Details

sample44.0ms

Algorithm

intervals

Results

17.0ms	292×	body	80	valid
6.0ms	98×	body	80	nan

simplify52.0ms

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: 16.9b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

2.9b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b	(/ (* M D) (* 2.0 d))
13.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite29.0ms

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))

series1.6s

Counts

4 → 12

Calls

4 calls:

405.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
351.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
31.0ms	(/ (* M D) (* 2.0 d))
829.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify74.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (62.0ms)

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

prune380.0ms

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: 9.4b

Counts

126 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

4.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.7b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.9b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.5b	(/ (* M D) (* 2.0 d))

rewrite31.0ms

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:

7.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
7.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
8.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0ms	(/ (* M D) (* 2.0 d))

series1.7s

Counts

4 → 12

Calls

4 calls:

700.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
667.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
355.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
27.0ms	(/ (* M D) (* 2.0 d))

simplify73.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (56.0ms)

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

prune376.0ms

Filtered

108 candidates to 71 candidates (65.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	106	11	117

Merged error: 8.7b

Counts

117 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.5b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

series1.2s

Counts

4 → 12

Calls

4 calls:

363.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
734.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
27.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	443	917
1	1894	812
2	5001	810

prune357.0ms

Filtered

102 candidates to 65 candidates (63.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 8.7b

Counts

113 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (/ (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.5b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(/ (* M D) (* 2.0 d))
5.6b	(* (* M D) (/ 1 (* 2.0 d)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-exp-log`
42×	`prod-exp`
39×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
16×	`div-exp` `cbrt-unprod`
12×	`*-un-lft-identity`
10×	`pow1` `add-cube-cbrt` `associate-r` `associate-l`
8×	`cbrt-undiv`
6×	`unpow-prod-down`
5×	`times-frac` `pow-exp` `sqrt-prod`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow-prod-down` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 109

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (/ (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms	(/ (* M D) (* 2.0 d))
9.0ms	(* (* M D) (/ 1 (* 2.0 d)))

series1.1s

Counts

4 → 12

Calls

4 calls:

360.0ms	(sqrt (- 1.0 (/ (* (pow (* (* M D) (/ 1 (* 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)
27.0ms	(/ (* M D) (* 2.0 d))
31.0ms	(* (* M D) (/ 1 (* 2.0 d)))

simplify78.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	640	1036
1	3104	901
2	5001	897

prune353.0ms

Filtered

121 candidates to 68 candidates (56.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	122	9	131

Merged error: 8.7b

Counts

131 → 9

regimes932.0ms

Accuracy

0% (1.6b remaining)

Error of 9.3b against oracle of 7.7b and baseline of 9.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	17
1	32	17

end0.0ms

sample1.2s

Algorithm

intervals

Results

576.0ms	9356×	body	80	valid
204.0ms	3083×	body	80	nan