Details

sample40.0ms

Algorithm

intervals

Results

7.0ms	181×	body	80	valid
7.0ms	29×	body	2560	valid
6.0ms	105×	body	80	nan
5.0ms	26×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	10×	body	160	valid
1.0ms	5×	body	320	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

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: 34.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
2.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

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:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

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

prune195.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 6.4b

Counts

83 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* (* 4.0 a) c))
2.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

14.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	481	920
1	2189	790
2	5001	777

prune204.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	92	8	100

Merged error: 6.4b

Counts

100 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

2.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `sum-log` `add-cbrt-cube` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 60

Calls

4 calls:

7.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	217	598
1	808	556
2	3289	534
3	5001	530

prune224.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Merged error: 6.4b

Counts

80 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`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 → 154

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
145.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
176.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2426

prune355.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	165	9	174

Merged error: 6.3b

Counts

174 → 9

regimes237.0ms

Accuracy

82.1% (5.1b remaining)

Error of 10.6b against oracle of 5.4b and baseline of 34.2b

bsearch123.0ms

Steps

Iters	Range		Point
10	9.690537272714817e-102	1.7794146904278537e-90	1.761458221173807e-90
8	-1.0818597257815559e+95	-2.772945999025709e+91	-9.612795529269333e+93

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	25
1	35	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

265.0ms	1077×	body	2560	valid
234.0ms	5829×	body	80	valid
171.0ms	881×	body	1280	valid
117.0ms	3043×	body	80	nan
72.0ms	445×	body	640	valid
31.0ms	111×	body	5120	valid
28.0ms	248×	body	320	valid
10.0ms	124×	body	160	valid