Details

sample52.0ms

Algorithm

intervals

Results

9.0ms	35×	body	2560	valid
8.0ms	178×	body	80	valid
6.0ms	29×	body	1280	valid
4.0ms	98×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	5×	body	160	valid

simplify6.0ms

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 39.1b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.3b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

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:

11.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune451.0ms

Filtered

103 candidates to 72 candidates (30.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Merged error: 5.3b

Counts

104 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
4.4b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.4b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
26.6b	(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)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
44.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
60.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	704	2894
1	3112	2747
2	5001	2727

prune1.6s

Filtered

196 candidates to 144 candidates (26.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	197	9	206

Merged error: 5.3b

Counts

206 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
14.2b	(/ a (* a c))
26.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(/ a (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
2.0ms	(/ a (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	272	415
1	924	374
2	4132	370
3	5001	369

prune371.0ms

Filtered

75 candidates to 53 candidates (29.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	75	9	84

Merged error: 5.3b

Counts

84 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

4.4b	(/ (/ (* (/ a (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ c (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
26.6b	(sqrt (- (* b_2 b_2) (* a c)))
26.6b	(sqrt (- (* b_2 b_2) (* a c)))
26.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac`
54×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`add-cube-cbrt`
29×	`add-exp-log`
24×	`cbrt-prod`
20×	`add-cbrt-cube`
15×	`cbrt-undiv` `div-exp` `associate-/l*`
13×	`sqrt-prod`
8×	`cbrt-div` `associate-/r/` `difference-of-squares`
7×	`pow1` `flip3--` `flip--`
6×	`sqrt-div`
5×	`div-inv`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r*`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 131

Calls

4 calls:

34.0ms	(/ (/ (* (/ a (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ c (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (/ (* (/ a (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ c (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify82.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	692	3067
1	3120	2867
2	5001	2855

prune946.0ms

Filtered

143 candidates to 110 candidates (23.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	5	5
Picked	1	0	1
Done	0	3	3
Total	143	9	152

Merged error: 5.3b

Counts

152 → 9

regimes458.0ms

Accuracy

88.4% (3.1b remaining)

Error of 8.7b against oracle of 5.6b and baseline of 32.6b

bsearch151.0ms

Steps

Iters	Range	Point
4	3.1466272044128187e+123	6.05509838734878e+123	3.2255380126760236e+123
7	-5.545031260635621e-126	-2.0276992683658464e-127	-2.0621693002555343e-127
7	-2.2866437577973832e+39	-1.76991664288792e+37	-6.647348784598862e+38

Iters

Range

Point

3.1466272044128187e+123

6.05509838734878e+123

3.2255380126760236e+123

-5.545031260635621e-126

-2.0276992683658464e-127

-2.0621693002555343e-127

-2.2866437577973832e+39

-1.76991664288792e+37

-6.647348784598862e+38

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	39
1	44	39

end0.0ms

sample1.4s

Algorithm

intervals

Results

269.0ms	1075×	body	2560	valid
258.0ms	5876×	body	80	valid
184.0ms	868×	body	1280	valid
119.0ms	2910×	body	80	nan
72.0ms	452×	body	640	valid
38.0ms	126×	body	5120	valid
31.0ms	238×	body	320	valid
8.0ms	97×	body	160	valid

Details

sample52.0ms

simplify6.0ms

prune5.0ms

localize9.0ms

rewrite33.0ms

series55.0ms

simplify45.0ms

prune451.0ms

localize10.0ms

rewrite45.0ms

series125.0ms

simplify100.0ms

prune1.6s

localize11.0ms

rewrite20.0ms

series37.0ms

simplify119.0ms

prune371.0ms

localize16.0ms

rewrite55.0ms

series83.0ms

simplify82.0ms

prune946.0ms

regimes458.0ms

bsearch151.0ms

simplify2.0ms

end0.0ms

sample1.4s

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