Details

analyze1.8s

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample132.0ms

Algorithm

intervals

Results

54.0ms	57×	body	1280	valid
25.0ms	133×	body	80	valid
23.0ms	35×	body	640	valid
11.0ms	23×	body	320	valid
3.0ms	8×	body	160	valid
2.0ms	10×	body	80	invalid
1.0ms	5×	body	80	nan

simplify707.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (198.0ms)

Iter	Nodes	Cost
0	4665	32
1	4665	32

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 13.0b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
6.2b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

4.0ms	(/.f64 F (sin.f64 B))
4.0ms	(/.f64 x (tan.f64 B))
15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series392.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/.f64 F (sin.f64 B))
124.0ms	(/.f64 x (tan.f64 B))
145.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
65.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify82.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5156	2525

prune174.0ms

Filtered

100 candidates to 127 candidates (-27.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	116	11	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	11	129

Merged error: 0.0b

Counts

129 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `prod-exp_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series329.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/.f64 x (tan.f64 B))
130.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
47.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
47.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify80.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4970	2141
1	4970	2141

prune109.0ms

Filtered

76 candidates to 105 candidates (-38.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	106	10	116

Merged error: 0.0b

Counts

116 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)))
0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.5b	(/.f64 1 (/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
36×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
26×	`div-exp_binary64`
20×	`add-cbrt-cube_binary64`
15×	`prod-exp_binary64`
8×	`associate-/r*_binary64`
7×	`associate-r_binary64` `cbrt-undiv_binary64` `unpow-prod-down_binary64`
6×	`pow-to-exp_binary64` `pow1_binary64` `associate-/l*_binary64` `div-inv_binary64` `pow-exp_binary64`
5×	`1-exp_binary64` `rec-exp_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 127

Calls

4 calls:

12.0ms	(/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)))
11.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
16.0ms	(/.f64 1 (/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series380.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)))
47.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
156.0ms	(/.f64 1 (/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
48.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify109.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4929	3731
1	4929	3731

prune137.0ms

Filtered

88 candidates to 139 candidates (-58.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	139	10	149

Merged error: 0.0b

Counts

149 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
16.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`associate-r_binary64` `unpow-prod-down_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
16.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
11.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series415.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 x (tan.f64 B))
142.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
116.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
47.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify131.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4944	3927
1	4944	3927

prune164.0ms

Filtered

115 candidates to 150 candidates (-30.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	151	9	160

Merged error: 0.0b

Counts

160 → 9

regimes97.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.6b

bsearch176.0ms

Steps

Iters	Range		Point
9	397.7565433842507	3179667635.762545	108858170.1752173
8	-4.1309589443277e+14	-521016154263.7056	-165734231225465.62

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	79	96
1	79	96

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	1673×	body	1280	valid
818.0ms	1342×	body	640	valid
562.0ms	3941×	body	80	valid
296.0ms	699×	body	320	valid
108.0ms	718×	body	80	invalid
101.0ms	345×	body	160	valid
13.0ms	123×	body	80	nan

Details

analyze1.8s

sample132.0ms

simplify707.0ms

prune9.0ms

localize23.0ms

rewrite46.0ms

series392.0ms

simplify82.0ms

prune174.0ms

localize23.0ms

rewrite38.0ms

series329.0ms

simplify80.0ms

prune109.0ms

localize22.0ms

rewrite52.0ms

series380.0ms

simplify109.0ms

prune137.0ms

localize21.0ms

rewrite46.0ms

series415.0ms

simplify131.0ms

prune164.0ms

regimes97.0ms

bsearch176.0ms

simplify4.0ms

end0.0ms

sample3.7s

Profiling