Details

sample2.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.292969%

Guaranteed chance to sample good point: 62.826797%

Results

10.0ms	165×	body	80	valid
9.0ms	27×	body	2560	valid
8.0ms	28×	body	1280	valid
5.0ms	22×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	160	valid
0.0ms	7×	body	80	invalid
0.0ms	6×	body	80	nan

simplify14.0ms

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

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: 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))
1.2b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
25.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (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))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (40.0ms)

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

prune169.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	9	90

Merged error: 7.1b

Counts

90 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

2.6b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.2b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.0b	(- (pow b 2) (pow b 2))
25.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite69.0ms

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))
23.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
7.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
32.0ms	(/ (+ (- (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))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify194.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (166.0ms)

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

prune374.0ms

Filtered

124 candidates to 187 candidates (-50.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	190	6	196

Merged error: 7.1b

Counts

196 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
14.7b	(/ (* 4.0 (* a c)) a)
25.9b	(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:

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

series39.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify44.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

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

prune112.0ms

Filtered

54 candidates to 77 candidates (-42.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	76	7	83

Merged error: 7.0b

Counts

83 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
25.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

10.0ms	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	354	766
1	1439	683
2	5001	679

prune111.0ms

Filtered

61 candidates to 83 candidates (-36.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	84	6	90

Merged error: 7.0b

Counts

90 → 6

regimes293.0ms

Accuracy

89.3% (2.8b remaining)

Error of 8.5b against oracle of 5.7b and baseline of 32.1b

bsearch132.0ms

Steps

Iters	Range	Point
9	4.880676122959305e+126	1.6874745041883248e+132	7.165775553570599e+126
9	-1.1410601569845324e-97	-3.11646147152481e-103	-1.9328404402975615e-100
9	-6.879391679013253e+106	-1.1315520404963029e+101	-4.139456257932803e+101

Iters

Range

Point

4.880676122959305e+126

1.6874745041883248e+132

7.165775553570599e+126

-1.1410601569845324e-97

-3.11646147152481e-103

-1.9328404402975615e-100

-6.879391679013253e+106

-1.1315520404963029e+101

-4.139456257932803e+101

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	27
1	45	27

end0.0ms

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.292969%

Guaranteed chance to sample good point: 62.826797%

Results

333.0ms	1058×	body	2560	valid
303.0ms	5119×	body	80	valid
241.0ms	917×	body	1280	valid
99.0ms	463×	body	640	valid
49.0ms	124×	body	5120	valid
41.0ms	222×	body	320	valid
18.0ms	314×	body	80	invalid
17.0ms	321×	body	80	nan
10.0ms	97×	body	160	valid

Details

sample2.0s

simplify14.0ms

prune4.0ms

localize12.0ms

rewrite32.0ms

series56.0ms

simplify50.0ms

prune169.0ms

localize16.0ms

rewrite69.0ms

series77.0ms

simplify194.0ms

prune374.0ms

localize15.0ms

rewrite21.0ms

series39.0ms

simplify44.0ms

prune112.0ms

localize15.0ms

rewrite25.0ms

series89.0ms

simplify45.0ms

prune111.0ms

regimes293.0ms

bsearch132.0ms

simplify2.0ms

end0.0ms

sample3.4s

Profiling