Details

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample260.0ms

Algorithm

intervals

Results

177.0ms	58×	body	2560	valid
50.0ms	86×	body	1280	valid
15.0ms	60×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	9×	body	80	valid

simplify474.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

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: 32.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.8b	(-.f64 x (tan.f64 x))
2.8b	(-.f64 x (sin.f64 x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 78

Calls

3 calls:

9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
6.0ms	(-.f64 x (sin.f64 x))

series46.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
19.0ms	(-.f64 x (tan.f64 x))
14.0ms	(-.f64 x (sin.f64 x))

simplify67.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune52.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0b

Counts

88 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(.f64 (.f64 x x) 9/40)
0.3b	(*.f64 27/2800 (pow.f64 x 4))
14.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 57

Calls

3 calls:

6.0ms	(.f64 (.f64 x x) 9/40)
6.0ms	(*.f64 27/2800 (pow.f64 x 4))
10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

series14.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(.f64 (.f64 x x) 9/40)
5.0ms	(*.f64 27/2800 (pow.f64 x 4))
6.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

simplify29.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4961	578
1	4961	578

prune37.0ms

Filtered

40 candidates to 66 candidates (-65.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	66	4	70

Merged error: 0b

Counts

70 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
2.6b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
2.8b	(-.f64 x (tan.f64 x))
2.8b	(-.f64 x (tan.f64 x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
18×	`distribute-lft-out--_binary64`
16×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
6×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `flip--_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
31.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series55.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
25.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
9.0ms	(-.f64 x (tan.f64 x))
10.0ms	(-.f64 x (tan.f64 x))

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5028	1430

prune37.0ms

Filtered

80 candidates to 103 candidates (-28.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	103	4	107

Merged error: 0b

Counts

107 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

2.8b	(-.f64 x (tan.f64 x))
2.8b	(-.f64 x (tan.f64 x))
2.8b	(-.f64 x (sin.f64 x))
2.8b	(-.f64 x (sin.f64 x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 52

Calls

4 calls:

4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
6.0ms	(-.f64 x (sin.f64 x))

series28.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 x (tan.f64 x))
9.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
5.0ms	(-.f64 x (sin.f64 x))

simplify92.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4847	504
1	4847	504

prune27.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	64	4	68

Merged error: 0b

Counts

68 → 4

regimes50.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.9b

bsearch37.0ms

Steps

Iters	Range		Point
9	0.0011663235205985043	101.24460400143968	1.580616986681567
10	-17451870968834.057	-1.705503789536893e-06	-1.5678631412367456

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	43
1	88	43

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.0s	1594×	body	2560	valid
1.7s	2813×	body	1280	valid
465.0ms	1819×	body	640	valid
166.0ms	944×	body	320	valid
60.0ms	479×	body	160	valid
26.0ms	351×	body	80	valid

Details

analyze1.2s

sample260.0ms

simplify474.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series46.0ms

simplify67.0ms

prune52.0ms

localize8.0ms

rewrite23.0ms

series14.0ms

simplify29.0ms

prune37.0ms

localize9.0ms

rewrite49.0ms

series55.0ms

simplify54.0ms

prune37.0ms

localize10.0ms

rewrite19.0ms

series28.0ms

simplify92.0ms

prune27.0ms

regimes50.0ms

bsearch37.0ms

simplify3.0ms

end0.0ms

sample6.6s

Profiling