Details

analyze1.3s

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	65×	body	80	nan
1.0ms	23×	body	80	invalid

simplify238.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (236.0ms)

Iter	Nodes	Cost
0	1745	14
1	1745	14

prune18.0ms

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: 21.5b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
1.8b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.9b	(* y (/ z (sqrt (- (* z z) (* t a)))))
25.2b	(sqrt (- (* z z) (* t a)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
11.0ms	(* 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 (sqrt (- (* z z) (* t a))))
31.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
18.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5073	1760

prune215.0ms

Filtered

97 candidates to 133 candidates (-37.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	121	12	133
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	122	13	135

Merged error: 3.4b

Counts

135 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
1.3b	(* (/ z (sqrt (- (* z z) (* t a)))) x)
1.7b	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
25.2b	(sqrt (- (* z z) (* t a)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

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

series66.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ z (sqrt (- (* z z) (* t a))))
18.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) x)
26.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify59.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5247	1792

prune224.0ms

Filtered

99 candidates to 133 candidates (-34.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	133	13	146

Merged error: 3.4b

Counts

146 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
1.8b	(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
1.9b	(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
25.2b	(sqrt (- (* z z) (* t a)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

268×	`times-frac`
166×	`add-sqr-sqrt`
147×	`*-un-lft-identity`
144×	`add-cube-cbrt`
72×	`associate-r`
68×	`sqrt-prod`
62×	`add-exp-log`
32×	`add-cbrt-cube`
22×	`prod-exp` `associate-/r*`
21×	`div-exp`
13×	`pow1`
10×	`cbrt-unprod`
9×	`cbrt-undiv` `div-inv`
7×	`unswap-sqr`
6×	`rec-exp` `1-exp` `associate-l`
4×	`associate-*r/` `pow-prod-down` `add-log-exp`
3×	`associate-/l*`
2×	`sqrt-div` `associate-/r/` `un-div-inv` `*-commutative`
1×	`rem-sqrt-square` `flip3--` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--` `inv-pow`

Counts

4 → 257

Calls

4 calls:

9.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
15.0ms	(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
24.0ms	(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
30.0ms	(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
24.0ms	(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify97.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4957	4227
1	4957	4227

prune275.0ms

Filtered

153 candidates to 269 candidates (-75.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	268	1	269
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	269	13	282

Merged error: 3.4b

Counts

282 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
1.8b	(* x (* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
25.2b	(sqrt (- (* z z) (* t a)))
25.2b	(sqrt (- (* z z) (* t a)))

rewrite73.0ms

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:

29.0ms	(* (* 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)))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
33.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
17.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify79.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4984	3138
1	4984	3138

prune139.0ms

Filtered

92 candidates to 170 candidates (-84.8%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	170	13	183

Merged error: 3.4b

Counts

183 → 13

regimes1.0s

Accuracy

84.4% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 22.5b

bsearch49.0ms

Steps

Iters	Range		Point
8	8.108676085730805e+50	7.196636041116294e+54	5.331137027891388e+54
8	-2.7694010922156483e+158	-1.2322463585321781e+154	-1.3266678793411263e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	139	40
1	139	40

end0.0ms

sample938.0ms

Algorithm

intervals

Results

422.0ms	8000×	body	80	valid
107.0ms	2226×	body	80	nan
45.0ms	831×	body	80	invalid

Details

analyze1.3s

sample34.0ms

simplify238.0ms

prune18.0ms

localize10.0ms

rewrite34.0ms

series71.0ms

simplify56.0ms

prune215.0ms

localize12.0ms

rewrite36.0ms

series66.0ms

simplify59.0ms

prune224.0ms

localize12.0ms

rewrite66.0ms

series76.0ms

simplify97.0ms

prune275.0ms

localize16.0ms

rewrite73.0ms

series86.0ms

simplify79.0ms

prune139.0ms

regimes1.0s

bsearch49.0ms

simplify2.0ms

end0.0ms

sample938.0ms

Profiling