Details

sample53.0ms

Algorithm

intervals

Results

10.0ms	196×	body	80	valid
7.0ms	26×	body	2560	valid
7.0ms	75×	body	80	nan
6.0ms	26×	body	1280	valid
3.0ms	16×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify10.0ms

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

prune4.0ms

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: 31.8b

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))
1.2b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (* b b) (* (* 4.0 a) c))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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:

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

series67.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
17.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5001	673

prune163.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 6.3b

Counts

83 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (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))
9.6b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

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))))
19.0ms	(/ (/ (+ 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)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
62.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	646	2693
1	3163	2447
2	5003	2434

prune303.0ms

Filtered

111 candidates to 166 candidates (-49.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	166	8	174

Merged error: 6.2b

Counts

174 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.2b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (* b b) (* (* 4.0 a) c))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

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

series78.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	528	1588
1	2590	1372
2	5001	1305

prune154.0ms

Filtered

71 candidates to 126 candidates (-77.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	126	8	134

Merged error: 6.2b

Counts

134 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (* b b) (* (* 4.0 a) c))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

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

series51.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	147	474
1	570	446
2	2550	444
3	5001	442

prune134.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	66	8	74

Merged error: 6.2b

Counts

74 → 8

regimes265.0ms

Accuracy

82.6% (4.8b remaining)

Error of 9.8b against oracle of 5.0b and baseline of 32.3b

bsearch56.0ms

Steps

Iters	Range		Point
8	3.4713192377217875e-36	1.5663447360869123e-31	2.8203535769129045e-33
7	-6.682283173913537e+118	-3.724757707733592e+117	-2.4933470885408413e+118

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

302.0ms	5853×	body	80	valid
295.0ms	999×	body	2560	valid
229.0ms	919×	body	1280	valid
150.0ms	3010×	body	80	nan
82.0ms	412×	body	640	valid
44.0ms	123×	body	5120	valid
40.0ms	261×	body	320	valid
13.0ms	131×	body	160	valid

Details

sample53.0ms

simplify10.0ms

prune4.0ms

localize12.0ms

rewrite30.0ms

series67.0ms

simplify45.0ms

prune163.0ms

localize17.0ms

rewrite51.0ms

series138.0ms

simplify115.0ms

prune303.0ms

localize13.0ms

rewrite35.0ms

series78.0ms

simplify68.0ms

prune154.0ms

localize15.0ms

rewrite17.0ms

series51.0ms

simplify81.0ms

prune134.0ms

regimes265.0ms

bsearch56.0ms

simplify1.0ms

end0.0ms

sample1.6s

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