Details

analyze777.0ms

Algorithm

Search

True	Other	False	Iter
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
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample94.0ms

Algorithm

intervals

Results

44.0ms	112×	body	1280	valid
25.0ms	29×	body	2560	valid
12.0ms	55×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	36×	body	80	valid
0.0ms	4×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune6.0ms

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: 38.2b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.9b	(tan.f64 (+.f64 x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

series47.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
19.0ms	(tan.f64 (+.f64 x eps))

simplify69.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5307	332

prune50.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 17.3b

Counts

31 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
1.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series259.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
29.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
29.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
128.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify54.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5109	1560

prune134.0ms

Filtered

73 candidates to 97 candidates (-32.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	13	97
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	89	16	105

Merged error: 17.2b

Counts

105 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
1.6b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))))) (/.f64 (sin.f64 x) (cos.f64 x)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
8×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `sin-mult_binary64` `times-frac_binary64` `frac-sub_binary64`
2×	`associate-/l/_binary64` `associate-/r_binary64` `diff-log_binary64` `cos-mult_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `frac-add_binary64` `unswap-sqr_binary64` `flip--_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
9.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
9.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
26.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))))) (/.f64 (sin.f64 x) (cos.f64 x)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
30.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
32.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
139.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))))) (/.f64 (sin.f64 x) (cos.f64 x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4981	2341
1	4981	2341

prune138.0ms

Filtered

66 candidates to 97 candidates (-47.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	88	9	97
Fresh	11	4	15
Picked	1	0	1
Done	0	0	0
Total	100	13	113

Merged error: 14.8b

Counts

113 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
2.4b	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`times-frac_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `sin-mult_binary64` `difference-of-sqr--1_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `associate-/r_binary64` `distribute-lft-out_binary64` `cos-mult_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
8.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
9.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
15.0ms	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)

series116.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
30.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
30.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
42.0ms	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)

simplify47.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4983	1230
1	4983	1230

prune96.0ms

Filtered

60 candidates to 93 candidates (-55.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	92	14	106

Merged error: 14.7b

Counts

106 → 14

regimes183.0ms

Accuracy

0% (1.2b remaining)

Error of 13.8b against oracle of 12.6b and baseline of 13.8b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	134
1	61	134

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3328×	body	1280	valid
555.0ms	640×	body	2560	valid
417.0ms	1848×	body	640	valid
115.0ms	749×	body	320	valid
52.0ms	1114×	body	80	valid
31.0ms	321×	body	160	valid

Details

analyze777.0ms

sample94.0ms

simplify7.0ms

prune6.0ms

localize9.0ms

rewrite12.0ms

series47.0ms

simplify69.0ms

prune50.0ms

localize11.0ms

rewrite36.0ms

series259.0ms

simplify54.0ms

prune134.0ms

localize25.0ms

rewrite52.0ms

series216.0ms

simplify59.0ms

prune138.0ms

localize23.0ms

rewrite39.0ms

series116.0ms

simplify47.0ms

prune96.0ms

regimes183.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.7s

Profiling