Details

Time bar (total: 6.4s)

analyze1.0s (16.3%)

Algorithm
1×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)

sample177.0ms (2.8%)

Algorithm
1×intervals
Results
25.0ms60×body1024valid
14.0ms145×body128valid
7.0ms28×body512valid
5.0ms22×body256valid
1.0ms1×body2048valid
0.0ms1×body128invalid
Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify13.0ms (0.2%)

Algorithm
1×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

prune3.0ms (0.1%)

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
▶0.1b
(-.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)

localize7.0ms (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 x (tan.f64 B))
✓0.1b
(/.f64 1 (sin.f64 B))

series87.0ms (1.4%)

Counts
3 → 52
Calls

3 calls:

41.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
39.0ms
(/.f64 x (tan.f64 B))
7.0ms
(/.f64 1 (sin.f64 B))

rewrite60.0ms (0.9%)

Algorithm
1×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:

17.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
2.0ms
(/.f64 1 (sin.f64 B))
2.0ms
(/.f64 x (tan.f64 B))

simplify354.0ms (5.6%)

Algorithm
1×egg-herbie
Rules
908×fma-def_binary64
454×times-frac_binary64
255×fma-neg_binary64
182×associate-/l/_binary64
153×cancel-sign-sub-inv_binary64
Counts
347 → 336
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
031211199
17497806
217756080
343566080
448286080
549966080
647886080

prune452.0ms (7.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New32610336
Fresh101
Picked101
Done000
Total32810338
Error
0b
Counts
338 → 10
Alt Table
StatusErrorProgram
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)))))
0.8b
(-.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 1 (cbrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
0.2b
(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B))))
20.3b
(-.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)))
27.4b
(/.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 (cos.f64 B)) (sin.f64 B)))
0.6b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 x (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (cbrt.f64 (tan.f64 B))))
34.6b
(/.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))))))
15.6b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
Compiler

Compiled 12087 to 3809 computations (68.5% 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))

series54.0ms (0.9%)

Counts
3 → 35
Calls

3 calls:

25.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
21.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
8.0ms
(*.f64 x (cos.f64 B))

rewrite39.0ms (0.6%)

Algorithm
1×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:

12.0ms
(-.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))

simplify207.0ms (3.3%)

Algorithm
1×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

prune309.0ms (4.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2573260
Fresh369
Picked101
Done000
Total2619270
Error
0b
Counts
270 → 9
Alt Table
StatusErrorProgram
0.8b
(-.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 1 (cbrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
0.2b
(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B))))
▶0.1b
(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
20.3b
(-.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)))
0.2b
(*.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (*.f64 x (cos.f64 B))))
27.4b
(/.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))))
17.7b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 B))) (sqrt.f64 (cos.f64 B))) (sin.f64 B)))
15.6b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
Compiler

Compiled 8562 to 2589 computations (69.8% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series19.0ms (0.3%)

Counts
1 → 24
Calls

1 calls:

19.0ms
(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))

rewrite7.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
9×*-un-lft-identity_binary64
9×times-frac_binary64
9×add-sqr-sqrt_binary64
9×add-cube-cbrt_binary64
3×associate-/r*_binary64
Counts
1 → 32
Calls

1 calls:

5.0ms
(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))

simplify127.0ms (2%)

Algorithm
1×egg-herbie
Rules
406×fma-def_binary64
324×distribute-rgt-in_binary64
312×distribute-lft-in_binary64
299×associate-+l+_binary64
245×fma-neg_binary64
Counts
56 → 49
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01101158
12721083
27981076
328561072
448311072
549971072
649501072

prune73.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New77178
Fresh178
Picked101
Done000
Total79887
Error
0b
Counts
87 → 8
Alt Table
StatusErrorProgram
0.8b
(-.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 1 (cbrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
▶0.2b
(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B))))
20.3b
(-.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)))
0.2b
(*.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (*.f64 x (cos.f64 B))))
17.7b
(/.f64 (-.f64 1 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 B))) (sqrt.f64 (cos.f64 B)))) (sin.f64 B))
27.4b
(/.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))))
15.6b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
Compiler

Compiled 1635 to 823 computations (49.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B))))
0.1b
(/.f64 1 (sin.f64 B))
✓0.1b
(/.f64 1 (tan.f64 B))
✓0.2b
(*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B)))

series135.0ms (2.1%)

Counts
3 → 60
Calls

3 calls:

51.0ms
(/.f64 1 (tan.f64 B))
43.0ms
(*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B)))
41.0ms
(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B))))

rewrite24.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
35×add-sqr-sqrt_binary64
29×times-frac_binary64
29×*-un-lft-identity_binary64
28×add-cube-cbrt_binary64
16×add-exp-log_binary64
Counts
3 → 110
Calls

3 calls:

9.0ms
(*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B)))
6.0ms
(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B))))
3.0ms
(/.f64 1 (tan.f64 B))

simplify87.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
677×fma-def_binary64
421×fma-neg_binary64
335×associate-+l+_binary64
248×times-frac_binary64
238×associate-+r+_binary64
Counts
170 → 175
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01692178
14542027
213852008
344252008
451082008

prune201.0ms (3.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2170217
Fresh077
Picked011
Done000
Total2178225
Error
0b
Counts
225 → 8
Alt Table
StatusErrorProgram
0.8b
(-.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 1 (cbrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
✓0.2b
(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B))))
20.3b
(-.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)))
0.2b
(*.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (*.f64 x (cos.f64 B))))
17.7b
(/.f64 (-.f64 1 (*.f64 (*.f64 x (sqrt.f64 (cos.f64 B))) (sqrt.f64 (cos.f64 B)))) (sin.f64 B))
27.4b
(/.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))))
15.6b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
Compiler

Compiled 4065 to 2149 computations (47.1% saved)

regimes550.0ms (8.7%)

Accuracy

Total 0.1b remaining (80.6%)

Threshold costs 0.1b (80.6%)

Counts
156 → 1
Compiler

Compiled 7636 to 5250 computations (31.2% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
11514
22014
32414
42714
52814
62614

end1.0ms (0%)

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample2.3s (36.2%)

Algorithm
1×intervals
Results
1.1s2257×body1024valid
416.0ms4049×body128valid
305.0ms1119×body512valid
110.0ms571×body256valid
16.0ms162×body128invalid
3.0ms4×body2048valid
1.0ms2×body512invalid
0.0ms1×body1024invalid
Compiler

Compiled 170 to 115 computations (32.4% saved)

Profiling

Loading profile data...