Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	36×	body	2560	valid
7.0ms	180×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	75×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Filtered

1 candidates to 0 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: 35.0b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune207.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 5.9b

Counts

83 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.7b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
143.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
185.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2426

prune394.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	163	11	174

Merged error: 5.8b

Counts

174 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
8.7b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
11×	`sqrt-prod`
8×	`cbrt-undiv` `distribute-rgt-neg-in` `cbrt-unprod` `add-log-exp`
7×	`pow1` `associate-r` `associate-/r*`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 149

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
144.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
303.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify134.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	743	2415
1	3914	2081
2	5003	2074

prune359.0ms

Filtered

161 candidates to 103 candidates (64.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	4	4	8
Picked	0	1	1
Done	1	1	2
Total	164	8	172

Merged error: 5.8b

Counts

172 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.9b	(/ (* 4.0 (* a c)) (* 2.0 a))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	436	637
1	2555	544
2	5002	544

prune157.0ms

Filtered

82 candidates to 55 candidates (67.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	4	5
Picked	1	0	1
Done	1	1	2
Total	84	6	90

Merged error: 5.8b

Counts

90 → 6

regimes232.0ms

Accuracy

93.2% (1.6b remaining)

Error of 7.0b against oracle of 5.4b and baseline of 29.4b

bsearch192.0ms

Steps

Iters	Range	Point
9	1.314833454423355e+61	1.6016599845544569e+66	7.7076257484328935e+65
10	-4.4782599006234366e-147	-2.1964053429920463e-160	-2.2271387790640654e-160
10	-1.5021501144069279e+69	-2.501148282372368e+59	-1.2963688795759268e+64

Iters

Range

Point

1.314833454423355e+61

1.6016599845544569e+66

7.7076257484328935e+65

-4.4782599006234366e-147

-2.1964053429920463e-160

-2.2271387790640654e-160

-1.5021501144069279e+69

-2.501148282372368e+59

-1.2963688795759268e+64

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	40	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

250.0ms	1049×	body	2560	valid
241.0ms	5827×	body	80	valid
173.0ms	883×	body	1280	valid
110.0ms	2908×	body	80	nan
72.0ms	486×	body	640	valid
28.0ms	244×	body	320	valid
27.0ms	92×	body	5120	valid
12.0ms	129×	body	160	valid