Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample34.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	71×	body	80	nan
1.0ms	29×	body	80	invalid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune19.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 18.3b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* z z) (* t a))
4.2b	(* (* x y) z)
6.8b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
20.3b	(sqrt (- (* z z) (* t a)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 75

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
4.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
7.0ms	(* (* x y) z)
29.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify34.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5307	972

prune150.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	12	87
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	76	13	89

Merged error: 2.1b

Counts

89 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* z z) (* t a))
0.1b	(/ z (sqrt (- (* z z) (* t a))))
3.5b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
20.3b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-r` `sqrt-prod`
18×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`sqrt-div` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 111

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
6.0ms	(/ z (sqrt (- (* z z) (* t a))))
13.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
10.0ms	(/ z (sqrt (- (* z z) (* t a))))
30.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5256	1640

prune147.0ms

Filtered

83 candidates to 123 candidates (-48.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	124	12	136

Merged error: 2.1b

Counts

136 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (sqrt (- (* z z) (* t a))) (* z (* x y))))
4.2b	(* z (* x y))
6.7b	(/ (sqrt (- (* z z) (* t a))) (* z (* x y)))
20.3b	(sqrt (- (* z z) (* t a)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
52×	`add-exp-log`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-cbrt-cube`
21×	`sqrt-prod`
20×	`div-exp`
15×	`prod-exp`
11×	`pow1` `associate-/r*`
10×	`cbrt-undiv`
9×	`cbrt-unprod` `associate-/l*`
6×	`div-inv`
4×	`rec-exp` `sqrt-div` `1-exp` `add-log-exp`
3×	`associate-l` `pow-prod-down`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `associate-r` `associate-/r/` `*-commutative` `inv-pow`

Counts

4 → 136

Calls

4 calls:

18.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) (* z (* x y))))
7.0ms	(* z (* x y))
9.0ms	(/ (sqrt (- (* z z) (* t a))) (* z (* x y)))
5.0ms	(sqrt (- (* z z) (* t a)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) (* z (* x y))))
5.0ms	(* z (* x y))
36.0ms	(/ (sqrt (- (* z z) (* t a))) (* z (* x y)))
20.0ms	(sqrt (- (* z z) (* t a)))

simplify72.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5007	2277

prune156.0ms

Filtered

85 candidates to 148 candidates (-74.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	149	11	160

Merged error: 2.1b

Counts

160 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (- (* z z) (* t a))))
0.2b	(* z (/ 1 (sqrt (- (* z z) (* t a)))))
3.5b	(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
20.3b	(sqrt (- (* z z) (* t a)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
47×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-cbrt-cube`
27×	`prod-exp`
26×	`sqrt-prod`
25×	`associate-r`
21×	`pow1`
15×	`cbrt-unprod`
9×	`pow-prod-down`
8×	`div-exp`
6×	`sqrt-div` `associate-/r*`
5×	`unswap-sqr`
4×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `associate-l*` `associate-/r/` `add-log-exp`
3×	`flip3--` `pow-flip` `flip--` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `un-div-inv` `*-commutative` `div-inv`
1×	`rem-sqrt-square` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 143

Calls

4 calls:

7.0ms	(/ 1 (sqrt (- (* z z) (* t a))))
14.0ms	(* z (/ 1 (sqrt (- (* z z) (* t a)))))
12.0ms	(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1 (sqrt (- (* z z) (* t a))))
10.0ms	(* z (/ 1 (sqrt (- (* z z) (* t a)))))
31.0ms	(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5169	1920

prune112.0ms

Filtered

87 candidates to 155 candidates (-78.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	155	11	166

Merged error: 2.1b

Counts

166 → 11

regimes903.0ms

Accuracy

82.7% (3.7b remaining)

Error of 6.6b against oracle of 3.0b and baseline of 24.3b

bsearch75.0ms

Steps

Iters	Range	Point
10	1.0427785030714023e+120	1.2677856444439123e+132	2.4622880997986805e+126
6	1.6463076439653053e-234	2.3917792425964447e-233	1.5617269975664624e-233
8	-2.0980071817166854e+106	-3.8258674860644536e+102	-4.097858287678136e+102

Iters

Range

Point

1.0427785030714023e+120

1.2677856444439123e+132

2.4622880997986805e+126

1.6463076439653053e-234

2.3917792425964447e-233

1.5617269975664624e-233

-2.0980071817166854e+106

-3.8258674860644536e+102

-4.097858287678136e+102

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	49
1	79	49

end0.0ms

sample1.0s

Algorithm

intervals

Results

477.0ms	8000×	body	80	valid
127.0ms	2293×	body	80	nan
48.0ms	864×	body	80	invalid

Details

analyze1.1s

sample34.0ms

simplify31.0ms

prune19.0ms

localize10.0ms

rewrite23.0ms

series56.0ms

simplify34.0ms

prune150.0ms

localize10.0ms

rewrite31.0ms

series59.0ms

simplify55.0ms

prune147.0ms

localize14.0ms

rewrite49.0ms

series88.0ms

simplify72.0ms

prune156.0ms

localize12.0ms

rewrite43.0ms

series66.0ms

simplify58.0ms

prune112.0ms

regimes903.0ms

bsearch75.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling