Details

sample1.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.306274%

Guaranteed chance to sample good point: 70.196172%

Results

12.0ms	27×	body	2560	valid
9.0ms	160×	body	80	valid
7.0ms	29×	body	1280	valid
5.0ms	25×	body	640	valid
1.0ms	22×	body	80	invalid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	15×	body	80	nan
1.0ms	5×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	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: 36.6b

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))
1.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b	(- (* b b) (* 4.0 (* a c)))
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

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)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune303.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	9	90

Merged error: 4.7b

Counts

90 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.8b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.3b	(- (pow b 2) (pow b 2))
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
78×	`times-frac`
68×	`*-un-lft-identity`
44×	`add-cube-cbrt`
36×	`difference-of-squares`
27×	`associate-/l*`
22×	`unpow-prod-down`
18×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
13×	`sqrt-prod`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`div-sub` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `+-inverses` `diff-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

28.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
25.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms	(- (pow b 2) (pow b 2))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
34.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.0ms	(- (pow b 2) (pow b 2))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify210.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	760	2835
1	3914	2397
2	5002	2370

prune385.0ms

Filtered

124 candidates to 187 candidates (-50.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	183	4	187
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	186	10	196

Merged error: 4.7b

Counts

196 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* 4.0 (* a c)))
1.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.8b	(/ (* 4.0 (* a c)) a)
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.0ms	(/ (* 4.0 (* a c)) a)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.0ms	(/ (* 4.0 (* a c)) a)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	340	517
1	1512	468
2	5002	450

prune126.0ms

Filtered

54 candidates to 77 candidates (-42.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	78	9	87

Merged error: 4.6b

Counts

87 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 4.0 (/ 1 c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.6b	(- (* b b) (* 4.0 (* a c)))
1.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

726×	`times-frac`
480×	`add-sqr-sqrt`
387×	`*-un-lft-identity`
295×	`add-cube-cbrt`
92×	`difference-of-squares`
49×	`sqrt-prod`
46×	`distribute-lft-out--`
44×	`associate-/l*`
29×	`div-inv`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`div-exp`
9×	`associate-/r/`
8×	`add-log-exp`
6×	`cbrt-undiv` `associate-/r*`
5×	`pow1`
4×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num` `associate-/l/`

Counts

4 → 377

Calls

4 calls:

22.0ms	(/ (/ 4.0 (/ 1 c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (/ 4.0 (/ 1 c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm

egg-herbie

Counts

389 → 389

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1531	7322
1	5001	6804

prune639.0ms

Filtered

206 candidates to 389 candidates (-88.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	387	2	389
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	389	9	398

Merged error: 4.6b

Counts

398 → 9

regimes312.0ms

Accuracy

93.5% (1.6b remaining)

Error of 7.1b against oracle of 5.5b and baseline of 29.8b

bsearch87.0ms

Steps

Iters	Range		Point
8	5.7509668250777875e+65	6.276869227824861e+69	5.2859986424752965e+67
9	3.4836605671798083e-256	1.1957858889591068e-246	5.566062849154005e-255
4	-7.283566220576807e+90	-4.015560400392505e+90	-6.347983209572217e+90

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	27
1	46	27

end0.0ms

sample3.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.306274%

Guaranteed chance to sample good point: 70.196172%

Results

346.0ms	1101×	body	2560	valid
279.0ms	5030×	body	80	valid
232.0ms	909×	body	1280	valid
100.0ms	494×	body	640	valid
47.0ms	122×	body	5120	valid
37.0ms	232×	body	320	valid
34.0ms	621×	body	80	invalid
18.0ms	358×	body	80	nan
13.0ms	112×	body	160	valid

Details

sample1.6s

simplify13.0ms

prune3.0ms

localize12.0ms

rewrite30.0ms

series61.0ms

simplify46.0ms

prune303.0ms

localize16.0ms

rewrite75.0ms

series80.0ms

simplify210.0ms

prune385.0ms

localize16.0ms

rewrite21.0ms

series39.0ms

simplify42.0ms

prune126.0ms

localize14.0ms

rewrite66.0ms

series94.0ms

simplify97.0ms

prune639.0ms

regimes312.0ms

bsearch87.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling