Details

sample295.0ms

Algorithm

intervals

Results

11.0ms	38×	body	2560	valid
8.0ms	181×	body	80	valid
6.0ms	30×	body	1280	valid
4.0ms	96×	body	80	nan
3.0ms	19×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify13.0ms

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: 35.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.4b	(- (* b_2 b_2) (* a c))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

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:

25.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (34.0ms)

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

prune253.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 5.8b

Counts

104 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.4b	(/ (/ (+ 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))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite52.0ms

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)
16.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
15.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
158.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
192.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (84.0ms)

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

prune488.0ms

Filtered

199 candidates to 148 candidates (74.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	195	4	199
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	199	9	208

Merged error: 5.7b

Counts

208 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.3b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.4b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite87.0ms

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)
12.0ms	(/ 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)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
173.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
142.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1571	7388
1	5001	6820

prune1.0s

Filtered

452 candidates to 301 candidates (66.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	451	1	452
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	453	8	461

Merged error: 5.7b

Counts

461 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

5.7b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
9.6b	(/ (+ 0 (* a c)) (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2))
15.0b	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
21×	`times-frac`
20×	`add-cube-cbrt`
16×	`log-prod` `exp-sum`
15×	`difference-of-squares`
11×	`sqrt-prod`
7×	`pow1` `associate-/r*`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out--`
4×	`flip3--` `sqrt-div` `flip--`
3×	`log-pow` `associate-/l*`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 100

Calls

4 calls:

6.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms	(/ (+ 0 (* a c)) (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2))
10.0ms	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
191.0ms	(/ (+ 0 (* a c)) (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2))
68.0ms	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	415	1314
1	1539	1176
2	5001	1142

prune275.0ms

Filtered

112 candidates to 82 candidates (73.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	112	8	120

Merged error: 5.7b

Counts

120 → 8

regimes198.0ms

Accuracy

85.4% (4.1b remaining)

Error of 9.9b against oracle of 5.8b and baseline of 33.6b

bsearch151.0ms

Steps

Iters	Range		Point
6	2087876908255263.8	9946277058360104.0	9787957843074626.0
9	-4.9573805767806585e-301	-7.083727823843107e-308	-3.8234222669553895e-306
9	-2.9777074523227444e+74	-9.540315001687748e+64	-7.825514768656328e+65

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	24
1	43	24
2	43	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

263.0ms	5938×	body	80	valid
263.0ms	1068×	body	2560	valid
176.0ms	852×	body	1280	valid
120.0ms	2829×	body	80	nan
69.0ms	435×	body	640	valid
33.0ms	109×	body	5120	valid
29.0ms	213×	body	320	valid
9.0ms	112×	body	160	valid

Details

sample295.0ms

simplify13.0ms

prune4.0ms

localize12.0ms

rewrite48.0ms

series267.0ms

simplify48.0ms

prune253.0ms

localize11.0ms

rewrite52.0ms

series484.0ms

simplify113.0ms

prune488.0ms

localize15.0ms

rewrite87.0ms

series450.0ms

simplify95.0ms

prune1.0s

localize15.0ms

rewrite41.0ms

series385.0ms

simplify62.0ms

prune275.0ms

regimes198.0ms

bsearch151.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling