Details

Time bar (total: 18.7s)

analyze1.0s (5.5%)

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)

sample200.0ms (1.1%)

Algorithm
1×intervals
Results
27.0ms66×body1024valid
13.0ms137×body128valid
9.0ms35×body512valid
3.0ms18×body256valid
1.0ms6×body128invalid
Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify15.0ms (0.1%)

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

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%)

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))

series95.0ms (0.5%)

Counts
3 → 52
Calls

3 calls:

50.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
39.0ms
(/.f64 x (tan.f64 B))
6.0ms
(/.f64 1 (sin.f64 B))

rewrite61.0ms (0.3%)

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:

16.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
3.0ms
(/.f64 x (tan.f64 B))
3.0ms
(/.f64 1 (sin.f64 B))

simplify311.0ms (1.7%)

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

prune493.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3279336
Fresh101
Picked101
Done000
Total3299338
Error
0.0b
Counts
338 → 9
Alt Table
StatusErrorProgram
▶0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
0.2b
(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 x) (/.f64 1 (tan.f64 B))))
26.4b
(/.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))))
26.0b
(-.f64 (/.f64 1 (sin.f64 B)) (fma.f64 (*.f64 B x) -1/3 (/.f64 x B)))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
11.3b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
17.8b
(-.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)))
0.8b
(-.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)))
30.5b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 11969 to 3765 computations (68.5% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

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

series113.0ms (0.6%)

Counts
3 → 72
Calls

3 calls:

43.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
39.0ms
(/.f64 1 (/.f64 (tan.f64 B) x))
30.0ms
(/.f64 (tan.f64 B) x)

rewrite213.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
1447×times-frac_binary64
907×add-sqr-sqrt_binary64
881×*-un-lft-identity_binary64
860×add-cube-cbrt_binary64
572×prod-diff_binary64
Counts
3 → 773
Calls

3 calls:

41.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
4.0ms
(/.f64 1 (/.f64 (tan.f64 B) x))
3.0ms
(/.f64 (tan.f64 B) x)

simplify1.0s (5.5%)

Algorithm
1×egg-herbie
Rules
410×fma-neg_binary64
391×cancel-sign-sub-inv_binary64
275×associate-/l/_binary64
265×distribute-rgt-out_binary64
204×distribute-rgt-neg-in_binary64
Counts
845 → 806
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037335425
185721208
2252215811
3441015811
4463615811
5496315811
6463015811

prune918.0ms (4.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New8462848
Fresh178
Picked101
Done000
Total8489857
Error
0.0b
Counts
857 → 9
Alt Table
StatusErrorProgram
▶0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
7.1b
(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
26.4b
(/.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))))
26.0b
(-.f64 (/.f64 1 (sin.f64 B)) (fma.f64 (*.f64 B x) -1/3 (/.f64 x B)))
0.3b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x)))
11.3b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
17.8b
(-.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)))
0.8b
(-.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)))
30.5b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 43604 to 21543 computations (50.6% saved)

localize8.0ms (0%)

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))

series66.0ms (0.4%)

Counts
3 → 35
Calls

3 calls:

32.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
26.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
8.0ms
(*.f64 x (cos.f64 B))

rewrite41.0ms (0.2%)

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)))
6.0ms
(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
3.0ms
(*.f64 x (cos.f64 B))

simplify224.0ms (1.2%)

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

prune215.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2600260
Fresh088
Picked011
Done000
Total2609269
Error
0.0b
Counts
269 → 9
Alt Table
StatusErrorProgram
✓0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
7.1b
(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
26.4b
(/.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))))
26.0b
(-.f64 (/.f64 1 (sin.f64 B)) (fma.f64 (*.f64 B x) -1/3 (/.f64 x B)))
▶0.3b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x)))
11.3b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
17.8b
(-.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)))
0.8b
(-.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)))
30.5b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 8560 to 2586 computations (69.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x)))
0.1b
(/.f64 1 (sin.f64 B))
✓0.2b
(/.f64 1 (tan.f64 B))
✓0.4b
(/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x))

series99.0ms (0.5%)

Counts
3 → 60
Calls

3 calls:

42.0ms
(/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x))
41.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x)))
16.0ms
(/.f64 1 (tan.f64 B))

rewrite1.8s (9.8%)

Algorithm
1×rewrite-expression-head
Rules
8185×times-frac_binary64
4305×add-sqr-sqrt_binary64
4233×*-un-lft-identity_binary64
4190×add-cube-cbrt_binary64
2431×prod-diff_binary64
Counts
3 → 2958
Calls

3 calls:

243.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x)))
9.0ms
(/.f64 (/.f64 1 (tan.f64 B)) (/.f64 1 x))
3.0ms
(/.f64 1 (tan.f64 B))

simplify4.6s (24.5%)

Algorithm
1×egg-herbie
Rules
624×fma-def_binary64
433×associate-*r/_binary64
358×associate-*l/_binary64
204×fma-udef_binary64
186×associate-*r*_binary64
Counts
3018 → 2592
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0630306209
11660148868
24336148862
34992148862

prune4.1s (21.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New263312634
Fresh167
Picked101
Done011
Total263582643
Error
0b
Counts
2643 → 8
Alt Table
StatusErrorProgram
0.3b
(/.f64 (-.f64 (*.f64 1 (/.f64 1 x)) (*.f64 (sin.f64 B) (/.f64 1 (tan.f64 B)))) (*.f64 (sin.f64 B) (/.f64 1 x)))
26.4b
(/.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))))
26.0b
(-.f64 (/.f64 1 (sin.f64 B)) (fma.f64 (*.f64 B x) -1/3 (/.f64 x B)))
✓0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
11.3b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
17.8b
(-.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)))
0.8b
(-.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)))
30.5b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 191735 to 122396 computations (36.2% saved)

regimes791.0ms (4.2%)

Accuracy

Total 0.1b remaining (82.4%)

Threshold costs 0.1b (82.4%)

Counts
185 → 1
Compiler

Compiled 9142 to 6729 computations (26.4% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
3×+-commutative_binary64
3×sub-neg_binary64
2×*-commutative_binary64
2×distribute-rgt-neg-in_binary64
2×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01014
11914
22514
32814
43114
53214
63014

end1.0ms (0%)

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample2.2s (11.9%)

Algorithm
1×intervals
Results
965.0ms2286×body1024valid
411.0ms3940×body128valid
322.0ms1161×body512valid
108.0ms606×body256valid
15.0ms176×body128invalid
6.0ms7×body2048valid
1.0ms2×body1024invalid
0.0ms1×body512invalid
Compiler

Compiled 180 to 123 computations (31.7% saved)

Profiling

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