Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	183×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	23×	body	640	valid
3.0ms	91×	body	80	nan
1.0ms	10×	body	320	valid
0.0ms	1×	body	160	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: 32.5b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.1b	(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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

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

prune223.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 5.6b

Counts

83 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b b) (* (* 4.0 a) c))
0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
106.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (48.0ms)

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

prune226.0ms

Filtered

92 candidates to 66 candidates (71.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	93	6	99

Merged error: 5.6b

Counts

99 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.8b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3--` `flip--` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `sum-log`
1×	`+-commutative` `pow2` `neg-sub0` `associate-+l-` `flip3-+` `pow-plus` `sqrt-unprod` `neg-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 126

Calls

4 calls:

14.0ms	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))
81.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	337	1382
1	1404	1213
2	5001	1175

prune304.0ms

Filtered

138 candidates to 78 candidates (56.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	138	6	144

Merged error: 5.6b

Counts

144 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- 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))
10.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

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:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
28.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
16.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
170.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (88.0ms)

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

prune407.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	164	8	172

Merged error: 5.5b

Counts

172 → 8

regimes240.0ms

Accuracy

84.4% (4.5b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 34.3b

bsearch101.0ms

Steps

Iters	Range		Point
8	4.5357946366764547e-85	1.1233411478654938e-80	5.393697111460973e-81
7	-2.7078859601421552e+87	-1.2247309707199115e+86	-1.444358566469145e+87

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	38	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

250.0ms	1086×	body	2560	valid
240.0ms	5891×	body	80	valid
168.0ms	882×	body	1280	valid
111.0ms	2942×	body	80	nan
70.0ms	466×	body	640	valid
29.0ms	102×	body	5120	valid
23.0ms	204×	body	320	valid
10.0ms	116×	body	160	valid