Details

analyze483.0ms

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

sample40.0ms

Algorithm

intervals

Results

9.0ms	30×	body	2560	valid
9.0ms	172×	body	80	valid
7.0ms	26×	body	1280	valid
3.0ms	16×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	17×	body	80	nan
0.0ms	3×	body	80	invalid
0.0ms	1×	body	160	valid

simplify305.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (296.0ms)

Iter	Nodes	Cost
0	1835	24
1	1835	24

prune4.0ms

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: 33.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite29.0ms

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:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
66.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify85.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4988	1963
1	4988	1963

prune97.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 6.8b

Counts

83 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.6b	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
10.1b	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`sqrt-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 102

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
14.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
154.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
192.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4935	3094
1	4935	3094

prune106.0ms

Filtered

78 candidates to 114 candidates (-46.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	114	8	122

Merged error: 6.7b

Counts

122 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
14×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`distribute-lft-out_binary64`
3×	`associate-l_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

12.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
63.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5194	1901

prune77.0ms

Filtered

66 candidates to 87 candidates (-31.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	88	7	95

Merged error: 6.7b

Counts

95 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64`
10×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`difference-of-squares_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
14.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
106.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4957	2223
1	4957	2223

prune74.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	91	7	98

Merged error: 6.7b

Counts

98 → 7

regimes128.0ms

Accuracy

95.7% (1.1b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 30.1b

bsearch95.0ms

Steps

Iters	Range	Point
6	2.080907647498648e+117	8.807253502256733e+117	5.421378530068417e+117
8	-1.7798087789445338e-257	-3.0288427818681465e-260	-3.561644019231982e-259
8	-3.5120050791365185e+148	-7.844161924352053e+145	-8.273540851308956e+145

Iters

Range

Point

2.080907647498648e+117

8.807253502256733e+117

5.421378530068417e+117

-1.7798087789445338e-257

-3.0288427818681465e-260

-3.561644019231982e-259

-3.5120050791365185e+148

-7.844161924352053e+145

-8.273540851308956e+145

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	102	82
1	102	82

end0.0ms

sample1.3s

Algorithm

intervals

Results

333.0ms	1035×	body	2560	valid
299.0ms	5181×	body	80	valid
228.0ms	865×	body	1280	valid
99.0ms	470×	body	640	valid
45.0ms	112×	body	5120	valid
42.0ms	258×	body	320	valid
37.0ms	662×	body	80	nan
22.0ms	390×	body	80	invalid
8.0ms	79×	body	160	valid

Details

analyze483.0ms

sample40.0ms

simplify305.0ms

prune4.0ms

localize14.0ms

rewrite29.0ms

series255.0ms

simplify85.0ms

prune97.0ms

localize15.0ms

rewrite40.0ms

series469.0ms

simplify111.0ms

prune106.0ms

localize11.0ms

rewrite29.0ms

series338.0ms

simplify68.0ms

prune77.0ms

localize11.0ms

rewrite33.0ms

series265.0ms

simplify69.0ms

prune74.0ms

regimes128.0ms

bsearch95.0ms

simplify5.0ms

end0.0ms

sample1.3s

Profiling