Details

sample73.0ms

Algorithm

intervals

Results

26.0ms	289×	body	80	valid
9.0ms	90×	body	80	nan

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	81	18
3	181	18
4	457	18
5	2678	18
done	5001	18

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize23.0ms

Local error

Found 4 expressions with local error:

1.4b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.7b	(/ (* M D) (* 2.0 d))
9.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite116.0ms

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×	`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` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 121

Calls

4 calls:

25.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
7.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
23.0ms	(/ (* M D) (* 2.0 d))
51.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts

4 → 12

Calls

4 calls:

617.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
563.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
47.0ms	(/ (* M D) (* 2.0 d))
1.1s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.9s

Counts

133 → 133

Iterations

Useful iterations: 2 (464.0ms)

Iter	Nodes	Cost
0	244	2427
1	644	2218
2	3132	2042
done	5000	2042

prune615.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.0b

localize38.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.7b	(/ (* M D) (* 2.0 d))
5.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
40×	`div-exp`
30×	`add-cbrt-cube`
25×	`pow-exp`
21×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac` `cbrt-unprod`
10×	`associate-l`
8×	`rec-exp` `1-exp`
7×	`pow1`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 136

Calls

4 calls:

11.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
27.0ms	(/ (* M D) (* 2.0 d))
31.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
71.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))

series2.7s

Counts

4 → 12

Calls

4 calls:

532.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
44.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
1.0s	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))

simplify3.5s

Counts

148 → 148

Iterations

Useful iterations: 2 (681.0ms)

Iter	Nodes	Cost
0	277	2631
1	788	2327
2	4588	1990
done	5001	1990

prune605.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.5b

localize29.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* M D) (* 2.0 d))
4.7b	(/ (* M D) (* 2.0 d))
4.9b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

rewrite327.0ms

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×	`add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `associate-/l*` `sqr-pow`
1×	`associate-*r/` `pow-prod-down` `un-div-inv`

Counts

4 → 340

Calls

4 calls:

24.0ms	(/ (* M D) (* 2.0 d))
30.0ms	(/ (* M D) (* 2.0 d))
34.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
189.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

series2.1s

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (* M D) (* 2.0 d))
57.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
986.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

simplify1.5s

Counts

352 → 352

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	447	10610
1	1724	9093
done	5001	5818

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.5b

localize30.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* M D) (* 2.0 d))
4.7b	(/ (* M D) (* 2.0 d))
4.9b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.2b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

rewrite137.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `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 → 108

Calls

4 calls:

25.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
61.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
17.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

series2.2s

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (* M D) (* 2.0 d))
49.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
1.0s	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

simplify1.2s

Counts

120 → 120

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	194	1838
1	516	1758
2	2619	1496
done	5000	1490

prune490.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.5b

regimes1.0s

Accuracy

27.3% (1.0b remaining)

Error of 8.0b against oracle of 7.0b and baseline of 8.4b

bsearch1.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	98
1	56	98
done	56	98

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	9326×	body	80	valid
383.0ms	3100×	body	80	nan