Details

sample52.0ms

Algorithm

intervals

Results

10.0ms	36×	body	2560	valid
9.0ms	184×	body	80	valid
5.0ms	23×	body	1280	valid
4.0ms	89×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	8×	body	160	valid

simplify9.0ms

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

prune6.0ms

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: 35.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.7b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.1b	(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:

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

series66.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	394	773
1	1501	683
2	5002	673

prune163.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	11	83

Merged error: 5.7b

Counts

83 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (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))
9.3b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

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)))))
18.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series137.0ms

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))
61.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	635	2693
1	2974	2447
2	5001	2434

prune284.0ms

Filtered

111 candidates to 166 candidates (-49.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	166	11	177

Merged error: 5.6b

Counts

177 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
0.7b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.8b	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`flip3--` `sqrt-prod` `flip--`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 72

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	470	942
1	2684	750
2	5002	742

prune130.0ms

Filtered

58 candidates to 84 candidates (-44.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	85	10	95

Merged error: 5.6b

Counts

95 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.7b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`add-log-exp`
7×	`div-exp` `associate-/r*`
5×	`pow1` `cbrt-undiv` `div-inv`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `prod-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `neg-log` `clear-num` `associate-/r/` `cbrt-unprod`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c))
4.0ms	(- (* 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))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c))
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify63.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	545	1186
1	2319	1074
2	5001	1074

prune152.0ms

Filtered

80 candidates to 106 candidates (-32.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	3	4	7
Picked	1	0	1
Done	1	1	2
Total	109	7	116

Merged error: 5.6b

Counts

116 → 7

regimes350.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.8b

bsearch103.0ms

Steps

Iters	Range	Point
7	7.012417207579252e+108	1.3633655355432952e+110	2.821264388342136e+109
10	-7.55890950842511e-252	-1.434145681223809e-265	-2.6427022137303496e-260
9	-8.123118303304505e+80	-8.66777673642249e+74	-3.453036615513107e+80

Iters

Range

Point

7.012417207579252e+108

1.3633655355432952e+110

2.821264388342136e+109

-7.55890950842511e-252

-1.434145681223809e-265

-2.6427022137303496e-260

-8.123118303304505e+80

-8.66777673642249e+74

-3.453036615513107e+80

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	46	26

end0.0ms

sample1.5s

Algorithm

intervals

Results

321.0ms	1105×	body	2560	valid
296.0ms	5835×	body	80	valid
207.0ms	853×	body	1280	valid
144.0ms	2894×	body	80	nan
87.0ms	472×	body	640	valid
39.0ms	112×	body	5120	valid
34.0ms	232×	body	320	valid
12.0ms	125×	body	160	valid

Details

sample52.0ms

simplify9.0ms

prune6.0ms

localize11.0ms

rewrite27.0ms

series66.0ms

simplify44.0ms

prune163.0ms

localize14.0ms

rewrite48.0ms

series137.0ms

simplify102.0ms

prune284.0ms

localize14.0ms

rewrite31.0ms

series86.0ms

simplify65.0ms

prune130.0ms

localize15.0ms

rewrite30.0ms

series74.0ms

simplify63.0ms

prune152.0ms

regimes350.0ms

bsearch103.0ms

simplify1.0ms

end0.0ms

sample1.5s

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