Details

sample237.0ms

Algorithm

intervals

Results

10.0ms	182×	body	80	valid
8.0ms	32×	body	2560	valid
5.0ms	24×	body	1280	valid
4.0ms	106×	body	80	nan
3.0ms	19×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid

simplify364.0ms

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

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: 31.0b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.5b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
20.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms

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)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

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

prune135.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	9	104

Merged error: 4.4b

Counts

104 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
4.4b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.5b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

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:

6.0ms	(- (* b_2 b_2) (* a c))
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))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
53.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (77.0ms)

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

prune222.0ms

Filtered

144 candidates to 196 candidates (-36.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	195	10	205

Merged error: 4.3b

Counts

205 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
3.2b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.4b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
20.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

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))
22.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
53.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
39.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1530	7327
1	5001	6764

prune301.0ms

Filtered

297 candidates to 449 candidates (-51.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	446	3	449
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	449	10	459

Merged error: 4.3b

Counts

459 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(- (* b_2 b_2) (* a c))
20.0b	(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:

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	586	1945
1	2424	1777
2	5001	1652

prune91.0ms

Filtered

80 candidates to 166 candidates (-107.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	166	10	176

Merged error: 4.3b

Counts

176 → 10

regimes366.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.6b against oracle of 5.3b and baseline of 29.3b

bsearch86.0ms

Steps

Iters	Range	Point
9	1.4207218227508602e+125	1.7687561556963888e+130	7.71972254051459e+125
8	3.745107425184035e-251	3.1240333333520096e-248	6.0544446045401805e-251
8	-3.692428373978256e+65	-6.580007695244171e+62	-1.0441198894524072e+64

Iters

Range

Point

1.4207218227508602e+125

1.7687561556963888e+130

7.71972254051459e+125

3.745107425184035e-251

3.1240333333520096e-248

6.0544446045401805e-251

-3.692428373978256e+65

-6.580007695244171e+62

-1.0441198894524072e+64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	18
1	34	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

290.0ms	1151×	body	2560	valid
247.0ms	5783×	body	80	valid
171.0ms	838×	body	1280	valid
115.0ms	2824×	body	80	nan
78.0ms	469×	body	640	valid
30.0ms	100×	body	5120	valid
29.0ms	242×	body	320	valid
10.0ms	119×	body	160	valid

Details

sample237.0ms

simplify364.0ms

prune5.0ms

localize26.0ms

rewrite34.0ms

series65.0ms

simplify43.0ms

prune135.0ms

localize10.0ms

rewrite43.0ms

series116.0ms

simplify102.0ms

prune222.0ms

localize10.0ms

rewrite79.0ms

series111.0ms

simplify94.0ms

prune301.0ms

localize9.0ms

rewrite32.0ms

series58.0ms

simplify65.0ms

prune91.0ms

regimes366.0ms

bsearch86.0ms

simplify2.0ms

end0.0ms

sample1.4s

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