Details

analyze1.2s

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

sample40.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
6.0ms	43×	body	80	invalid
4.0ms	84×	body	80	nan

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune13.0ms

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: 19.8b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.0b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.9b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.8b	(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)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
19.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
30.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
16.0ms	(sqrt (- (* z z) (* t a)))

simplify45.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune140.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Merged error: 1.7b

Counts

105 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.3b	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
1.4b	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
23.8b	(sqrt (- (* z z) (* t a)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
31×	`pow1` `add-cbrt-cube`
27×	`prod-exp` `cbrt-unprod`
18×	`pow-prod-down`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`associate-l`
3×	`cbrt-undiv` `associate-*r/` `div-exp` `sqrt-prod`
2×	`flip3--` `sqrt-div` `associate-r` `associate-l/` `-commutative` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 80

Calls

4 calls:

6.0ms	(- (* z z) (* t a))
16.0ms	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
11.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
4.0ms	(sqrt (- (* z z) (* t a)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
36.0ms	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
37.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4960	1162
1	4960	1162

prune102.0ms

Filtered

55 candidates to 92 candidates (-67.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	93	8	101

Merged error: 1.6b

Counts

101 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.1b	(* y (/ x (/ (sqrt (- (* z z) (* t a))) z)))
1.2b	(/ x (/ (sqrt (- (* z z) (* t a))) z))
23.8b	(sqrt (- (* z z) (* t a)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 226

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
21.0ms	(* y (/ x (/ (sqrt (- (* z z) (* t a))) z)))
9.0ms	(/ x (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
42.0ms	(* y (/ x (/ (sqrt (- (* z z) (* t a))) z)))
19.0ms	(/ x (/ (sqrt (- (* z z) (* t a))) z))
18.0ms	(sqrt (- (* z z) (* t a)))

simplify87.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4922	4133
1	4922	4133

prune259.0ms

Filtered

167 candidates to 238 candidates (-42.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	239	7	246

Merged error: 1.6b

Counts

246 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(* y (* (/ z (* (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (cbrt (sqrt (- (* z z) (* t a)))))) (cbrt x)))
23.8b	(sqrt (- (* z z) (* t a)))
23.8b	(sqrt (- (* z z) (* t a)))
23.8b	(sqrt (- (* z z) (* t a)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
16×	`add-cbrt-cube`
12×	`pow1` `prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-exp` `associate-l` `pow-prod-down` `flip--`
1×	`associate-r/` `associate-r` `associate-l/` `*-commutative`

Counts

4 → 70

Calls

4 calls:

27.0ms	(* y (* (/ z (* (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (cbrt (sqrt (- (* z z) (* t a)))))) (cbrt x)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* y (* (/ z (* (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (cbrt (sqrt (- (* z z) (* t a)))))) (cbrt x)))
12.0ms	(sqrt (- (* z z) (* t a)))
15.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4921	953
1	4921	953

prune85.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	82	7	89

Merged error: 1.6b

Counts

89 → 7

regimes948.0ms

Accuracy

82.3% (3.5b remaining)

Error of 7.0b against oracle of 3.5b and baseline of 23.3b

bsearch63.0ms

Steps

Iters	Range		Point
6	1.7577560972588873e+25	1.0348260300798866e+26	9.586635798481338e+25
9	-1.2468134608248228e+75	-2.897339701627297e+69	-6.199495381344021e+71

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	90
1	90	90

end0.0ms

sample910.0ms

Algorithm

intervals

Results

413.0ms	8000×	body	80	valid
108.0ms	2284×	body	80	nan
48.0ms	890×	body	80	invalid

Details

analyze1.2s

sample40.0ms

simplify31.0ms

prune13.0ms

localize10.0ms

rewrite32.0ms

series72.0ms

simplify45.0ms

prune140.0ms

localize14.0ms

rewrite40.0ms

series93.0ms

simplify49.0ms

prune102.0ms

localize14.0ms

rewrite51.0ms

series86.0ms

simplify87.0ms

prune259.0ms

localize18.0ms

rewrite41.0ms

series78.0ms

simplify66.0ms

prune85.0ms

regimes948.0ms

bsearch63.0ms

simplify2.0ms

end0.0ms

sample910.0ms

Profiling