Details

sample52.0ms

Algorithm

intervals

Results

10.0ms	193×	body	80	valid
10.0ms	34×	body	2560	valid
7.0ms	30×	body	1280	valid
6.0ms	85×	body	80	nan
2.0ms	13×	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

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: 34.3b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

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

series307.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
107.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

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

prune210.0ms

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: 7.0b

Counts

83 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.8b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite52.0ms

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	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
16.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
150.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
181.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (89.0ms)

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

prune387.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	165	9	174

Merged error: 6.9b

Counts

174 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b b) (* (* 4.0 a) c))
0.2b	(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

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))
15.0ms	(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(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	(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
80.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (52.0ms)

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

prune203.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	92	9	101

Merged error: 6.9b

Counts

101 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(/ 4.0 (/ 2.0 (* a c)))
16.4b	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

221×	`times-frac`
165×	`add-sqr-sqrt`
138×	`*-un-lft-identity`
103×	`add-exp-log`
96×	`add-cube-cbrt`
85×	`associate-r`
67×	`add-cbrt-cube`
54×	`div-exp`
32×	`cbrt-undiv`
26×	`associate-l` `prod-exp`
20×	`distribute-lft-out--` `difference-of-squares`
16×	`cbrt-unprod`
13×	`sqrt-prod` `div-inv`
10×	`distribute-rgt-neg-in`
8×	`associate-/r/` `add-log-exp` `unswap-sqr`
7×	`pow1` `associate-/r*`
5×	`flip3--` `flip--`
4×	`rec-exp` `1-exp`
3×	`associate-/l*`
2×	`sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 244

Calls

4 calls:

9.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(/ 4.0 (/ 2.0 (* a c)))
59.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(/ 4.0 (/ 2.0 (* a c)))
151.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1396	3426
1	5001	2942

prune579.0ms

Filtered

256 candidates to 165 candidates (64.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	4	5
Picked	0	1	1
Done	1	2	3
Total	257	8	265

Merged error: 6.9b

Counts

265 → 8

regimes243.0ms

Accuracy

85.8% (3.8b remaining)

Error of 9.4b against oracle of 5.6b and baseline of 32.4b

bsearch224.0ms

Steps

Iters	Range		Point
10	2.564731655063431e+70	8.71581363662453e+81	2.1868634635914353e+71
11	3.073059094578084e-151	9.813570662590159e-116	3.288204035546746e-123
6	-1.555584016455579e+44	-1.807486675368764e+43	-1.5338208594244521e+44

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	27
1	43	27

end0.0ms

sample1.5s

Algorithm

intervals

Results

349.0ms	1112×	body	2560	valid
321.0ms	5838×	body	80	valid
230.0ms	917×	body	1280	valid
153.0ms	2863×	body	80	nan
90.0ms	447×	body	640	valid
43.0ms	113×	body	5120	valid
35.0ms	222×	body	320	valid
12.0ms	118×	body	160	valid

Details

sample52.0ms

simplify11.0ms

prune2.0ms

localize12.0ms

rewrite28.0ms

series307.0ms

simplify46.0ms

prune210.0ms

localize17.0ms

rewrite52.0ms

series481.0ms

simplify116.0ms

prune387.0ms

localize13.0ms

rewrite32.0ms

series305.0ms

simplify61.0ms

prune203.0ms

localize17.0ms

rewrite97.0ms

series316.0ms

simplify65.0ms

prune579.0ms

regimes243.0ms

bsearch224.0ms

simplify2.0ms

end0.0ms

sample1.5s

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