Details

analyze411.0ms

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%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample43.0ms

Algorithm

intervals

Results

10.0ms	36×	body	2560	valid
10.0ms	163×	body	80	valid
5.0ms	26×	body	1280	valid
2.0ms	12×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	25×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	11×	body	80	invalid

simplify478.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	713	13
1	713	13

prune4.0ms

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: 35.7b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
16.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
25.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune85.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	10	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	10	102

Merged error: 4.6b

Counts

102 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
2.7b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
8.4b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`associate-/r/_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 126

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
14.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
14.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series141.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
47.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
65.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5022	2592

prune77.0ms

Filtered

105 candidates to 138 candidates (-31.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 4.6b

Counts

148 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 81

Calls

4 calls:

11.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
17.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4871	1374
1	4871	1374

prune53.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Merged error: 4.6b

Counts

101 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
24×	`associate-r_binary64`
20×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `difference-of-squares_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

17.0ms	(.f64 c (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(.f64 c (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4940	1230
1	4940	1230

prune42.0ms

Filtered

70 candidates to 99 candidates (-41.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	99	8	107

Merged error: 4.6b

Counts

107 → 8

regimes200.0ms

Accuracy

94% (1.4b remaining)

Error of 7.1b against oracle of 5.6b and baseline of 29.6b

bsearch82.0ms

Steps

Iters	Range	Point
11	1.5327933279306835e+58	2.9955852661786647e+80	7.145575742995441e+73
8	5.492604020642912e-189	1.1532734588266859e-185	5.57002644027495e-189
8	-2.7286057626802198e+163	-7.411983375304952e+159	-7.574554406152596e+159

Iters

Range

Point

1.5327933279306835e+58

2.9955852661786647e+80

7.145575742995441e+73

5.492604020642912e-189

1.1532734588266859e-185

5.57002644027495e-189

-2.7286057626802198e+163

-7.411983375304952e+159

-7.574554406152596e+159

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	119	55
1	119	55

end0.0ms

sample1.0s

Algorithm

intervals

Results

265.0ms	1091×	body	2560	valid
222.0ms	5149×	body	80	valid
176.0ms	881×	body	1280	valid
69.0ms	437×	body	640	valid
31.0ms	108×	body	5120	valid
30.0ms	764×	body	80	nan
25.0ms	214×	body	320	valid
12.0ms	252×	body	80	invalid
9.0ms	120×	body	160	valid

Details

analyze411.0ms

sample43.0ms

simplify478.0ms

prune4.0ms

localize20.0ms

rewrite37.0ms

series72.0ms

simplify62.0ms

prune85.0ms

localize9.0ms

rewrite46.0ms

series141.0ms

simplify53.0ms

prune77.0ms

localize9.0ms

rewrite31.0ms

series95.0ms

simplify66.0ms

prune53.0ms

localize13.0ms

rewrite38.0ms

series96.0ms

simplify69.0ms

prune42.0ms

regimes200.0ms

bsearch82.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling