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

sample39.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
3.0ms	59×	body	80	nan
2.0ms	37×	body	80	invalid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune14.0ms

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: 21.9b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
0.8b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.5b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.7b	(sqrt (- (* z z) (* t a)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
18.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
29.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
15.0ms	(sqrt (- (* z z) (* t a)))

simplify47.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune149.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Merged error: 3.8b

Counts

105 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
2.2b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.7b	(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(- (* z z) (* t a))
11.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5256	1640

prune159.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	121	13	134

Merged error: 3.7b

Counts

134 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
0.2b	(- (* z z) (* t a))
2.2b	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
24.7b	(sqrt (- (* z z) (* t a)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
143×	`add-sqr-sqrt`
142×	`add-cube-cbrt` `*-un-lft-identity`
71×	`associate-r`
66×	`sqrt-prod`
60×	`add-exp-log`
30×	`add-cbrt-cube`
22×	`associate-/r*`
21×	`div-exp` `prod-exp`
11×	`pow1`
9×	`cbrt-undiv` `cbrt-unprod` `div-inv`
6×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow-prod-down` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 242

Calls

4 calls:

11.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(- (* z z) (* t a))
19.0ms	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
7.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4965	4096
1	4965	4096

prune226.0ms

Filtered

142 candidates to 254 candidates (-78.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	253	1	254
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	256	11	267

Merged error: 3.7b

Counts

267 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.2b	(- (* z z) (* t a))
2.2b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.7b	(sqrt (- (* z z) (* t a)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
3×	`flip3--` `flip--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 131

Calls

4 calls:

6.0ms	(/ (sqrt (- (* z z) (* t a))) z)
4.0ms	(- (* z z) (* t a))
10.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (sqrt (- (* z z) (* t a))) z)
7.0ms	(- (* z z) (* t a))
32.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify44.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5053	2219

prune114.0ms

Filtered

100 candidates to 143 candidates (-43.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	143	11	154

Merged error: 3.7b

Counts

154 → 11

regimes1.3s

Accuracy

82.3% (3.6b remaining)

Error of 6.8b against oracle of 3.1b and baseline of 23.7b

bsearch46.0ms

Steps

Iters	Range		Point
9	1.365417150782335e+33	2.057785312570676e+41	1.5076725501489753e+41
7	-1.9786610820483492e+138	-5.063684580530288e+136	-7.285238985507498e+137

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	52
1	73	52

end0.0ms

sample884.0ms

Algorithm

intervals

Results

401.0ms	8000×	body	80	valid
103.0ms	2233×	body	80	nan
41.0ms	866×	body	80	invalid

Details

analyze1.1s

sample39.0ms

simplify32.0ms

prune14.0ms

localize11.0ms

rewrite32.0ms

series70.0ms

simplify47.0ms

prune149.0ms

localize11.0ms

rewrite28.0ms

series60.0ms

simplify51.0ms

prune159.0ms

localize12.0ms

rewrite50.0ms

series62.0ms

simplify71.0ms

prune226.0ms

localize11.0ms

rewrite28.0ms

series64.0ms

simplify44.0ms

prune114.0ms

regimes1.3s

bsearch46.0ms

simplify2.0ms

end0.0ms

sample884.0ms

Profiling