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

sample32.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	67×	body	80	nan
2.0ms	33×	body	80	invalid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	805	14
1	805	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: 23.3b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
0.5b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
27.0b	(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))
12.0ms	(* 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)))))
33.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
13.0ms	(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

prune154.0ms

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: 3.3b

Counts

105 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
2.0b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
27.0b	(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
33.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5256	1640

prune150.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	121	13	134

Merged error: 3.3b

Counts

134 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
0.2b	(- (* z z) (* t a))
2.0b	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
27.0b	(sqrt (- (* z z) (* t a)))

rewrite52.0ms

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:

10.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(- (* z z) (* t a))
21.0ms	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
8.0ms	(- (* z z) (* t a))
31.0ms	(* (* x y) (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
18.0ms	(sqrt (- (* z z) (* t a)))

simplify78.0ms

Algorithm

egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4965	4096
1	4965	4096

prune220.0ms

Filtered

140 candidates to 254 candidates (-81.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	251	3	254
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	254	13	267

Merged error: 3.3b

Counts

267 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(* (/ z (sqrt (- (* z z) (* t a)))) (cbrt y))
1.6b	(* x (* (* (cbrt y) (cbrt y)) (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt y))))
27.0b	(sqrt (- (* z z) (* t a)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`add-exp-log`
27×	`associate-l`
26×	`add-cbrt-cube`
25×	`pow1`
22×	`add-cube-cbrt` `*-un-lft-identity` `times-frac` `prod-exp` `cbrt-unprod`
14×	`pow-prod-down` `sqrt-prod`
9×	`cbrt-prod`
7×	`associate-r`
6×	`unswap-sqr`
4×	`sqrt-div` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`flip3--` `associate-r/` `associate-l/` `associate-/r/` `*-commutative` `flip--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `div-inv`

Counts

4 → 108

Calls

4 calls:

1.0ms	(cbrt y)
13.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) (cbrt y))
19.0ms	(* x (* (* (cbrt y) (cbrt y)) (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt y))))
4.0ms	(sqrt (- (* z z) (* t a)))

series129.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt y)
36.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) (cbrt y))
59.0ms	(* x (* (* (cbrt y) (cbrt y)) (* (/ z (sqrt (- (* z z) (* t a)))) (cbrt y))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5024	1526

prune95.0ms

Filtered

82 candidates to 120 candidates (-46.3%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	3	7	10
Picked	0	1	1
Done	0	2	2
Total	120	13	133

Merged error: 3.3b

Counts

133 → 13

regimes1.1s

Accuracy

85.2% (2.9b remaining)

Error of 6.2b against oracle of 3.3b and baseline of 23.1b

bsearch45.0ms

Steps

Iters	Range		Point
8	2.5673547920683853e+137	1.0255128468192735e+142	1.1766069837345114e+141
8	-2.6832860829267227e+158	-5.291945674439152e+153	-1.2687202986189205e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	42
1	67	42

end0.0ms

sample885.0ms

Algorithm

intervals

Results

414.0ms	8000×	body	80	valid
96.0ms	2217×	body	80	nan
43.0ms	885×	body	80	invalid

Details

analyze1.1s

sample32.0ms

simplify31.0ms

prune18.0ms

localize10.0ms

rewrite32.0ms

series72.0ms

simplify47.0ms

prune154.0ms

localize10.0ms

rewrite29.0ms

series64.0ms

simplify54.0ms

prune150.0ms

localize13.0ms

rewrite52.0ms

series68.0ms

simplify78.0ms

prune220.0ms

localize14.0ms

rewrite41.0ms

series129.0ms

simplify54.0ms

prune95.0ms

regimes1.1s

bsearch45.0ms

simplify2.0ms

end0.0ms

sample885.0ms

Profiling