Details

analyze455.0ms

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

sample44.0ms

Algorithm

intervals

Results

12.0ms	34×	body	2560	valid
9.0ms	167×	body	80	valid
7.0ms	28×	body	1280	valid
3.0ms	15×	body	640	valid
1.0ms	16×	body	80	nan
1.0ms	5×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	12×	body	80	invalid
0.0ms	5×	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: 35.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b	(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))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5946	1448

prune156.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	9	88

Merged error: 8.1b

Counts

88 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.6b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
12.7b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.4b	(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))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series129.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (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))
56.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify37.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5232	2497

prune186.0ms

Filtered

84 candidates to 124 candidates (-47.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	123	10	133

Merged error: 8.0b

Counts

133 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

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)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (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 (56.0ms)

Iter	Nodes	Cost
0	4943	1600
1	4943	1600

prune151.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	93	10	103

Merged error: 7.9b

Counts

103 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 88

Calls

4 calls:

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

series65.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 2.0 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4969	1782
1	4969	1782

prune131.0ms

Filtered

71 candidates to 100 candidates (-40.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	98	12	110

Merged error: 7.9b

Counts

110 → 12

regimes427.0ms

Accuracy

95.2% (1.1b remaining)

Error of 7.0b against oracle of 5.8b and baseline of 29.0b

bsearch86.0ms

Steps

Iters	Range	Point
8	9.410589117386009e+88	2.500375124013091e+93	1.342597879577989e+92
6	-1.4080609620407604e-297	-1.8297885750190512e-298	-1.8516422739532216e-298
9	-3.124175929605594e+131	-7.890578420652415e+125	-8.400344984829291e+127

Iters

Range

Point

9.410589117386009e+88

2.500375124013091e+93

1.342597879577989e+92

-1.4080609620407604e-297

-1.8297885750190512e-298

-1.8516422739532216e-298

-3.124175929605594e+131

-7.890578420652415e+125

-8.400344984829291e+127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	125	69
1	125	69

end0.0ms

sample1.2s

Algorithm

intervals

Results

309.0ms	1052×	body	2560	valid
266.0ms	5114×	body	80	valid
232.0ms	930×	body	1280	valid
83.0ms	429×	body	640	valid
39.0ms	111×	body	5120	valid
38.0ms	236×	body	320	valid
33.0ms	671×	body	80	nan
20.0ms	398×	body	80	invalid
12.0ms	128×	body	160	valid

Details

analyze455.0ms

sample44.0ms

simplify211.0ms

prune7.0ms

localize11.0ms

rewrite30.0ms

series59.0ms

simplify44.0ms

prune156.0ms

localize12.0ms

rewrite43.0ms

series129.0ms

simplify37.0ms

prune186.0ms

localize14.0ms

rewrite27.0ms

series85.0ms

simplify65.0ms

prune151.0ms

localize13.0ms

rewrite31.0ms

series65.0ms

simplify59.0ms

prune131.0ms

regimes427.0ms

bsearch86.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling