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

sample60.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune15.0ms

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: 20.6b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.6b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.1b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.3b	(sqrt (- (* z z) (* t a)))

rewrite35.0ms

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))
12.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* z z) (* t a))
19.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
30.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify46.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune144.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	95	10	105

Merged error: 3.8b

Counts

105 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
2.1b	(* x (* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
24.3b	(sqrt (- (* z z) (* t a)))
24.3b	(sqrt (- (* z z) (* t a)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
61×	`associate-r`
60×	`sqrt-prod`
58×	`add-cbrt-cube`
54×	`times-frac`
46×	`add-sqr-sqrt`
45×	`prod-exp` `cbrt-unprod`
44×	`add-cube-cbrt` `*-un-lft-identity`
29×	`pow1`
27×	`cbrt-prod`
16×	`pow-prod-down`
13×	`associate-*r/`
12×	`cbrt-undiv` `div-exp`
8×	`sqrt-div`
4×	`associate-l` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `associate-/r/` `-commutative`
1×	`div-inv`

Counts

4 → 158

Calls

4 calls:

31.0ms	(* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
28.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
6.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series87.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
34.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
16.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4968	3722
1	4968	3722

prune177.0ms

Filtered

102 candidates to 170 candidates (-66.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	169	11	180

Merged error: 3.8b

Counts

180 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
1.4b	(* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))
1.6b	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
24.3b	(sqrt (- (* z z) (* t a)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
38×	`add-sqr-sqrt`
34×	`add-cbrt-cube`
33×	`pow1`
29×	`prod-exp` `cbrt-unprod`
28×	`associate-l`
22×	`times-frac`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow-prod-down`
14×	`sqrt-prod`
8×	`associate-r`
6×	`cbrt-prod` `unswap-sqr`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `add-log-exp`
3×	`associate-r/` `associate-l/` `*-commutative`
2×	`flip3--` `associate-/r/` `flip--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 119

Calls

4 calls:

17.0ms	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
13.0ms	(* (/ 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)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
31.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))
41.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify84.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4977	1825
1	4977	1825

prune146.0ms

Filtered

83 candidates to 131 candidates (-57.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	130	12	142

Merged error: 3.8b

Counts

142 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.4b	(* y (/ x (/ (sqrt (- (* z z) (* t a))) z)))
1.9b	(/ x (/ (sqrt (- (* z z) (* t a))) z))
24.3b	(sqrt (- (* z z) (* t a)))

rewrite54.0ms

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))
24.0ms	(* y (/ x (/ (sqrt (- (* z z) (* t a))) z)))
9.0ms	(/ x (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
35.0ms	(* y (/ x (/ (sqrt (- (* z z) (* t a))) z)))
19.0ms	(/ x (/ (sqrt (- (* z z) (* t a))) z))
13.0ms	(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

prune225.0ms

Filtered

167 candidates to 238 candidates (-42.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	234	4	238
Fresh	4	5	9
Picked	0	1	1
Done	1	1	2
Total	239	11	250

Merged error: 3.8b

Counts

250 → 11

regimes1.0s

Accuracy

79.8% (4.0b remaining)

Error of 7.2b against oracle of 3.3b and baseline of 22.9b

bsearch130.0ms

Steps

Iters	Range		Point
4	1.5446577253821425e+132	2.805087780465077e+132	1.584046164603484e+132
9	1.215590351800438e-182	7.735443068654259e-174	1.3233303272720813e-182
9	1.5427532642588953e-239	5.74281685695778e-233	1.2268572723557027e-234
5	-1.1331840239386615e+117	-3.299015396196143e+116	-3.38525079024628e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	75
1	95	75

end0.0ms

sample1.8s

Algorithm

intervals

Results

357.0ms

8000×

body

valid

Details

analyze1.1s

sample60.0ms

simplify32.0ms

prune15.0ms

localize11.0ms

rewrite35.0ms

series71.0ms

simplify46.0ms

prune144.0ms

localize17.0ms

rewrite77.0ms

series87.0ms

simplify71.0ms

prune177.0ms

localize15.0ms

rewrite49.0ms

series120.0ms

simplify84.0ms

prune146.0ms

localize13.0ms

rewrite54.0ms

series75.0ms

simplify87.0ms

prune225.0ms

regimes1.0s

bsearch130.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling