Details

sample66.0ms

Algorithm

intervals

Results

13.0ms	34×	body	2560	valid
11.0ms	179×	body	80	valid
10.0ms	29×	body	1280	valid
7.0ms	17×	body	640	valid
5.0ms	85×	body	80	nan
2.0ms	5×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	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: 35.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

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

series312.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune294.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Merged error: 4.9b

Counts

103 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

11.0ms	(- (- 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))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
155.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
190.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify148.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	829	5121
1	3763	3863
2	5001	3860

prune548.0ms

Filtered

244 candidates to 141 candidates (57.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	242	10	252

Merged error: 4.8b

Counts

252 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
48×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
8×	`distribute-rgt-neg-in`
6×	`pow1`
5×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 134

Calls

4 calls:

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

series353.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify76.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	556	1665
1	2707	1442
2	5001	1371

prune299.0ms

Filtered

146 candidates to 90 candidates (61.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	146	10	156

Merged error: 4.8b

Counts

156 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
1.0b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.0b	(- (* b b) (* (* 4.0 a) c))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
55×	`prod-diff`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-cbrt-cube`
10×	`prod-exp`
8×	`add-log-exp`
7×	`pow1` `fma-neg` `associate-l`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`times-frac`
2×	`cbrt-undiv` `frac-times` `rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 154

Calls

4 calls:

19.0ms	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
8.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
82.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
45.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify89.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	651	2395
1	3130	1719
2	5001	1591

prune468.0ms

Filtered

166 candidates to 86 candidates (51.8%)

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: 4.8b

Counts

176 → 10

regimes219.0ms

Accuracy

85.7% (3.9b remaining)

Error of 9.3b against oracle of 5.4b and baseline of 32.6b

bsearch233.0ms

Steps

Iters	Range		Point
9	14028.172733867412	3007116902181.375	4662246.201750503
8	-4.654091770266614e-259	-1.1349992526466847e-263	-3.0161999035837213e-263
10	-1.552489725432399e+46	-8.211399685419546e+34	-1.4899647929737788e+46

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	29
1	51	29
2	51	29

end0.0ms

sample1.5s

Algorithm

intervals

Results

334.0ms	1101×	body	2560	valid
301.0ms	5800×	body	80	valid
226.0ms	887×	body	1280	valid
152.0ms	2958×	body	80	nan
93.0ms	469×	body	640	valid
48.0ms	117×	body	5120	valid
31.0ms	215×	body	320	valid
11.0ms	110×	body	160	valid