Details

analyze16.7s

Algorithm

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0%	0.2%	99.8%	3
0%	0.2%	99.8%	4
0%	0.2%	99.8%	5
0%	0.2%	99.8%	6
0%	0.2%	99.8%	7
0%	0.2%	99.8%	8
0%	0.2%	99.8%	9
0%	0.2%	99.8%	10
0%	0.2%	99.8%	11
0%	0.2%	99.8%	12
0%	0.2%	99.8%	13
0%	0.2%	99.8%	14

sample114.0ms

Algorithm

intervals

Results

59.0ms	118×	body	1280	valid
18.0ms	256×	pre	80	true
18.0ms	74×	body	640	valid
3.0ms	17×	body	320	valid
2.0ms	36×	body	80	valid
1.0ms	11×	body	160	valid

simplify501.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	187	14
1	187	14

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.4b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
0.1b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
4.5b	(tan.f64 (+.f64 y z))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`tan-quot_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`tan-sum_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `flip3--_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

3 → 40

Calls

3 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
13.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
6.0ms	(tan.f64 (+.f64 y z))

series409.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
175.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
82.0ms	(tan.f64 (+.f64 y z))

simplify80.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4975	890
1	4975	890

prune53.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Merged error: 0.1b

Counts

50 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
0.1b	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
0.2b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
0.3b	(*.f64 (tan.f64 y) (tan.f64 z))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
11×	`add-log-exp_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`tan-quot_binary64`
6×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `associate-+r-_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `frac-add_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

9.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
16.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

series1.5s

Counts

4 → 12

Calls

4 calls:

276.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
542.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
549.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
101.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify94.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5260	3074

prune114.0ms

Filtered

74 candidates to 100 candidates (-35.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	99	9	108

Merged error: 0.0b

Counts

108 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a)))
0.2b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a))
0.2b	(/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y))
0.2b	(*.f64 (tan.f64 z) (sin.f64 y))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`
4×	`times-frac_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `tan-quot_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `associate-+r-_binary64` `flip3--_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64` `frac-sub_binary64` `-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

19.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a)))
19.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a))
6.0ms	(/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y))
6.0ms	(*.f64 (tan.f64 z) (sin.f64 y))

series1.3s

Counts

4 → 12

Calls

4 calls:

569.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a)))
583.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a))
104.0ms	(/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y))
72.0ms	(*.f64 (tan.f64 z) (sin.f64 y))

simplify95.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4969	2412
1	4969	2412

prune79.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 0.0b

Counts

93 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (tan.f64 y) (tan.f64 z))
0.3b	(*.f64 (tan.f64 y) (tan.f64 z))
0.3b	(*.f64 (tan.f64 y) (tan.f64 z))
0.3b	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`tan-quot_binary64`
13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `frac-times_binary64` `associate-l/_binary64`
3×	`pow-unpow_binary64` `cube-div_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
2×	`pow-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 88

Calls

4 calls:

5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
8.0ms	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)

series492.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
102.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
100.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
189.0ms	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)

simplify59.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5303	1226

prune112.0ms

Filtered

69 candidates to 100 candidates (-44.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	100	9	109

Merged error: 0.0b

Counts

109 → 9

regimes249.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	34
1	63	34

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.6s	3902×	body	1280	valid
533.0ms	8000×	pre	80	true
495.0ms	2069×	body	640	valid
115.0ms	708×	body	320	valid
52.0ms	1074×	body	80	valid
28.0ms	247×	body	160	valid

Details

analyze16.7s

sample114.0ms

simplify501.0ms

prune3.0ms

localize12.0ms

rewrite29.0ms

series409.0ms

simplify80.0ms

prune53.0ms

localize16.0ms

rewrite47.0ms

series1.5s

simplify94.0ms

prune114.0ms

localize20.0ms

rewrite52.0ms

series1.3s

simplify95.0ms

prune79.0ms

localize23.0ms

rewrite26.0ms

series492.0ms

simplify59.0ms

prune112.0ms

regimes249.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample3.2s

Profiling