Details

sample252.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 99.986886%

Space saved by search: 99.987313%

Guaranteed chance to sample good point: 0%

Results

23.0ms	541×	pre	80	true
20.0ms	106×	body	320	valid
17.0ms	285×	body	80	nan
13.0ms	108×	body	160	valid
5.0ms	21×	body	640	valid
1.0ms	21×	body	80	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

prune3.0ms

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: 53.6b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.8b	(+ (neg b) (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:

3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
10.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
15.0ms	(+ (neg b) (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	396	773
1	1550	683
2	5001	673

prune124.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 0.1b

Counts

83 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-rgt-neg-in` `sqrt-prod`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (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))

series130.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
61.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify115.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	643	2666
1	3210	2408
2	5002	2396

prune292.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	157	6	163
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	158	8	166

Merged error: 0b

Counts

166 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-exp-log`
92×	`add-cbrt-cube`
73×	`prod-exp`
46×	`div-exp`
41×	`cbrt-unprod`
26×	`cbrt-undiv`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`pow1`
8×	`add-cube-cbrt` `rec-exp` `1-exp`
7×	`associate-r`
6×	`add-log-exp`
5×	`flip3--` `times-frac` `associate-l` `associate-/r/` `flip--`
4×	`frac-times` `associate-r/` `associate-/l`
3×	`sub-neg` `div-inv`
2×	`distribute-rgt-in` `pow-flip` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-neg-in` `diff-log` `sqrt-prod` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 139

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
19.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
2.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
47.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
27.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify38.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	816	2127
1	5001	1586

prune167.0ms

Filtered

72 candidates to 151 candidates (-109.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	152	7	159

Merged error: 0b

Counts

159 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

20548×	`times-frac`
9815×	`add-sqr-sqrt` `*-un-lft-identity`
7499×	`add-cube-cbrt`
1158×	`distribute-lft-out--` `difference-of-squares`
879×	`div-inv`
621×	`associate-/l*`
579×	`distribute-rgt-neg-in` `sqrt-prod`
200×	`add-exp-log`
169×	`div-exp`
129×	`associate-/r/`
54×	`add-cbrt-cube`
37×	`cbrt-undiv`
30×	`rec-exp` `1-exp`
20×	`associate-/r*`
10×	`add-log-exp`
4×	`pow1`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `frac-2neg` `clear-num` `associate-/l/`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 5377

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
177.0ms	(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))

series84.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms	(- (* b b) (* (* 4.0 a) c))
2.0ms	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))

simplify1.3s

Algorithm

egg-herbie

Counts

5389 → 5389

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5494	146352

prune51.8s

Filtered

2864 candidates to 5389 candidates (-88.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	5387	2	5389
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	5390	6	5396

Merged error: 0b

Counts

5396 → 6

regimes179.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	9
1	17	9

end0.0ms

sample2.4s

Algorithm

intervals

sampling

Space saved by range analysis: 99.986886%

Space saved by search: 99.987313%

Guaranteed chance to sample good point: 0%

Results

516.0ms	3593×	body	320	valid
461.0ms	15970×	pre	80	true
373.0ms	7970×	body	80	nan
286.0ms	2965×	body	160	valid
106.0ms	559×	body	640	valid
46.0ms	883×	body	80	valid

Details

sample252.0ms

simplify9.0ms

prune3.0ms

localize11.0ms

rewrite30.0ms

series65.0ms

simplify44.0ms

prune124.0ms

localize16.0ms

rewrite50.0ms

series130.0ms

simplify115.0ms

prune292.0ms

localize16.0ms

rewrite55.0ms

series85.0ms

simplify38.0ms

prune167.0ms

localize15.0ms

rewrite1.2s

series84.0ms

simplify1.3s

prune51.8s

regimes179.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

Profiling