Details

sample54.0ms

Algorithm

intervals

Results

10.0ms	146×	body	160	valid
10.0ms	512×	pre	80	true
9.0ms	256×	body	80	nan
5.0ms	48×	body	320	valid
2.0ms	62×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

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: 42.9b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
36.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune186.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 0.2b

Counts

83 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series464.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
189.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
156.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify115.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	640	2579
1	3157	2332
2	5003	2319

prune419.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	152	8	160
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	154	9	163

Merged error: 0b

Counts

163 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`sqrt-prod`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `distribute-rgt-neg-in` `associate-r` `associate-/r*`
6×	`add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 143

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
190.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
154.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

simplify140.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	732	2304
1	3926	1974
2	5002	1967

prune378.0ms

Filtered

155 candidates to 100 candidates (64.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	156	8	164

Merged error: 0b

Counts

164 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2.0 (* a c))
0.3b	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.3b	(/ 4.0 (/ 2.0 (* a c)))
0.3b	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

389×	`times-frac`
281×	`add-sqr-sqrt`
255×	`*-un-lft-identity`
169×	`add-cube-cbrt`
117×	`add-exp-log`
85×	`associate-r`
77×	`add-cbrt-cube`
62×	`div-exp`
42×	`distribute-lft-out--` `difference-of-squares`
37×	`cbrt-undiv`
33×	`associate-/l*`
27×	`prod-exp`
26×	`associate-l`
21×	`distribute-rgt-neg-in` `sqrt-prod`
19×	`div-inv`
17×	`cbrt-unprod`
16×	`associate-/r/`
11×	`associate-/r*`
8×	`unswap-sqr`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 360

Calls

4 calls:

4.0ms	(/ 2.0 (* a c))
16.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
6.0ms	(/ 4.0 (/ 2.0 (* a c)))
60.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series311.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 2.0 (* a c))
119.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
24.0ms	(/ 4.0 (/ 2.0 (* a c)))
147.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify83.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1477	5495
1	5002	4888

prune781.0ms

Filtered

372 candidates to 218 candidates (58.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	371	1	372
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	372	8	380

Merged error: 0b

Counts

380 → 8

regimes124.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	31	14
2	31	14

end0.0ms

sample1.5s

Algorithm

intervals

Results

347.0ms	4844×	body	160	valid
298.0ms	16358×	pre	80	true
277.0ms	8358×	body	80	nan
147.0ms	1319×	body	320	valid
67.0ms	1837×	body	80	valid