Details

analyze471.0ms

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample46.0ms

Algorithm

intervals

Results

13.0ms	43×	body	2560	valid
8.0ms	34×	body	1280	valid
8.0ms	152×	body	80	valid
3.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	15×	body	80	nan
0.0ms	7×	body	80	invalid
0.0ms	3×	body	160	valid

simplify276.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (273.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 36.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
21.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune132.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 6.5b

Counts

83 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
3.7b	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
10.5b	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac_binary64`
77×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
19×	`distribute-lft-out_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`div-inv_binary64`
3×	`flip3-+_binary64` `div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `flip--_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 → 158

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
16.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
11.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
56.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
72.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
22.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4977	3981
1	4977	3981

prune228.0ms

Filtered

126 candidates to 170 candidates (-34.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	172	8	180

Merged error: 6.5b

Counts

180 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
19.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
21.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify82.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4930	1299
1	4930	1299

prune100.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	83	8	91

Merged error: 6.5b

Counts

91 → 8

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify5.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	3	3
Total	8	8

Merged error: 6.5b

Counts

8 → 8

regimes272.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 30.0b

bsearch77.0ms

Steps

Iters	Range	Point
7	2.225872940459687e+100	2.9814383966772936e+102	2.425599302719474e+102
6	-1.0676346551229214e-298	-1.1179846591094473e-299	-8.299193755122384e-299
8	-6.217592569728448e+112	-1.141697663647829e+110	-2.0801679587946785e+111

Iters

Range

Point

2.225872940459687e+100

2.9814383966772936e+102

2.425599302719474e+102

-1.0676346551229214e-298

-1.1179846591094473e-299

-8.299193755122384e-299

-6.217592569728448e+112

-1.141697663647829e+110

-2.0801679587946785e+111

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	123	61
1	123	61

end0.0ms

sample1.3s

Algorithm

intervals

Results

328.0ms	1087×	body	2560	valid
272.0ms	5080×	body	80	valid
221.0ms	898×	body	1280	valid
96.0ms	491×	body	640	valid
39.0ms	108×	body	5120	valid
37.0ms	244×	body	320	valid
31.0ms	637×	body	80	nan
22.0ms	383×	body	80	invalid
9.0ms	92×	body	160	valid

Details

analyze471.0ms

sample46.0ms

simplify276.0ms

prune10.0ms

localize11.0ms

rewrite33.0ms

series84.0ms

simplify63.0ms

prune132.0ms

localize14.0ms

rewrite44.0ms

series161.0ms

simplify74.0ms

prune228.0ms

localize14.0ms

rewrite27.0ms

series112.0ms

simplify82.0ms

prune100.0ms

localize4.0ms

rewrite0.0ms

series0.0ms

simplify5.0ms

prune0.0ms

regimes272.0ms

bsearch77.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling