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

sample40.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	67×	body	80	nan
1.0ms	23×	body	80	invalid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

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: 24.2b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.0b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.9b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
28.5b	(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))
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)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
18.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
31.0ms	(* 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

prune157.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	93	12	105

Merged error: 3.8b

Counts

105 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

1.3b	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
1.4b	(* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))
1.9b	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
28.5b	(sqrt (- (* z z) (* t a)))

rewrite50.0ms

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:

11.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
13.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))
18.0ms	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
4.0ms	(sqrt (- (* z z) (* t a)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x)))
31.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))
37.0ms	(* (* (cbrt x) (cbrt x)) (* y (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt x))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify87.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4977	1825
1	4977	1825

prune157.0ms

Filtered

86 candidates to 131 candidates (-52.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	129	14	143

Merged error: 3.8b

Counts

143 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(* y (/ x (/ (sqrt (- (* z z) (* t a))) z)))
0.8b	(- (* z z) (* t a))
2.4b	(/ x (/ (sqrt (- (* z z) (* t a))) z))
28.5b	(sqrt (- (* z z) (* t a)))

rewrite52.0ms

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:

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

series72.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* y (/ x (/ (sqrt (- (* z z) (* t a))) z)))
7.0ms	(- (* z z) (* t a))
18.0ms	(/ x (/ (sqrt (- (* z z) (* t a))) z))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify129.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4922	4133
1	4922	4133

prune275.0ms

Filtered

167 candidates to 238 candidates (-42.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	234	4	238
Fresh	3	8	11
Picked	1	0	1
Done	0	2	2
Total	238	14	252

Merged error: 3.8b

Counts

252 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(* y (* (/ x (sqrt (- (* z z) (* t a)))) z))
0.8b	(- (* z z) (* t a))
11.0b	(* (/ x (sqrt (- (* z z) (* t a)))) z)
28.5b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`associate-l`
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×	`add-log-exp`
4×	`sqrt-div` `associate-r` `pow-prod-down`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-/r/` `-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `div-inv`

Counts

4 → 91

Calls

4 calls:

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

series69.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* y (* (/ x (sqrt (- (* z z) (* t a)))) z))
9.0ms	(- (* z z) (* t a))
18.0ms	(* (/ x (sqrt (- (* z z) (* t a)))) z)
12.0ms	(sqrt (- (* z z) (* t a)))

simplify34.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5346	1270

prune114.0ms

Filtered

79 candidates to 103 candidates (-30.4%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	103	14	117

Merged error: 3.8b

Counts

117 → 14

regimes1.3s

Accuracy

81% (3.7b remaining)

Error of 7.0b against oracle of 3.3b and baseline of 22.8b

bsearch99.0ms

Steps

Iters	Range		Point
7	1.5287276865751645e+75	3.247511979981193e+77	2.8288936700686717e+75
6	-8.231917329393536e-243	-1.834770738530566e-243	-8.151714677345732e-243
8	-7.1797054452758434e-189	-2.5714475420956414e-191	-2.5938209576510873e-191
7	-1.1283331382687853e+136	-3.0429526614222326e+134	-5.6186452759089954e+135

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	89
1	90	89

end0.0ms

sample943.0ms

Algorithm

intervals

Results

429.0ms	8000×	body	80	valid
103.0ms	2227×	body	80	nan
43.0ms	865×	body	80	invalid

Details

analyze1.1s

sample40.0ms

simplify32.0ms

prune14.0ms

localize11.0ms

rewrite35.0ms

series68.0ms

simplify46.0ms

prune157.0ms

localize14.0ms

rewrite50.0ms

series117.0ms

simplify87.0ms

prune157.0ms

localize13.0ms

rewrite52.0ms

series72.0ms

simplify129.0ms

prune275.0ms

localize12.0ms

rewrite31.0ms

series69.0ms

simplify34.0ms

prune114.0ms

regimes1.3s

bsearch99.0ms

simplify2.0ms

end0.0ms

sample943.0ms

Profiling