Details

sample59.0ms

Algorithm

intervals

Results

22.0ms	305×	body	80	valid
7.0ms	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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 14.3b

Counts

2 → 1

localize14.0ms

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))

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:

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))
13.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series528.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
142.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
207.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (59.0ms)

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

prune260.0ms

Filtered

125 candidates to 81 candidates (35.2%)

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

localize16.0ms

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))

series558.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
207.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
200.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms	(/ (* M D) (* 2.0 d))

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (55.0ms)

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

prune212.0ms

Filtered

108 candidates to 69 candidates (36.1%)

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))

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)
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))

series419.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
201.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

simplify88.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (68.0ms)

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

prune243.0ms

Filtered

162 candidates to 72 candidates (55.6%)

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

localize16.0ms

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)

rewrite31.0ms

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:

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

series424.0ms

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))
209.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (14.0ms)

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

prune199.0ms

Filtered

112 candidates to 71 candidates (36.6%)

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

regimes1.9s

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

708.0ms	9355×	body	80	valid
242.0ms	3090×	body	80	nan

Details

sample59.0ms

simplify53.0ms

prune5.0ms

localize14.0ms

rewrite30.0ms

series528.0ms

simplify72.0ms

prune260.0ms

localize16.0ms

rewrite26.0ms

series558.0ms

simplify66.0ms

prune212.0ms

localize16.0ms

rewrite42.0ms

series419.0ms

simplify88.0ms

prune243.0ms

localize16.0ms

rewrite31.0ms

series424.0ms

simplify63.0ms

prune199.0ms

regimes1.9s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.7s

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