Details

sample98.0ms

Algorithm

intervals

Results

34.0ms	289×	body	80	valid
13.0ms	99×	body	80	nan

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	81	18
3	181	18
4	460	18
5	2702	18
done	5001	18

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize36.0ms

Local error

Found 4 expressions with local error:

1.6b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
3.4b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.6b	(/ (* M D) (* 2.0 d))
9.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite70.0ms

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×	`*-un-lft-identity` `add-cube-cbrt`
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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-/l`

Counts

4 → 121

Calls

4 calls:

5.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
14.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
21.0ms	(/ (* M D) (* 2.0 d))
26.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.4s

Counts

4 → 12

Calls

4 calls:

624.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
669.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
57.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.3s

Counts

133 → 133

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	244	2427
1	643	2218
2	3150	2042
done	5000	2040

prune908.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize55.0ms

Local error

Found 4 expressions with local error:

3.4b	(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
5.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.6b	(/ (* M D) (* 2.0 d))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-exp-log`
92×	`prod-exp`
40×	`div-exp`
32×	`add-cbrt-cube`
26×	`add-sqr-sqrt`
25×	`pow-exp`
22×	`associate-r`
17×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-l`
12×	`cbrt-unprod`
11×	`times-frac`
8×	`pow1` `rec-exp` `1-exp`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `-commutative` `div-inv`
2×	`sqrt-div` `pow-prod-down` `sqr-pow`
1×	`clear-num` `associate-/r` `frac-2neg` `flip3--` `un-div-inv` `flip--` `associate-/l`

Counts

4 → 145

Calls

4 calls:

28.0ms	(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
37.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
32.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
10.0ms	(/ (* M D) (* 2.0 d))

series3.2s

Counts

4 → 12

Calls

4 calls:

634.0ms	(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
1.5s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
1.1s	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
53.0ms	(/ (* M D) (* 2.0 d))

simplify2.2s

Counts

157 → 157

Iterations

Useful iterations: 2 (629.0ms)

Iter	Nodes	Cost
0	295	2859
1	831	2549
2	4480	2176
done	5001	2176

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize61.0ms

Local error

Found 4 expressions with local error:

5.4b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
5.6b	(/ (* M D) (* 2.0 d))
5.6b	(/ (* M D) (* 2.0 d))
7.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

1402×	`add-exp-log`
907×	`prod-exp`
366×	`div-exp`
305×	`pow-exp`
61×	`pow-to-exp`
57×	`rec-exp` `1-exp`
51×	`add-cbrt-cube`
21×	`cbrt-unprod`
19×	`add-sqr-sqrt`
16×	`associate-r`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
11×	`cbrt-undiv`
10×	`associate-l`
6×	`pow1` `unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`clear-num` `associate-/r` `frac-2neg` `-commutative` `associate-/l*` `sqr-pow`
1×	`pow-prod-down` `associate-*r/` `un-div-inv`

Counts

4 → 340

Calls

4 calls:

138.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
9.0ms	(/ (* M D) (* 2.0 d))
16.0ms	(/ (* M D) (* 2.0 d))
48.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series2.1s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
38.0ms	(/ (* M D) (* 2.0 d))
38.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify1.8s

Counts

352 → 352

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	447	10610
1	1719	9123
done	5001	5818

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize53.0ms

Local error

Found 4 expressions with local error:

5.6b	(/ (* M D) (* 2.0 d))
5.6b	(/ (* M D) (* 2.0 d))
5.7b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
7.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite75.0ms

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×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`unpow-prod-down` `times-frac`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `associate-/l*` `unswap-sqr`
2×	`pow-to-exp` `sqr-pow`
1×	`*-commutative`

Counts

4 → 108

Calls

4 calls:

19.0ms	(/ (* M D) (* 2.0 d))
12.0ms	(/ (* M D) (* 2.0 d))
13.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
25.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series2.2s

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (* M D) (* 2.0 d))
54.0ms	(/ (* M D) (* 2.0 d))
971.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
1.1s	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify1.1s

Counts

120 → 120

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	194	1838
1	512	1758
2	2565	1498
done	5001	1490

prune786.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

regimes1.7s

Accuracy

0% (1.5b remaining)

Error of 8.1b against oracle of 6.6b and baseline of 8.1b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	67
1	29	67
done	29	67

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.8s	9318×	body	80	valid
377.0ms	3055×	body	80	nan