Details

sample1.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.402832%

Guaranteed chance to sample good point: 74.774996%

Results

12.0ms	40×	body	2560	valid
9.0ms	161×	body	80	valid
6.0ms	23×	body	1280	valid
2.0ms	11×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	10×	body	320	valid
1.0ms	13×	body	80	nan
1.0ms	11×	body	80	invalid
1.0ms	6×	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

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: 35.2b

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))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.6b	(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))
8.0ms	(+ (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:

26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(+ (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	396	773
1	1550	683
2	5002	673

prune159.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

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

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.2b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

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

series134.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (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))
61.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (87.0ms)

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

prune302.0ms

Filtered

111 candidates to 166 candidates (-49.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	165	9	174

Merged error: 6.9b

Counts

174 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

10.2b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
21×	`times-frac`
19×	`add-cube-cbrt`
13×	`sqrt-prod`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1` `associate-/r*`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
4×	`flip3--` `distribute-rgt-neg-in` `flip--` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 92

Calls

4 calls:

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

series103.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	348	1249
1	1732	1181
2	5001	1174

prune387.0ms

Filtered

79 candidates to 104 candidates (-31.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	104	9	113

Merged error: 6.9b

Counts

113 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.5b	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

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))))
14.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series87.0ms

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))))
47.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	486	952
1	2894	749
2	5002	741

prune113.0ms

Filtered

58 candidates to 84 candidates (-44.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	85	8	93

Merged error: 6.9b

Counts

93 → 8

regimes394.0ms

Accuracy

93.7% (1.5b remaining)

Error of 7.4b against oracle of 5.9b and baseline of 29.5b

bsearch139.0ms

Steps

Iters	Range		Point
6	5.511026700313779e+49	5.28654188286082e+50	6.338315486262781e+49
9	2.435413523468213e-290	9.996778654235684e-282	2.4711791449185284e-290
8	-2.3921345205031928e+157	-2.3424649586159117e+153	-3.085063109409604e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	27
1	49	27
2	49	27

end0.0ms

sample2.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.402832%

Guaranteed chance to sample good point: 74.774996%

Results

339.0ms	1094×	body	2560	valid
292.0ms	5136×	body	80	valid
220.0ms	881×	body	1280	valid
85.0ms	430×	body	640	valid
44.0ms	115×	body	5120	valid
34.0ms	229×	body	320	valid
20.0ms	388×	body	80	nan
17.0ms	306×	body	80	invalid
12.0ms	115×	body	160	valid

Details

sample1.2s

simplify9.0ms

prune4.0ms

localize12.0ms

rewrite27.0ms

series66.0ms

simplify44.0ms

prune159.0ms

localize16.0ms

rewrite49.0ms

series134.0ms

simplify112.0ms

prune302.0ms

localize23.0ms

rewrite28.0ms

series103.0ms

simplify75.0ms

prune387.0ms

localize17.0ms

rewrite34.0ms

series87.0ms

simplify73.0ms

prune113.0ms

regimes394.0ms

bsearch139.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling