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

sample148.0ms

Algorithm

intervals

Results

57.0ms	53×	body	1280	valid
28.0ms	43×	body	640	valid
17.0ms	116×	body	80	valid
16.0ms	35×	body	320	valid
4.0ms	23×	body	80	invalid
3.0ms	9×	body	160	valid
0.0ms	2×	body	80	nan

simplify567.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5518	32

prune34.0ms

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: 13.1b

Counts

2 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
4.8b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite38.0ms

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))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series380.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/.f64 F (sin.f64 B))
120.0ms	(/.f64 x (tan.f64 B))
140.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
70.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify104.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5056	2519

prune629.0ms

Filtered

100 candidates to 127 candidates (-27.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	111	16	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	16	129

Merged error: 0.0b

Counts

129 → 16

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.7b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
17.0b	(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))
11.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
12.0ms	(/.f64 (.f64 F (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)

series350.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/.f64 x (tan.f64 B))
47.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
138.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
49.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify77.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4960	2141
1	4960	2141

prune518.0ms

Filtered

76 candidates to 105 candidates (-38.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	106	15	121

Merged error: 0.0b

Counts

121 → 15

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.4b	(/.f64 1 (/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
0.6b	(/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)))
17.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log_binary64`
36×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
17×	`div-exp_binary64`
12×	`prod-exp_binary64`
8×	`associate-/r*_binary64`
7×	`associate-r_binary64` `cbrt-undiv_binary64` `unpow-prod-down_binary64`
6×	`pow1_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`pow-to-exp_binary64` `rec-exp_binary64` `pow-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 → 122

Calls

4 calls:

11.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
13.0ms	(/.f64 1 (/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
11.0ms	(/.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)

series404.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
162.0ms	(/.f64 1 (/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
142.0ms	(/.f64 (sin.f64 B) (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)))
52.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify86.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5029	3636

prune570.0ms

Filtered

88 candidates to 134 candidates (-52.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	134	15	149

Merged error: 0.0b

Counts

149 → 15

localize29.0ms

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)))
0.3b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
17.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite49.0ms

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))
21.0ms	(.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)

series471.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/.f64 x (tan.f64 B))
132.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
115.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
49.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify106.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5190	3917

prune752.0ms

Filtered

115 candidates to 150 candidates (-30.4%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	149	16	165

Merged error: 0.0b

Counts

165 → 16

regimes560.0ms

Accuracy

97.7% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.4b

bsearch130.0ms

Steps

Iters	Range		Point
8	2201574127954719/18014398509481984	4126920244666395/549755813888	7379.805553361057
3	-1152543570298809/2147483648	-7088846092816121/17179869184	-508391.5278730379

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	129	105
1	129	105

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	1729×	body	1280	valid
870.0ms	1413×	body	640	valid
555.0ms	3807×	body	80	valid
315.0ms	728×	body	320	valid
100.0ms	684×	body	80	invalid
93.0ms	323×	body	160	valid
12.0ms	114×	body	80	nan
1.0ms	1×	body	640	invalid
0.0ms	1×	body	320	invalid

Details

analyze1.8s

sample148.0ms

simplify567.0ms

prune34.0ms

localize32.0ms

rewrite38.0ms

series380.0ms

simplify104.0ms

prune629.0ms

localize38.0ms

rewrite38.0ms

series350.0ms

simplify77.0ms

prune518.0ms

localize41.0ms

rewrite49.0ms

series404.0ms

simplify86.0ms

prune570.0ms

localize29.0ms

rewrite49.0ms

series471.0ms

simplify106.0ms

prune752.0ms

regimes560.0ms

bsearch130.0ms

simplify5.0ms

end0.0ms

sample3.9s

Profiling