ms (7.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New32911340
Fresh101
Picked101
Done000
Total33111342
Error
0.0b
Counts
342 → 11
Alt Table
StatusErrorProgram
32.8b
(-.f64 (fma.f64 (pow.f64 B 5) 31/15120 (fma.f64 (pow.f64 B 3) 7/360 (fma.f64 B 1/6 (/.f64 1 B)))) (/.f64 x (tan.f64 B)))
18.3b
(-.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
34.1b
(/.f64 (-.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (+.f64 (*.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B))) (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))))
0.6b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 x (cbrt.f64 (tan.f64 B)))))
28.7b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
0.6b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
27.0b
(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
0.7b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
13.0b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
Compiler

Compiled 12237 to 3884 computations (68.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
0.1b
(*.f64 x (cos.f64 B))
0.1b
(/.f64 1 (sin.f64 B))
0.2b
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

series55.0ms (0.7%)

Counts
3 → 35
Calls

3 calls:

25.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
22.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
7.0ms
(*.f64 x (cos.f64 B))

rewrite43.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
120×times-frac_binary64
100×add-sqr-sqrt_binary64
98×*-un-lft-identity_binary64
91×prod-diff_binary64
91×add-cube-cbrt_binary64
Counts
3 → 177
Calls

3 calls:

11.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
4.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
3.0ms
(*.f64 x (cos.f64 B))

simplify271.0ms (3.5%)

Algorithm
egg-herbie
Rules
319×associate-/l/_binary64
318×fma-neg_binary64
292×associate-/r*_binary64
287×cancel-sign-sub-inv_binary64
231×distribute-rgt-neg-in_binary64
Counts
212 → 218
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02526796
15915509
220824195
344074192
449364192
549904192
648564192

prune390.0ms (5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2573260
Fresh3710
Picked011
Done000
Total26011271
Error
0.0b
Counts
271 → 11
Alt Table
StatusErrorProgram
0.6b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B)))))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
18.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 B))) (sqrt.f64 (cos.f64 B))) (sin.f64 B)))
18.3b
(-.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
34.2b
(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B))) (*.f64 (/.f64 (*.f64 x (cos.f64 B)) (*.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (*.f64 x (cos.f64 B)) 1))))
28.7b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
27.0b
(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
0.7b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
34.1b
(/.f64 (-.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (+.f64 (*.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B))) (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))))
13.0b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
Compiler

Compiled 8756 to 2682 computations (69.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
0.1b
(/.f64 x (sin.f64 B))
0.1b
(/.f64 1 (sin.f64 B))
0.2b
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

series65.0ms (0.8%)

Counts
3 → 52
Calls

3 calls:

27.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
22.0ms
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
16.0ms
(/.f64 x (sin.f64 B))

rewrite25.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64
37×times-frac_binary64
33×*-un-lft-identity_binary64
33×add-cube-cbrt_binary64
13×fma-neg_binary64
Counts
3 → 105
Calls

3 calls:

9.0ms
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
7.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
2.0ms
(/.f64 x (sin.f64 B))

simplify186.0ms (2.4%)

Algorithm
egg-herbie
Rules
673×fma-def_binary64
414×fma-neg_binary64
372×associate-/l*_binary64
342×times-frac_binary64
338×associate-*l/_binary64
Counts
157 → 180
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01942974
14762749
214262544
343282511
449452511
549952511
649202511

prune316.0ms (4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2220222
Fresh099
Picked011
Done011
Total22211233
Error
0.0b
Counts
233 → 11
Alt Table
StatusErrorProgram
0.6b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B)))))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
18.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 B))) (sqrt.f64 (cos.f64 B))) (sin.f64 B)))
18.3b
(-.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
34.2b
(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B))) (*.f64 (/.f64 (*.f64 x (cos.f64 B)) (*.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (*.f64 x (cos.f64 B)) 1))))
28.7b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
27.0b
(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
0.7b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
34.1b
(/.f64 (-.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (+.f64 (*.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B))) (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))))
13.0b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
Compiler

Compiled 5020 to 1890 computations (62.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B)))
0.3b
(*.f64 (/.f64 x (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B))))
0.5b
(*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))
0.6b
(cbrt.f64 (sin.f64 B))

series743.0ms (9.5%)

Counts
4 → 60
Calls

4 calls:

254.0ms
(/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B)))
252.0ms
(*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))
214.0ms
(cbrt.f64 (sin.f64 B))
22.0ms
(*.f64 (/.f64 x (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B))))

rewrite38.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt_binary64
46×times-frac_binary64
43×*-un-lft-identity_binary64
43×add-cube-cbrt_binary64
42×cbrt-prod_binary64
Counts
4 → 157
Calls

4 calls:

14.0ms
(*.f64 (/.f64 x (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B))))
5.0ms
(*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))
5.0ms
(/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B)))
1.0ms
(cbrt.f64 (sin.f64 B))

simplify200.0ms (2.5%)

Algorithm
egg-herbie
Rules
484×fma-neg_binary64
271×fma-def_binary64
265×associate-/r/_binary64
260×sub-neg_binary64
189×sqr-pow_binary64
Counts
217 → 259
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02654523
16803356
224703265
338463197
449073197
548823197

prune351.0ms (4.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New3070307
Fresh088
Picked011
Done022
Total30711318
Error
0.0b
Counts
318 → 11
Alt Table
StatusErrorProgram
0.6b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 (cos.f64 B) (cbrt.f64 (sin.f64 B)))))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
18.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 B))) (sqrt.f64 (cos.f64 B))) (sin.f64 B)))
18.3b
(-.f64 (cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
34.2b
(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B))) (*.f64 (/.f64 (*.f64 x (cos.f64 B)) (*.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (*.f64 x (cos.f64 B)) 1))))
28.7b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
27.0b
(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
0.7b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
34.1b
(/.f64 (-.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (+.f64 (*.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B))) (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))))
13.0b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
Compiler

Compiled 8877 to 2753 computations (69% saved)

regimes590.0ms (7.5%)

Accuracy

Total 0.2b remaining (88.5%)

Threshold costs 0.2b (88.5%)

Counts
148 → 1
Compiler

Compiled 8092 to 5403 computations (33.2% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11714
22614
33214
43614
53714
63614

end1.0ms (0%)

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample2.2s (28.4%)

Algorithm
intervals
Results
964.0ms2228×body1024valid
387.0ms4035×body128valid
305.0ms1166×body512valid
100.0ms562×body256valid
17.0ms185×body128invalid
8.0msbody2048valid
0.0msbody512invalid
0.0msbody256invalid
Compiler

Compiled 288 to 175 computations (39.2% saved)

Profiling

Loading profile data...