Details

Time bar (total: 13.5s)

analyze808.0ms (6%)

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
25%74.9%0.1%4
25%74.9%0.1%5
37.5%62.4%0.1%6
37.5%62.4%0.1%7
43.7%56.2%0.1%8
43.7%56.2%0.1%9
46.8%53.1%0.1%10
46.8%53.1%0.1%11
48.4%51.5%0.1%12
48.4%51.5%0.1%13
49.2%50.7%0.1%14
Compiler

Compiled 15 to 12 computations (20% saved)

sample3.6s (26.4%)

Results
1.5s2043×body1024valid
947.0ms4641×body128valid
660.0ms1060×body512valid
201.0ms509×body256valid
5.0ms3×body2048valid
Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify30.0ms (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

prune7.0ms (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)

localize15.0ms (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))
✓0.1b
(/.f64 x (tan.f64 B))

series217.0ms (1.6%)

Counts
3 → 52
Calls

3 calls:

102.0ms
(/.f64 x (tan.f64 B))
100.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
14.0ms
(/.f64 1 (sin.f64 B))

rewrite120.0ms (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:

26.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
6.0ms
(/.f64 1 (sin.f64 B))
6.0ms
(/.f64 x (tan.f64 B))

simplify491.0ms (3.6%)

Algorithm
1×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

prune822.0ms (6.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New32713340
Fresh101
Picked101
Done000
Total32913342
Error
0b
Counts
342 → 13
Alt Table
StatusErrorProgram
28.2b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (/.f64 1 (sin.f64 B)) (log.f64 (exp.f64 (/.f64 x (tan.f64 B)))))
31.0b
(exp.f64 (log.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))
7.7b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
27.6b
(-.f64 (/.f64 1 (sin.f64 B)) (cbrt.f64 (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (tan.f64 B) (tan.f64 B)) (tan.f64 B)))))
33.1b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 x (sqrt.f64 (tan.f64 B))) (sqrt.f64 (tan.f64 B))))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
▶0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
30.9b
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
17.7b
(-.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)))
0.6b
(-.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)))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
Compiler

Compiled 12171 to 3874 computations (68.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series206.0ms (1.5%)

Counts
3 → 60
Calls

3 calls:

91.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
84.0ms
(*.f64 x (/.f64 1 (tan.f64 B)))
31.0ms
(/.f64 1 (tan.f64 B))

rewrite30.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64
38×times-frac_binary64
34×*-un-lft-identity_binary64
33×add-cube-cbrt_binary64
16×add-exp-log_binary64
Counts
3 → 115
Calls

3 calls:

9.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
8.0ms
(*.f64 x (/.f64 1 (tan.f64 B)))
3.0ms
(/.f64 1 (tan.f64 B))

simplify231.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
719×fma-neg_binary64
690×fma-def_binary64
330×associate-+l+_binary64
308×associate-*l*_binary64
263×associate-*r*_binary64
Counts
175 → 189
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01782673
14262347
212192210
339532177
446712175
548922175

prune464.0ms (3.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2301231
Fresh21012
Picked011
Done000
Total23212244
Error
0b
Counts
244 → 12
Alt Table
StatusErrorProgram
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (*.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B)))
28.2b
(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
31.5b
(-.f64 (/.f64 1 (sin.f64 B)) (log.f64 (exp.f64 (/.f64 x (tan.f64 B)))))
31.0b
(exp.f64 (log.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))
7.7b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
33.1b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 x (sqrt.f64 (tan.f64 B))) (sqrt.f64 (tan.f64 B))))
✓0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
▶0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
30.9b
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
17.7b
(-.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)))
0.6b
(-.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)))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
Compiler

Compiled 4562 to 2571 computations (43.6% saved)

localize17.0ms (0.1%)

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 1 (sin.f64 B))
✓0.1b
(/.f64 (tan.f64 B) x)
✓0.3b
(/.f64 1 (/.f64 (tan.f64 B) x))

series235.0ms (1.7%)

Counts
3 → 72
Calls

3 calls:

95.0ms
(/.f64 1 (/.f64 (tan.f64 B) x))
84.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
56.0ms
(/.f64 (tan.f64 B) x)

rewrite420.0ms (3.1%)

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:

49.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
7.0ms
(/.f64 1 (/.f64 (tan.f64 B) x))
5.0ms
(/.f64 (tan.f64 B) x)

simplify1.7s (12.5%)

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

prune2.2s (16.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New8471848
Fresh2810
Picked011
Done011
Total84911860
Error
0b
Counts
860 → 11
Alt Table
StatusErrorProgram
▶0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (*.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B)))
31.5b
(-.f64 (/.f64 1 (sin.f64 B)) (log.f64 (exp.f64 (/.f64 x (tan.f64 B)))))
7.4b
(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
31.0b
(exp.f64 (log.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))
7.7b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
33.1b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (/.f64 x (sqrt.f64 (tan.f64 B))) (sqrt.f64 (tan.f64 B))))
✓0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
✓0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
30.9b
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
17.7b
(-.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 (*.f64 x (cos.f64 B)) (sin.f64 B)))
Compiler

Compiled 43594 to 21541 computations (50.6% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series164.0ms (1.2%)

Counts
3 → 72
Calls

3 calls:

68.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (*.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B)))
48.0ms
(*.f64 (*.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B))
48.0ms
(*.f64 x (/.f64 1 (sin.f64 B)))

rewrite57.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64
29×times-frac_binary64
27×*-un-lft-identity_binary64
27×add-exp-log_binary64
26×add-cube-cbrt_binary64
Counts
3 → 108
Calls

3 calls:

17.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (*.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B)))
14.0ms
(*.f64 x (/.f64 1 (sin.f64 B)))
13.0ms
(*.f64 (*.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B))

simplify248.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
873×fma-def_binary64
372×fma-neg_binary64
308×associate-*l/_binary64
238×times-frac_binary64
206×cancel-sign-sub-inv_binary64
Counts
180 → 186
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01882995
14702737
215162443
342932410
449732410
549992410

prune534.0ms (4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New2682270
Fresh448
Picked011
Done022
Total2729281
Error
0b
Counts
281 → 9
Alt Table
StatusErrorProgram
✓0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (*.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B)))
7.4b
(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
7.7b
(/.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 1 (*.f64 x (cos.f64 B))))
✓0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
✓0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
30.9b
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
17.7b
(-.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 (*.f64 x (cos.f64 B))) (sin.f64 B))
Compiler

Compiled 5849 to 2984 computations (49% saved)

regimes617.0ms (4.6%)

Accuracy

Total 0.1b remaining (86.6%)

Threshold costs 0.1b (86.6%)

Counts
103 → 1
Compiler

Compiled 4657 to 3339 computations (28.3% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01016
11616
21816
31916
41816

end237.0ms (1.8%)

Compiler

Compiled 162 to 111 computations (31.5% saved)

Profiling

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