Details

sample471.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 5.867544%

Guaranteed chance to sample good point: 42.569946%

Results

12.0ms	26×	body	2560	valid
10.0ms	193×	body	80	valid
6.0ms	31×	body	1280	valid
4.0ms	84×	body	80	nan
3.0ms	17×	body	640	valid
2.0ms	6×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify402.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune5.0ms

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: 33.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune142.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Merged error: 6.7b

Counts

104 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.6b	(- (* b_2 b_2) (* a c))
0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

13.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	420	880
1	1816	791
2	5002	772

prune115.0ms

Filtered

70 candidates to 101 candidates (-44.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	102	9	111

Merged error: 6.7b

Counts

111 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
0.6b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.9b	(* (/ 1 a) (* a c))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
16×	`*-un-lft-identity` `add-cbrt-cube`
13×	`add-sqr-sqrt` `associate-l`
12×	`add-cube-cbrt` `prod-exp`
10×	`pow1` `add-log-exp`
9×	`times-frac`
6×	`cbrt-unprod`
4×	`div-exp`
3×	`pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `rec-exp` `flip3--` `sqrt-div` `1-exp` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r` `neg-log` `associate-l/` `-commutative` `flip-+` `div-inv`

Counts

4 → 79

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(* (/ 1 a) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms	(* (/ 1 a) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	411	489
1	1948	383
2	5001	371

prune118.0ms

Filtered

63 candidates to 91 candidates (-44.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	89	11	100

Merged error: 6.6b

Counts

100 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* (/ 1 a) 0) c) (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.6b	(- (* b_2 b_2) (* a c))
0.6b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 81

Calls

4 calls:

15.0ms	(/ (+ (* (/ 1 a) 0) c) (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (+ (* (/ 1 a) 0) c) (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	386	950
1	1549	835
2	5001	816

prune101.0ms

Filtered

71 candidates to 93 candidates (-31.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	5	7
Picked	1	0	1
Done	0	3	3
Total	94	10	104

Merged error: 6.6b

Counts

104 → 10

regimes433.0ms

Accuracy

87.1% (3.4b remaining)

Error of 9.1b against oracle of 5.6b and baseline of 32.4b

bsearch101.0ms

Steps

Iters	Range	Point
8	1.5899226579934786e+86	1.772173797690106e+90	1.3169442448748477e+90
9	-1.143859957059715e-225	-4.892276994531256e-232	-3.604894168941212e-229
9	-4.614558500810685e+27	-1.5335959160462621e+22	-2.6514850106522654e+26

Iters

Range

Point

1.5899226579934786e+86

1.772173797690106e+90

1.3169442448748477e+90

-1.143859957059715e-225

-4.892276994531256e-232

-3.604894168941212e-229

-4.614558500810685e+27

-1.5335959160462621e+22

-2.6514850106522654e+26

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	27
1	45	27

end0.0ms

sample1.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 5.867544%

Guaranteed chance to sample good point: 42.569946%

Results

262.0ms	5911×	body	80	valid
260.0ms	1036×	body	2560	valid
184.0ms	903×	body	1280	valid
92.0ms	2208×	body	80	nan
77.0ms	460×	body	640	valid
31.0ms	100×	body	5120	valid
24.0ms	202×	body	320	valid
11.0ms	129×	body	160	valid

Details

sample471.0ms

simplify402.0ms

prune5.0ms

localize12.0ms

rewrite30.0ms

series69.0ms

simplify42.0ms

prune142.0ms

localize10.0ms

rewrite33.0ms

series49.0ms

simplify51.0ms

prune115.0ms

localize17.0ms

rewrite24.0ms

series34.0ms

simplify59.0ms

prune118.0ms

localize14.0ms

rewrite30.0ms

series74.0ms

simplify53.0ms

prune101.0ms

regimes433.0ms

bsearch101.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling