Details

analyze778.0ms

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

sample85.0ms

Algorithm

intervals

Results

35.0ms	89×	body	1280	valid
20.0ms	74×	body	640	valid
16.0ms	19×	body	2560	valid
4.0ms	26×	body	320	valid
1.0ms	34×	body	80	valid
1.0ms	14×	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

prune2.0ms

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: 38.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.5b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.6b	(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))

series42.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
16.0ms	(tan.f64 (+.f64 x eps))

simplify53.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune37.0ms

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: 13.6b

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))
3.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite28.0ms

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:

4.0ms	(-.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))

series174.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
21.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
22.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
106.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify46.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4984	965
1	4984	965

prune87.0ms

Filtered

55 candidates to 72 candidates (-30.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	60	12	72
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	65	15	80

Merged error: 13.4b

Counts

80 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
3.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)))) (tan.f64 x))
25.9b	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`tan-quot_binary64`
10×	`*-un-lft-identity_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-cube-cbrt_binary64` `cbrt-prod_binary64`
6×	`add-log-exp_binary64` `cube-div_binary64`
3×	`cbrt-div_binary64` `pow-unpow_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-l_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `cube-prod_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `diff-log_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
24.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)))) (tan.f64 x))
5.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))

series199.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
42.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
111.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)))) (tan.f64 x))
23.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4951	1093
1	4951	1093

prune75.0ms

Filtered

65 candidates to 93 candidates (-43.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	93	15	108

Merged error: 13.4b

Counts

108 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) 3)
0.4b	(pow.f64 (cos.f64 eps) 3)
3.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) 3) (pow.f64 (cos.f64 eps) 3))))) (tan.f64 x))
25.9b	(cbrt.f64 (/.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) 3) (pow.f64 (cos.f64 eps) 3)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

100×	`cbrt-prod_binary64`
97×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
40×	`unpow-prod-down_binary64` `cube-prod_binary64`
22×	`sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64`
3×	`pow-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `difference-of-squares_binary64` `tan-quot_binary64`
1×	`cbrt-div_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `cube-div_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `flip--_binary64` `frac-sub_binary64` `associate-*l/_binary64`

Counts

4 → 170

Calls

4 calls:

5.0ms	(pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) 3)
3.0ms	(pow.f64 (cos.f64 eps) 3)
65.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) 3) (pow.f64 (cos.f64 eps) 3))))) (tan.f64 x))
9.0ms	(cbrt.f64 (/.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) 3) (pow.f64 (cos.f64 eps) 3)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) 3)
5.0ms	(pow.f64 (cos.f64 eps) 3)
110.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) 3) (pow.f64 (cos.f64 eps) 3))))) (tan.f64 x))
24.0ms	(cbrt.f64 (/.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) 3) (pow.f64 (cos.f64 eps) 3)))

simplify59.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5173	3196

prune76.0ms

Filtered

89 candidates to 182 candidates (-104.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	181	16	197

Merged error: 13.4b

Counts

197 → 16

regimes155.0ms

Accuracy

87.2% (1.0b remaining)

Error of 15.8b against oracle of 14.8b and baseline of 22.8b

bsearch77.0ms

Steps

Iters	Range		Point
7	1.4887492491719244e-80	1.7619768345778143e-78	5.0970138075245553e-79
10	-1.619396985955069e-46	-3.2701513056628557e-64	-2.8218801393676676e-60

simplify10.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	375	65
1	375	65

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3299×	body	1280	valid
594.0ms	676×	body	2560	valid
407.0ms	1859×	body	640	valid
105.0ms	743×	body	320	valid
49.0ms	1077×	body	80	valid
33.0ms	346×	body	160	valid

Details

analyze778.0ms

sample85.0ms

simplify7.0ms

prune2.0ms

localize8.0ms

rewrite12.0ms

series42.0ms

simplify53.0ms

prune37.0ms

localize11.0ms

rewrite28.0ms

series174.0ms

simplify46.0ms

prune87.0ms

localize17.0ms

rewrite42.0ms

series199.0ms

simplify43.0ms

prune75.0ms

localize21.0ms

rewrite89.0ms

series167.0ms

simplify59.0ms

prune76.0ms

regimes155.0ms

bsearch77.0ms

simplify10.0ms

end0.0ms

sample2.7s

Profiling