Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	299×	body	80	valid
7.0ms	98×	body	80	nan

simplify58.0ms

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

prune4.0ms

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

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.8b	(/ (* M D) (* 2.0 d))
5.2b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
9.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite30.0ms

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

series1.5s

Counts

4 → 12

Calls

4 calls:

404.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
32.0ms	(/ (* M D) (* 2.0 d))
366.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
691.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	609	1076
1	2742	997
2	5002	994

prune360.0ms

Filtered

125 candidates to 81 candidates (64.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Merged error: 7.9b

Counts

126 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) (* 2.0 d))
5.1b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.2b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.7b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite28.0ms

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:

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

series1.9s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
715.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
370.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
739.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify69.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (57.0ms)

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

prune305.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 7.5b

Counts

115 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) (* 2.0 d))
4.9b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.1b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.2b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

rewrite43.0ms

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×	`associate-/r*` `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 → 146

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(* (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)
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)))

series1.9s

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (* M D) (* 2.0 d))
744.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
707.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
377.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

simplify89.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	901	1944
1	3272	1558
2	5001	1548

prune329.0ms

Filtered

158 candidates to 70 candidates (44.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	159	7	166

Merged error: 7.3b

Counts

166 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) (* 2.0 d))
4.9b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.2b	(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))))
6.6b	(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
20.0ms	(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))))
7.0ms	(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

series1.7s

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
718.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
396.0ms	(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))))
609.0ms	(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

simplify73.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	675	1218
1	3096	1108
2	5001	1106

prune304.0ms

Filtered

111 candidates to 75 candidates (67.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	110	8	118

Merged error: 7.2b

Counts

118 → 8

regimes499.0ms

Accuracy

0% (1.2b remaining)

Error of 8.5b against oracle of 7.3b and baseline of 8.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	16
1	24	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

883.0ms	9293×	body	80	valid
242.0ms	3084×	body	80	nan