Details

sample49.0ms

Algorithm

intervals

Results

13.0ms	41×	body	2560	valid
8.0ms	172×	body	80	valid
7.0ms	34×	body	1280	valid
4.0ms	98×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune2.0ms

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: 32.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

10.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune216.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	11	104

Merged error: 3.3b

Counts

104 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.3b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
5.8b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
146.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
180.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	730	2960
1	3200	2803
2	5001	2783

prune444.0ms

Filtered

199 candidates to 148 candidates (74.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	195	4	199
Fresh	4	5	9
Picked	0	1	1
Done	1	0	1
Total	200	10	210

Merged error: 3.2b

Counts

210 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

12.6b	(cbrt (+ 0 (* a c)))
12.6b	(cbrt (+ 0 (* a c)))
18.6b	(sqrt (- (* b_2 b_2) (* a c)))
18.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip--` `flip-+`

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (+ 0 (* a c)))
2.0ms	(cbrt (+ 0 (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (+ 0 (* a c)))
67.0ms	(cbrt (+ 0 (* a c)))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	226	434
1	851	406
2	5001	386

prune289.0ms

Filtered

68 candidates to 64 candidates (94.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	68	10	78

Merged error: 3.2b

Counts

78 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0b	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
4.3b	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
18.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

3063×	`times-frac`
1689×	`add-sqr-sqrt`
1446×	`*-un-lft-identity`
1204×	`add-cube-cbrt`
242×	`difference-of-squares`
237×	`associate-/l*`
124×	`sqrt-prod`
121×	`distribute-lft-out--`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
6×	`associate-/r*` `add-log-exp`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1025

Calls

4 calls:

11.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
53.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
96.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
93.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify255.0ms

Algorithm

egg-herbie

Counts

1037 → 1037

Iterations

Useful iterations: 1 (70.0ms)

Iter	Nodes	Cost
0	4259	21067
1	5001	20479

prune2.0s

Filtered

1037 candidates to 576 candidates (55.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1036	1	1037
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	1038	9	1047

Merged error: 3.2b

Counts

1047 → 9

regimes249.0ms

Accuracy

90% (2.7b remaining)

Error of 8.4b against oracle of 5.7b and baseline of 32.4b

bsearch147.0ms

Steps

Iters	Range		Point
9	1.537663903506608e+146	1.524085477896404e+154	2.7744187296782597e+150
9	-4.593581389442884e-257	-3.786974856544585e-264	-3.8324699600337675e-264
6	-0.04325046342239626	-0.004915430213868263	-0.04248736169027556

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	42	24

end0.0ms

sample1.3s

Algorithm

intervals

Results

295.0ms	5855×	body	80	valid
282.0ms	1019×	body	2560	valid
203.0ms	896×	body	1280	valid
138.0ms	2933×	body	80	nan
80.0ms	451×	body	640	valid
39.0ms	119×	body	5120	valid
33.0ms	253×	body	320	valid
12.0ms	130×	body	160	valid