Details

analyze467.0ms

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample50.0ms

Algorithm

intervals

Results

16.0ms	47×	body	2560	valid
8.0ms	156×	body	80	valid
6.0ms	24×	body	1280	valid
3.0ms	18×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	25×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	15×	body	80	invalid
0.0ms	1×	body	160	valid

simplify211.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (210.0ms)

Iter	Nodes	Cost
0	1931	17
1	1931	17

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 36.5b

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))
0.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
24.6b	(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 → 75

Calls

4 calls:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* 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)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5946	1448

prune167.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	10	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	10	88

Merged error: 6.7b

Counts

88 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.4b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
12.6b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
12.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
45.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
61.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5232	2497

prune198.0ms

Filtered

84 candidates to 124 candidates (-47.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	124	10	134

Merged error: 6.6b

Counts

134 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

9.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 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)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4943	1600
1	4943	1600

prune165.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	93	10	103

Merged error: 6.5b

Counts

103 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 152

Calls

4 calls:

11.0ms	(/ 1 (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c))
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))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1 (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5290	3553

prune211.0ms

Filtered

96 candidates to 164 candidates (-70.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	164	10	174

Merged error: 6.5b

Counts

174 → 10

regimes333.0ms

Accuracy

94.4% (1.4b remaining)

Error of 7.2b against oracle of 5.8b and baseline of 30.4b

bsearch88.0ms

Steps

Iters	Range		Point
10	7.993648768459452e+52	4.051738333556185e+70	2.0984248321180817e+70
6	1.705307831583245e-296	2.4357605318345925e-295	8.663143669049511e-296
8	-5.676760822833496e+94	-1.165211036484065e+90	-1.6342944889415786e+91

simplify15.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	758	82
1	758	82

end0.0ms

sample1.3s

Algorithm

intervals

Results

336.0ms	1079×	body	2560	valid
274.0ms	5154×	body	80	valid
210.0ms	844×	body	1280	valid
94.0ms	472×	body	640	valid
42.0ms	116×	body	5120	valid
33.0ms	669×	body	80	nan
32.0ms	219×	body	320	valid
21.0ms	398×	body	80	invalid
12.0ms	116×	body	160	valid

Details

analyze467.0ms

sample50.0ms

simplify211.0ms

prune7.0ms

localize12.0ms

rewrite30.0ms

series61.0ms

simplify43.0ms

prune167.0ms

localize12.0ms

rewrite43.0ms

series137.0ms

simplify38.0ms

prune198.0ms

localize13.0ms

rewrite29.0ms

series89.0ms

simplify65.0ms

prune165.0ms

localize14.0ms

rewrite34.0ms

series67.0ms

simplify77.0ms

prune211.0ms

regimes333.0ms

bsearch88.0ms

simplify15.0ms

end0.0ms

sample1.3s

Profiling