Details

sample285.0ms

Algorithm

intervals

Results

8.0ms	33×	body	2560	valid
6.0ms	185×	body	80	valid
4.0ms	25×	body	1280	valid
3.0ms	97×	body	80	nan
2.0ms	17×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify15.0ms

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

prune4.0ms

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: 34.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

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:

23.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (35.0ms)

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

prune241.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 5.8b

Counts

104 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.3b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`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 → 184

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
12.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
154.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
187.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune476.0ms

Filtered

196 candidates to 144 candidates (73.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	197	7	204

Merged error: 5.7b

Counts

204 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.8b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.3b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
24.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
164.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
133.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5001	6762

prune990.0ms

Filtered

449 candidates to 297 candidates (66.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	447	2	449
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	448	8	456

Merged error: 5.7b

Counts

456 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.3b	(/ (* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a c)) a)
10.2b	(* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
34×	`add-cbrt-cube`
30×	`add-sqr-sqrt`
24×	`associate-l` `prod-exp`
23×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt` `div-exp`
12×	`cbrt-unprod`
10×	`pow1`
9×	`cbrt-undiv`
6×	`sqrt-prod` `add-log-exp` `difference-of-squares`
4×	`rec-exp` `1-exp`
3×	`flip3--` `pow-prod-down` `associate-/r*` `flip--` `distribute-lft-out--`
2×	`sqrt-div` `associate-*l/` `associate-/r/` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 107

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a c)) a)
15.0ms	(* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
95.0ms	(/ (* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a c)) a)
125.0ms	(* (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	572	1140
1	2858	910
2	5001	873

prune213.0ms

Filtered

119 candidates to 74 candidates (62.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	119	8	127

Merged error: 5.7b

Counts

127 → 8

regimes171.0ms

Accuracy

89.9% (2.7b remaining)

Error of 8.1b against oracle of 5.5b and baseline of 31.8b

bsearch160.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	1.6809283377365093e+101
11	1.8145151230270015e-269	9.272403512084269e-250	8.40594418978702e-269
10	-1.2131416731721854e+50	-2.1643807627199687e+37	-7.679227420164859e+47

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

1.6809283377365093e+101

1.8145151230270015e-269

9.272403512084269e-250

8.40594418978702e-269

-1.2131416731721854e+50

-2.1643807627199687e+37

-7.679227420164859e+47

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	23
1	41	23

end0.0ms

sample1.0s

Algorithm

intervals

Results

209.0ms	1052×	body	2560	valid
197.0ms	5925×	body	80	valid
140.0ms	900×	body	1280	valid
87.0ms	2937×	body	80	nan
57.0ms	438×	body	640	valid
27.0ms	115×	body	5120	valid
18.0ms	197×	body	320	valid
8.0ms	130×	body	160	valid