Details

sample35.0ms

Algorithm

intervals

Results

6.0ms	184×	body	80	valid
5.0ms	28×	body	2560	valid
5.0ms	31×	body	1280	valid
3.0ms	91×	body	80	nan
2.0ms	20×	body	640	valid
1.0ms	5×	body	5120	valid
0.0ms	6×	body	160	valid
0.0ms	3×	body	320	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: 33.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 79

Calls

3 calls:

10.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series210.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	352	884
1	1184	837
2	5001	827

prune198.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	9	89

Merged error: 5.6b

Counts

89 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.8b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

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)
14.0ms	(/ (/ (+ 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)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
150.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
184.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (79.0ms)

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

prune477.0ms

Filtered

199 candidates to 148 candidates (74.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	200	8	208

Merged error: 5.5b

Counts

208 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.8b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
3.2b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite78.0ms

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)
21.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
130.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
165.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1571	7388
1	5001	6820

prune1.0s

Filtered

452 candidates to 301 candidates (66.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	450	2	452
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	453	7	460

Merged error: 5.5b

Counts

460 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
0.3b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
148×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
79×	`add-cube-cbrt`
34×	`difference-of-squares`
25×	`associate-/r*`
20×	`sqrt-prod`
17×	`add-exp-log` `distribute-lft-out--`
11×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp`
6×	`pow1` `div-inv` `add-log-exp`
4×	`cbrt-undiv`
3×	`flip3--` `flip--`
2×	`rec-exp` `frac-2neg` `sqrt-div` `1-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-/r/` `inv-pow`

Counts

4 → 184

Calls

4 calls:

9.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
10.0ms	(/ 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)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
94.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify86.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	666	2355
1	2809	2165
2	5002	2046

prune296.0ms

Filtered

196 candidates to 103 candidates (52.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	195	8	203

Merged error: 5.5b

Counts

203 → 8

regimes220.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 29.7b

bsearch122.0ms

Steps

Iters	Range		Point
7	6.66182219120084e+105	6.051047097450507e+107	4.075293091096083e+107
9	4.731286836754826e-168	1.215082061958878e-162	4.80571676731806e-168
7	-2.7078859601421552e+87	-1.2247309707199115e+86	-6.22368915403742e+86

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	22
1	41	22

end0.0ms

sample1.0s

Algorithm

intervals

Results

219.0ms	1098×	body	2560	valid
197.0ms	5816×	body	80	valid
147.0ms	940×	body	1280	valid
94.0ms	2936×	body	80	nan
55.0ms	441×	body	640	valid
33.0ms	129×	body	5120	valid
21.0ms	230×	body	320	valid
6.0ms	92×	body	160	valid