Details

sample48.0ms

Algorithm

intervals

Results

10.0ms	39×	body	2560	valid
9.0ms	180×	body	80	valid
7.0ms	30×	body	1280	valid
5.0ms	100×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	3×	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

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: 33.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
0.9b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

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:

16.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
48.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	405	780
1	1563	685
2	5001	674

prune229.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 5.9b

Counts

83 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.0b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

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:

9.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
184.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	651	2692
1	3101	2439
2	5001	2426

prune414.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	165	10	175

Merged error: 5.9b

Counts

175 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

13.1b	(cbrt (+ 0 (* 4.0 (* a c))))
13.1b	(cbrt (+ 0 (* 4.0 (* a c))))
13.1b	(cbrt (+ 0 (* 4.0 (* a c))))
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `sqrt-prod` `flip-+`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 54

Calls

4 calls:

2.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
2.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
2.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
99.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
105.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	259	531
1	990	490
2	5001	456

prune286.0ms

Filtered

66 candidates to 61 candidates (92.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	66	10	76

Merged error: 5.9b

Counts

76 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

9.0b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
42×	`times-frac`
30×	`add-cube-cbrt`
16×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r*` `sqrt-prod`
8×	`add-exp-log` `distribute-rgt-neg-in` `add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`flip3--` `sqrt-div` `associate-/r/` `flip--` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 124

Calls

4 calls:

19.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (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)))

series694.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
179.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
267.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify83.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	346	1982
1	1675	1834
2	5001	1820

prune452.0ms

Filtered

136 candidates to 98 candidates (72.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	136	10	146

Merged error: 5.9b

Counts

146 → 10

regimes290.0ms

Accuracy

87.7% (3.4b remaining)

Error of 8.8b against oracle of 5.4b and baseline of 33.0b

bsearch216.0ms

Steps

Iters	Range		Point
8	4.1433580792185867e+68	2.296567048635946e+73	2.425005151022521e+69
9	8.879718769428669e-232	8.562504904991818e-226	9.159933660727599e-231
10	-1.218044689452388e+116	-9.206374310818687e+98	-3.4298668229790213e+115

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	29
1	52	29
2	52	29

end0.0ms

sample1.3s

Algorithm

intervals

Results

283.0ms	1019×	body	2560	valid
281.0ms	5854×	body	80	valid
214.0ms	919×	body	1280	valid
142.0ms	2973×	body	80	nan
83.0ms	458×	body	640	valid
37.0ms	105×	body	5120	valid
31.0ms	237×	body	320	valid
9.0ms	98×	body	160	valid

Details

sample48.0ms

simplify11.0ms

prune3.0ms

localize12.0ms

rewrite33.0ms

series302.0ms

simplify46.0ms

prune229.0ms

localize16.0ms

rewrite50.0ms

series486.0ms

simplify116.0ms

prune414.0ms

localize26.0ms

rewrite12.0ms

series372.0ms

simplify56.0ms

prune286.0ms

localize19.0ms

rewrite45.0ms

series694.0ms

simplify83.0ms

prune452.0ms

regimes290.0ms

bsearch216.0ms

simplify2.0ms

end0.0ms

sample1.3s

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