Details

Time bar (total: 9.8s)

analyze1.1s (11.6%)

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
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)

sample3.0s (30.2%)

Results
1.5s2409×body1024valid
662.0ms4086×body128valid
472.0ms1168×body512valid
167.0ms590×body256valid
28.0ms181×body128invalid
3.0ms3×body2048valid
3.0ms3×body1024invalid
0.0ms1×body256invalid
Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify14.0ms (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
▶0.1b
(-.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)

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))

series88.0ms (0.9%)

Counts
3 → 52
Calls

3 calls:

41.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
40.0ms
(/.f64 x (tan.f64 B))
7.0ms
(/.f64 1 (sin.f64 B))

rewrite59.0ms (0.6%)

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))
2.0ms
(/.f64 1 (sin.f64 B))

simplify304.0ms (3.1%)

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

prune361.0ms (3.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3319340
Fresh101
Picked101
Done000
Total3339342
Error
0.0b
Counts
342 → 9
Alt Table
StatusErrorProgram
37.5b
(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
33.2b
(/.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))))))
0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
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)))
12.0b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
29.7b
(-.f64 (log1p.f64 (expm1.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)))
0.9b
(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
30.7b
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 12095 to 3804 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 (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))

series63.0ms (0.6%)

Counts
3 → 52
Calls

3 calls:

26.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
21.0ms
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
16.0ms
(/.f64 x (sin.f64 B))

rewrite50.0ms (0.5%)

Algorithm
1×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:

6.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
5.0ms
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
2.0ms
(/.f64 x (sin.f64 B))

simplify148.0ms (1.5%)

Algorithm
1×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

prune170.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2193222
Fresh448
Picked011
Done000
Total2238231
Error
0b
Counts
231 → 8
Alt Table
StatusErrorProgram
12.0b
(/.f64 (*.f64 (sin.f64 B) (-.f64 1 (*.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
12.0b
(/.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 1 (/.f64 (tan.f64 B) x)))
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)))
29.7b
(-.f64 (log1p.f64 (expm1.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)))
0.9b
(+.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) 3) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) 0)
33.3b
(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (*.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
Compiler

Compiled 4834 to 1797 computations (62.8% saved)

localize9.0ms (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))
✓0.2b
(/.f64 (tan.f64 B) x)
✓0.3b
(/.f64 1 (/.f64 (tan.f64 B) x))

series105.0ms (1.1%)

Counts
3 → 72
Calls

3 calls:

41.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
40.0ms
(/.f64 1 (/.f64 (tan.f64 B) x))
24.0ms
(/.f64 (tan.f64 B) x)

rewrite274.0ms (2.8%)

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:

37.0ms
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
4.0ms
(/.f64 1 (/.f64 (tan.f64 B) x))
2.0ms
(/.f64 (tan.f64 B) x)

simplify831.0ms (8.5%)

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

prune957.0ms (9.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New8480848
Fresh066
Picked011
Done011
Total8488856
Error
0b
Counts
856 → 8
Alt Table
StatusErrorProgram
12.0b
(/.f64 (*.f64 (sin.f64 B) (-.f64 1 (*.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
12.0b
(/.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 1 (/.f64 (tan.f64 B) x)))
▶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)))
29.7b
(-.f64 (log1p.f64 (expm1.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)))
0.9b
(+.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) 3) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) 0)
33.3b
(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (*.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
Compiler

Compiled 43573 to 21518 computations (50.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 x (tan.f64 B))
✓0.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B))))
✓0.4b
(cbrt.f64 (/.f64 1 (sin.f64 B)))
✓0.5b
(*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B))))

series605.0ms (6.1%)

Counts
3 → 36
Calls

3 calls:

358.0ms
(*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B))))
240.0ms
(cbrt.f64 (/.f64 1 (sin.f64 B)))
6.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B))))

rewrite51.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
109×cbrt-prod_binary64
95×add-sqr-sqrt_binary64
72×times-frac_binary64
61×*-un-lft-identity_binary64
50×add-cube-cbrt_binary64
Counts
3 → 170
Calls

3 calls:

21.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B))))
12.0ms
(*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B))))
2.0ms
(cbrt.f64 (/.f64 1 (sin.f64 B)))

simplify143.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
674×associate-/r*_binary64
541×fma-def_binary64
539×associate-/l/_binary64
484×unswap-sqr_binary64
269×associate-/r/_binary64
Counts
206 → 239
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01623781
13163394
28203264
316823201
447473201
549643201

prune360.0ms (3.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New3502352
Fresh235
Picked101
Done022
Total3537360
Error
0b
Counts
360 → 7
Alt Table
StatusErrorProgram
12.0b
(/.f64 (*.f64 (sin.f64 B) (-.f64 1 (*.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
12.0b
(/.f64 (-.f64 (tan.f64 B) (*.f64 x (sin.f64 B))) (*.f64 (sin.f64 B) (tan.f64 B)))
0.7b
(-.f64 (/.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (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)))
✓0.2b
(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
12.9b
(-.f64 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (sin.f64 B) 2)) 1/3) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
33.3b
(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (*.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
Compiler

Compiled 10222 to 5961 computations (41.7% saved)

regimes972.0ms (9.9%)

Accuracy

Total 0.1b remaining (85%)

Threshold costs 0.1b (85%)

Counts
245 → 1
Compiler

Compiled 18031 to 12282 computations (31.9% saved)

simplify3.0ms (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

end122.0ms (1.2%)

Compiler

Compiled 167 to 105 computations (37.1% saved)

Profiling

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