Details

sample42.0ms

Algorithm

intervals

Results

17.0ms	300×	body	80	valid
5.0ms	88×	body	80	nan

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	178	9
3	446	9
4	1530	9
5	5001	9

prune3.0ms

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: 14.8b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

1.7b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.6b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.4b	(/ (* M D) (* 2.0 d))
10.5b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite28.0ms

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:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

419.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
349.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
33.0ms	(/ (* M D) (* 2.0 d))
665.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify70.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	609	1075
1	2742	997
2	5003	994

prune346.0ms

Filtered

125 candidates to 81 candidates (64.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	9	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 8.1b

Counts

126 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

4.6b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.7b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b	(/ (* M D) (* 2.0 d))

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×	`associate-/r*` `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 → 96

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
7.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
9.0ms	(/ (* M D) (* 2.0 d))

series2.0s

Counts

4 → 12

Calls

4 calls:

386.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
926.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
698.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
27.0ms	(/ (* M D) (* 2.0 d))

simplify67.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	560	828
1	2559	746
2	5001	744

prune275.0ms

Filtered

108 candidates to 70 candidates (64.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	107	10	117

Merged error: 7.5b

Counts

117 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.4b	(/ (* M D) (* 2.0 d))
5.4b	(/ (* M D) (* 2.0 d))
5.5b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

373×	`add-exp-log`
184×	`prod-exp`
129×	`div-exp`
80×	`pow-exp`
39×	`add-cbrt-cube`
16×	`pow-to-exp`
14×	`add-sqr-sqrt`
12×	`cbrt-unprod`
11×	`cbrt-undiv`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`unpow-prod-down` `times-frac`
5×	`associate-/r*`
4×	`pow1` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l*` `unswap-sqr`
2×	`sqr-pow`
1×	`*-commutative`

Counts

4 → 150

Calls

4 calls:

14.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.6s

Counts

4 → 12

Calls

4 calls:

808.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
36.0ms	(/ (* M D) (* 2.0 d))
26.0ms	(/ (* M D) (* 2.0 d))
715.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify79.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	836	1701
1	3118	1278
2	5001	1274

prune317.0ms

Filtered

162 candidates to 72 candidates (44.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	158	4	162
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	162	10	172

Merged error: 7.0b

Counts

172 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
5.4b	(/ (* M D) (* 2.0 d))
5.4b	(/ (* M D) (* 2.0 d))
5.5b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-exp-log`
34×	`div-exp` `prod-exp`
33×	`add-cbrt-cube`
16×	`add-sqr-sqrt` `unpow-prod-down`
15×	`pow-exp`
14×	`times-frac`
11×	`add-cube-cbrt` `-un-lft-identity` `associate-/l`
10×	`cbrt-undiv` `cbrt-unprod`
9×	`associate-l`
6×	`div-inv`
4×	`pow1` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `frac-2neg` `associate-r` `clear-num` `associate-/r*` `unswap-sqr`
1×	`*-commutative`

Counts

4 → 118

Calls

4 calls:

10.0ms	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.2s

Counts

4 → 12

Calls

4 calls:

458.0ms	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
26.0ms	(/ (* M D) (* 2.0 d))
31.0ms	(/ (* M D) (* 2.0 d))
697.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify61.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	541	1098
1	2333	967
2	5001	961

prune367.0ms

Filtered

130 candidates to 81 candidates (62.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	130	10	140

Merged error: 7.0b

Counts

140 → 10

regimes888.0ms

Accuracy

-16.3% (1.6b remaining)

Error of 8.8b against oracle of 7.3b and baseline of 8.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	76
1	56	76

end0.0ms

sample1.2s

Algorithm

intervals

Results

546.0ms	9299×	body	80	valid
195.0ms	3210×	body	80	nan