Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	185×	body	80	valid
7.0ms	29×	body	2560	valid
6.0ms	29×	body	1280	valid
3.0ms	88×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	7×	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: 33.7b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

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

series231.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

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

prune203.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	7	104

Merged error: 6.1b

Counts

104 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.1b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

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)
17.0ms	(/ (/ (+ 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)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
143.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
177.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	730	2960
1	3163	2803
2	5002	2783

prune452.0ms

Filtered

199 candidates to 148 candidates (74.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	194	5	199
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	197	9	206

Merged error: 6.0b

Counts

206 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.6b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.0b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
549×	`add-sqr-sqrt`
450×	`*-un-lft-identity`
352×	`add-cube-cbrt`
98×	`difference-of-squares`
74×	`associate-/l*`
52×	`sqrt-prod`
49×	`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 → 440

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
23.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
156.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
128.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1571	7388
1	5001	6820

prune868.0ms

Filtered

452 candidates to 301 candidates (66.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	449	3	452
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	452	9	461

Merged error: 6.0b

Counts

461 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
0.6b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 154

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
64.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	604	1945
1	2473	1776
2	5001	1651

prune203.0ms

Filtered

166 candidates to 80 candidates (48.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	168	7	175

Merged error: 6.0b

Counts

175 → 7

regimes148.0ms

Accuracy

95.7% (1.1b remaining)

Error of 6.5b against oracle of 5.4b and baseline of 30.1b

bsearch143.0ms

Steps

Iters	Range	Point
9	1.0750476286016474e+90	7.888871963785644e+94	1.8792881347214707e+92
8	1.1675345872147045e-263	5.004642265701124e-260	1.303436860894128e-261
9	-2.0560691900424517e+121	-1.9544616975333591e+114	-1.9852491311597963e+121

Iters

Range

Point

1.0750476286016474e+90

7.888871963785644e+94

1.8792881347214707e+92

1.1675345872147045e-263

5.004642265701124e-260

1.303436860894128e-261

-2.0560691900424517e+121

-1.9544616975333591e+114

-1.9852491311597963e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	19
1	38	19
2	38	19

end0.0ms

sample1.2s

Algorithm

intervals

Results

259.0ms	1058×	body	2560	valid
249.0ms	5966×	body	80	valid
180.0ms	904×	body	1280	valid
124.0ms	2958×	body	80	nan
67.0ms	441×	body	640	valid
35.0ms	105×	body	5120	valid
22.0ms	190×	body	320	valid
10.0ms	128×	body	160	valid

Details

sample39.0ms

simplify8.0ms

prune2.0ms

localize9.0ms

rewrite31.0ms

series231.0ms

simplify43.0ms

prune203.0ms

localize10.0ms

rewrite48.0ms

series446.0ms

simplify118.0ms

prune452.0ms

localize14.0ms

rewrite82.0ms

series406.0ms

simplify88.0ms

prune868.0ms

localize13.0ms

rewrite32.0ms

series252.0ms

simplify66.0ms

prune203.0ms

regimes148.0ms

bsearch143.0ms

simplify2.0ms

end0.0ms

sample1.2s

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