Details

analyze774.0ms

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

sample97.0ms

Algorithm

intervals

Results

46.0ms	104×	body	1280	valid
23.0ms	28×	body	2560	valid
12.0ms	55×	body	640	valid
6.0ms	20×	body	320	valid
2.0ms	40×	body	80	valid
1.0ms	9×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	73	11
1	73	11

prune1.0ms

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: 36.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.6b	(tan.f64 (+.f64 x eps))

rewrite11.0ms

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))

series170.0ms

Counts

2 → 6

Calls

2 calls:

108.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
61.0ms	(tan.f64 (+.f64 x eps))

simplify104.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4830	529
1	4830	529

prune34.0ms

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: 16.2b

Counts

31 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.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))
1.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`tan-quot_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `+-commutative_binary64` `flip-+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 60

Calls

4 calls:

3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
12.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series799.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
97.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
114.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
473.0ms	(-.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

72 → 72

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4977	1570
1	4977	1570

prune86.0ms

Filtered

55 candidates to 72 candidates (-30.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	61	11	72
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	64	16	80

Merged error: 16.1b

Counts

80 → 16

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 eps) (sin.f64 x))
1.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64`
5×	`tan-quot_binary64`
4×	`times-frac_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `frac-add_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 69

Calls

4 calls:

4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))
18.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))

series760.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
105.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
64.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))
499.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))

simplify88.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5027	1790

prune79.0ms

Filtered

61 candidates to 81 candidates (-32.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	81	16	97

Merged error: 16.1b

Counts

97 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
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)))
1.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `tan-quot_binary64`
2×	`difference-of-squares_binary64` `sin-mult_binary64` `times-frac_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cos-mult_binary64` `frac-add_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 70

Calls

4 calls:

4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
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)))
18.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

series729.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
39.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
109.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
487.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

simplify91.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5026	1982

prune71.0ms

Filtered

59 candidates to 82 candidates (-39.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	6	8	14
Picked	1	0	1
Done	0	1	1
Total	88	10	98

Merged error: 14.0b

Counts

98 → 10

regimes49.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	70
1	59	70

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3256×	body	1280	valid
556.0ms	640×	body	2560	valid
403.0ms	1870×	body	640	valid
108.0ms	750×	body	320	valid
49.0ms	1134×	body	80	valid
36.0ms	350×	body	160	valid

Details

analyze774.0ms

sample97.0ms

simplify15.0ms

prune1.0ms

localize8.0ms

rewrite11.0ms

series170.0ms

simplify104.0ms

prune34.0ms

localize11.0ms

rewrite27.0ms

series799.0ms

simplify54.0ms

prune86.0ms

localize18.0ms

rewrite35.0ms

series760.0ms

simplify88.0ms

prune79.0ms

localize20.0ms

rewrite37.0ms

series729.0ms

simplify91.0ms

prune71.0ms

regimes49.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample2.6s

Profiling