Details

analyze595.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample41.0ms

Algorithm

intervals

Results

8.0ms	38×	body	1280	valid
8.0ms	163×	body	80	valid
8.0ms	30×	body	2560	valid
2.0ms	12×	body	640	valid
1.0ms	28×	body	80	nan
1.0ms	9×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid
0.0ms	3×	body	80	invalid

simplify504.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	713	13
1	713	13

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: 33.1b

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)
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

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 → 89

Calls

4 calls:

11.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
22.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune141.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	92	9	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	9	102

Merged error: 5.3b

Counts

102 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 175

Calls

4 calls:

15.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5176	3699

prune157.0ms

Filtered

103 candidates to 187 candidates (-81.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	188	8	196

Merged error: 5.3b

Counts

196 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.4b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.6b	(/ (* a c) a)
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series35.0ms

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	(/ (* a c) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5179	644

prune87.0ms

Filtered

57 candidates to 74 candidates (-29.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	75	7	82

Merged error: 5.3b

Counts

82 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.0b	(- (* b_2 b_2) (* a c))
1.4b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms

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×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip--` `flip-+`
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 → 78

Calls

4 calls:

10.0ms	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms	(- (* 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)))

simplify57.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5677	1193

prune79.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	89	8	97

Merged error: 5.3b

Counts

97 → 8

regimes286.0ms

Accuracy

94.4% (1.4b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 29.8b

bsearch76.0ms

Steps

Iters	Range	Point
7	3.963800216912635e+124	2.690709854605475e+126	5.1705566396560645e+125
9	6.8922054227111525e-273	1.2931106526566346e-266	9.938321320749755e-267
7	-1.8146988650740042e+72	-1.778359534232584e+70	-1.768189770875938e+72

Iters

Range

Point

3.963800216912635e+124

2.690709854605475e+126

5.1705566396560645e+125

6.8922054227111525e-273

1.2931106526566346e-266

9.938321320749755e-267

-1.8146988650740042e+72

-1.778359534232584e+70

-1.768189770875938e+72

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	57
1	90	57

end0.0ms

sample1.1s

Algorithm

intervals

Results

262.0ms	1042×	body	2560	valid
225.0ms	5130×	body	80	valid
185.0ms	920×	body	1280	valid
79.0ms	463×	body	640	valid
37.0ms	117×	body	5120	valid
32.0ms	787×	body	80	nan
28.0ms	218×	body	320	valid
11.0ms	252×	body	80	invalid
9.0ms	110×	body	160	valid

Details

analyze595.0ms

sample41.0ms

simplify504.0ms

prune5.0ms

localize12.0ms

rewrite33.0ms

series67.0ms

simplify64.0ms

prune141.0ms

localize10.0ms

rewrite41.0ms

series66.0ms

simplify69.0ms

prune157.0ms

localize11.0ms

rewrite21.0ms

series35.0ms

simplify58.0ms

prune87.0ms

localize9.0ms

rewrite27.0ms

series81.0ms

simplify57.0ms

prune79.0ms

regimes286.0ms

bsearch76.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling