Details

sample48.0ms

Algorithm

intervals

Results

21.0ms	294×	body	80	valid
7.0ms	95×	body	80	nan

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	182	9
3	456	9
4	1557	9
5	5001	9

prune6.0ms

Filtered

1 candidates to 0 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: 14.1b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

3.4b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.9b	(/ (* M D) (* 2.0 d))
4.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
9.7b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite50.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `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 → 121

Calls

4 calls:

10.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
10.0ms	(/ (* M D) (* 2.0 d))
5.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
18.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

416.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
34.0ms	(/ (* M D) (* 2.0 d))
410.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
701.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify82.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	630	1135
1	2779	1057
2	5001	1054

prune563.0ms

Filtered

133 candidates to 89 candidates (66.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	126	7	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Merged error: 8.5b

Counts

134 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ (* M D) (* 2.0 d))
4.0b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.4b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
26×	`prod-exp`
23×	`add-cbrt-cube`
20×	`div-exp`
18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `pow-exp`
9×	`associate-l`
6×	`cbrt-undiv` `unpow-prod-down` `cbrt-unprod`
5×	`pow1` `times-frac` `sqrt-prod`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 104

Calls

4 calls:

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

series1.8s

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (* M D) (* 2.0 d))
354.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
707.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
681.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify67.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	576	880
1	2585	798
2	5001	796

prune326.0ms

Filtered

116 candidates to 78 candidates (67.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	114	9	123

Merged error: 7.8b

Counts

123 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ (* M D) (* 2.0 d))
4.0b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.7b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.4b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

361×	`add-exp-log`
180×	`prod-exp`
125×	`div-exp`
80×	`pow-exp`
27×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
16×	`pow-to-exp`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`associate-l`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`unpow-prod-down`
5×	`pow1` `times-frac` `sqrt-prod`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `div-inv` `unswap-sqr`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 154

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
14.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

series1.9s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
378.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
753.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
708.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

simplify97.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	952	2025
1	3336	1640
2	5001	1630

prune360.0ms

Filtered

166 candidates to 79 candidates (47.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	165	10	175

Merged error: 7.8b

Counts

175 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ (* M D) (* 2.0 d))
3.9b	(/ (* M D) (* 2.0 d))
4.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
10.4b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
33×	`add-cbrt-cube`
30×	`prod-exp`
28×	`add-sqr-sqrt`
23×	`div-exp`
15×	`times-frac`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`pow-exp` `cbrt-unprod`
9×	`cbrt-undiv` `associate-l`
7×	`unpow-prod-down`
6×	`unswap-sqr`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`sqrt-prod` `sqr-pow`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative` `flip--`

Counts

4 → 118

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
3.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
14.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.2s

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (* M D) (* 2.0 d))
29.0ms	(/ (* M D) (* 2.0 d))
384.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
708.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify75.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	595	1197
1	2618	1077
2	5001	1076

prune374.0ms

Filtered

130 candidates to 85 candidates (65.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	131	9	140

Merged error: 7.8b

Counts

140 → 9

regimes880.0ms

Accuracy

12.5% (1.6b remaining)

Error of 9.2b against oracle of 7.6b and baseline of 9.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	36
1	46	36

end0.0ms

sample1.4s

Algorithm

intervals

Results

703.0ms	9467×	body	80	valid
240.0ms	3134×	body	80	nan