Details

analyze2.3s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

sample47.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
6.0ms	79×	body	80	nan
3.0ms	37×	body	80	invalid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4904	18
1	4904	18

prune17.0ms

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: 15.1b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.2b	(/ (* M D) (* 2.0 d))
12.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 113

Calls

4 calls:

7.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series553.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
151.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
217.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify41.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5373	1965

prune251.0ms

Filtered

85 candidates to 125 candidates (-47.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	119	8	127

Merged error: 6.6b

Counts

127 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (- 1.0 (* (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) (/ 1 l))))
4.4b	(* h (pow (* (/ D d) (/ M 2.0)) 2.0))
5.1b	(* (/ D d) (/ M 2.0))
7.0b	(* (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) (/ 1 l))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
44×	`add-sqr-sqrt`
40×	`div-exp`
31×	`times-frac` `associate-r`
30×	`add-cbrt-cube`
28×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-exp`
17×	`associate-l`
11×	`cbrt-unprod`
9×	`pow1`
8×	`rec-exp` `1-exp`
6×	`cbrt-undiv` `unswap-sqr`
5×	`pow-to-exp`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative` `div-inv`
2×	`sqrt-div` `associate-*r/` `pow-prod-down` `sqr-pow`
1×	`frac-times` `unpow-prod-down` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-*l/` `un-div-inv` `flip--`

Counts

4 → 152

Calls

4 calls:

7.0ms	(sqrt (- 1.0 (* (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) (/ 1 l))))
6.0ms	(* h (pow (* (/ D d) (/ M 2.0)) 2.0))
10.0ms	(* (/ D d) (/ M 2.0))
11.0ms	(* (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) (/ 1 l))

series378.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt (- 1.0 (* (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) (/ 1 l))))
93.0ms	(* h (pow (* (/ D d) (/ M 2.0)) 2.0))
6.0ms	(* (/ D d) (/ M 2.0))
170.0ms	(* (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) (/ 1 l))

simplify79.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4969	2147
1	4969	2147

prune256.0ms

Filtered

97 candidates to 164 candidates (-69.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	0	6	6
Picked	1	0	1
Done	1	0	1
Total	164	8	172

Merged error: 6.6b

Counts

172 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (- 1.0 (* (* h (pow (/ (* D M) (* d 2.0)) 2.0)) (/ 1 l))))
4.2b	(/ (* D M) (* d 2.0))
4.4b	(* h (pow (/ (* D M) (* d 2.0)) 2.0))
7.0b	(* (* h (pow (/ (* D M) (* d 2.0)) 2.0)) (/ 1 l))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
40×	`div-exp`
30×	`add-cbrt-cube`
25×	`pow-exp`
22×	`associate-r`
21×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac` `cbrt-unprod`
8×	`rec-exp` `1-exp`
7×	`pow1`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp`
4×	`associate-l` `add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 128

Calls

4 calls:

5.0ms	(sqrt (- 1.0 (* (* h (pow (/ (* D M) (* d 2.0)) 2.0)) (/ 1 l))))
6.0ms	(/ (* D M) (* d 2.0))
7.0ms	(* h (pow (/ (* D M) (* d 2.0)) 2.0))
11.0ms	(* (* h (pow (/ (* D M) (* d 2.0)) 2.0)) (/ 1 l))

series392.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (- 1.0 (* (* h (pow (/ (* D M) (* d 2.0)) 2.0)) (/ 1 l))))
6.0ms	(/ (* D M) (* d 2.0))
93.0ms	(* h (pow (/ (* D M) (* d 2.0)) 2.0))
171.0ms	(* (* h (pow (/ (* D M) (* d 2.0)) 2.0)) (/ 1 l))

simplify61.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4988	1940
1	4988	1940

prune204.0ms

Filtered

77 candidates to 140 candidates (-81.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	140	8	148

Merged error: 6.6b

Counts

148 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (- 1.0 (* h (/ (pow (* (/ D d) (/ M 2.0)) 2.0) l))))
5.1b	(* (/ D d) (/ M 2.0))
5.4b	(* h (/ (pow (* (/ D d) (/ M 2.0)) 2.0) l))
5.7b	(/ (pow (* (/ D d) (/ M 2.0)) 2.0) l)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
59×	`add-sqr-sqrt`
54×	`times-frac`
39×	`add-cube-cbrt` `*-un-lft-identity`
32×	`associate-r`
26×	`div-exp`
23×	`add-cbrt-cube`
20×	`prod-exp`
16×	`associate-l`
10×	`pow-exp`
9×	`pow1`
8×	`sqr-pow`
7×	`unpow-prod-down` `unswap-sqr`
6×	`cbrt-undiv` `cbrt-unprod`
5×	`associate-/l*`
4×	`div-inv` `add-log-exp`
3×	`associate-/r*` `sqrt-prod`
2×	`pow-to-exp` `sqrt-div` `associate-r/` `pow-prod-down` `-commutative`
1×	`frac-times` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*l/` `clear-num` `flip--`

Counts

4 → 151

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (* h (/ (pow (* (/ D d) (/ M 2.0)) 2.0) l))))
10.0ms	(* (/ D d) (/ M 2.0))
9.0ms	(* h (/ (pow (* (/ D d) (/ M 2.0)) 2.0) l))
5.0ms	(/ (pow (* (/ D d) (/ M 2.0)) 2.0) l)

series456.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt (- 1.0 (* h (/ (pow (* (/ D d) (/ M 2.0)) 2.0) l))))
6.0ms	(* (/ D d) (/ M 2.0))
167.0ms	(* h (/ (pow (* (/ D d) (/ M 2.0)) 2.0) l))
174.0ms	(/ (pow (* (/ D d) (/ M 2.0)) 2.0) l)

simplify67.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4976	2326
1	4976	2326

prune282.0ms

Filtered

126 candidates to 163 candidates (-29.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	163	8	171

Merged error: 6.3b

Counts

171 → 8

regimes1.1s

Accuracy

0% (1.6b remaining)

Error of 9.0b against oracle of 7.4b and baseline of 9.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	32
1	67	32

end0.0ms

sample1.4s

Algorithm

intervals

Results

615.0ms	8000×	body	80	valid
256.0ms	3156×	body	80	nan
111.0ms	1306×	body	80	invalid

Details

analyze2.3s

sample47.0ms

simplify49.0ms

prune17.0ms

localize19.0ms

rewrite31.0ms

series553.0ms

simplify41.0ms

prune251.0ms

localize16.0ms

rewrite41.0ms

series378.0ms

simplify79.0ms

prune256.0ms

localize15.0ms

rewrite34.0ms

series392.0ms

simplify61.0ms

prune204.0ms

localize14.0ms

rewrite37.0ms

series456.0ms

simplify67.0ms

prune282.0ms

regimes1.1s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling