Details

sample59.0ms

Algorithm

intervals

Results

22.0ms	305×	body	80	valid
7.0ms	88×	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

prune5.0ms

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: 14.3b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

2.6b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.3b	(/ (* M D) (* 2.0 d))
11.5b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite27.0ms

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:

5.0ms	(* 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))))
5.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series551.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
150.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
212.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	738	1124
1	2959	1046
2	5001	1043

prune273.0ms

Filtered

81 candidates to 125 candidates (-54.3%)

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: 8.3b

Counts

126 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

2.8b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.9b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.3b	(/ (* M D) (* 2.0 d))

rewrite26.0ms

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

series610.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
218.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
233.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms	(/ (* M D) (* 2.0 d))

simplify65.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	693	924
1	2737	841
2	5002	839

prune221.0ms

Filtered

69 candidates to 108 candidates (-56.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Merged error: 7.0b

Counts

117 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.3b	(/ (* M D) (* 2.0 d))
5.3b	(/ (* M D) (* 2.0 d))

rewrite47.0ms

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:

13.0ms	(/ (* (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)
5.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

series440.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
205.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
8.0ms	(/ (* M D) (* 2.0 d))
15.0ms	(/ (* M D) (* 2.0 d))

simplify81.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	1048	1799
1	3497	1375
2	5002	1371

prune274.0ms

Filtered

72 candidates to 162 candidates (-125.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	162	8	170

Merged error: 6.5b

Counts

170 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.3b	(/ (* M D) (* 2.0 d))
5.3b	(/ (* M D) (* 2.0 d))
6.2b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
35×	`add-cbrt-cube`
30×	`prod-exp`
24×	`div-exp`
14×	`add-sqr-sqrt`
10×	`cbrt-undiv` `pow-exp` `cbrt-unprod`
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×	`pow-to-exp` `sqr-pow`
1×	`*-commutative`

Counts

4 → 100

Calls

4 calls:

6.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
9.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

series427.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
211.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

simplify59.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	639	914
1	2609	782
2	5001	782

prune211.0ms

Filtered

71 candidates to 112 candidates (-57.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	112	8	120

Merged error: 6.5b

Counts

120 → 8

regimes2.0s

Accuracy

2.8% (1.4b remaining)

Error of 8.3b against oracle of 7.0b and baseline of 8.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	65
1	55	65

end0.0ms

sample1.7s

Algorithm

intervals

Results

705.0ms	9355×	body	80	valid
239.0ms	3090×	body	80	nan

Details

sample59.0ms

simplify52.0ms

prune5.0ms

localize16.0ms

rewrite27.0ms

series551.0ms

simplify72.0ms

prune273.0ms

localize13.0ms

rewrite26.0ms

series610.0ms

simplify65.0ms

prune221.0ms

localize16.0ms

rewrite47.0ms

series440.0ms

simplify81.0ms

prune274.0ms

localize15.0ms

rewrite30.0ms

series427.0ms

simplify59.0ms

prune211.0ms

regimes2.0s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.7s

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