Details

sample107.0ms

Algorithm

intervals

Results

37.0ms	299×	body	80	valid
14.0ms	111×	body	80	nan

simplify5.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	81	18
3	180	18
4	432	18
5	1221	18
6	4692	18
done	5000	18

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize36.0ms

Local error

Found 4 expressions with local error:

1.9b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.7b	(/ (* M D) (* 2.0 d))
9.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite117.0ms

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:

22.0ms	(* 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))))
13.0ms	(/ (* M D) (* 2.0 d))
70.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.4s

Counts

4 → 12

Calls

4 calls:

746.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
592.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
63.0ms	(/ (* M D) (* 2.0 d))
952.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.6s

Counts

133 → 133

Iterations

Useful iterations: 2 (446.0ms)

Iter	Nodes	Cost
0	244	2427
1	598	2198
2	2296	2040
done	5002	2040

prune677.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.1b

localize22.0ms

Local error

Found 4 expressions with local error:

4.5b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.0b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.7b	(/ (* M D) (* 2.0 d))
6.1b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite130.0ms

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:

42.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
16.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
27.0ms	(/ (* M D) (* 2.0 d))
39.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.7s

Counts

4 → 12

Calls

4 calls:

956.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
565.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
47.0ms	(/ (* M D) (* 2.0 d))
1.2s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify1.6s

Counts

148 → 148

Iterations

Useful iterations: 2 (532.0ms)

Iter	Nodes	Cost
0	277	2631
1	668	2190
2	2515	1982
done	5000	1982

prune712.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize43.0ms

Local error

Found 4 expressions with local error:

5.0b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
5.2b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.7b	(/ (* M D) (* 2.0 d))
5.7b	(/ (* M D) (* 2.0 d))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
30×	`add-cbrt-cube`
19×	`prod-exp`
14×	`add-sqr-sqrt`
12×	`div-exp`
9×	`associate-l` `cbrt-unprod`
8×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
5×	`pow1` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `sqrt-prod` `div-inv` `unswap-sqr`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--`

Counts

4 → 96

Calls

4 calls:

7.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
30.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
36.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))

series1.9s

Counts

4 → 12

Calls

4 calls:

635.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
1.1s	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
56.0ms	(/ (* M D) (* 2.0 d))
60.0ms	(/ (* M D) (* 2.0 d))

simplify1.1s

Counts

108 → 108

Iterations

Useful iterations: 2 (305.0ms)

Iter	Nodes	Cost
0	177	2034
1	435	1654
2	1828	1418
done	5000	1418

prune680.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize42.0ms

Local error

Found 4 expressions with local error:

5.0b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
5.2b	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
5.6b	(/ (* 2.0 d) (* M D))
5.7b	(/ (* M D) (* 2.0 d))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-exp-log`
38×	`prod-exp`
30×	`div-exp` `add-cbrt-cube`
27×	`add-sqr-sqrt`
24×	`associate-l`
23×	`unpow-prod-down`
22×	`times-frac`
17×	`*-un-lft-identity`
16×	`add-cube-cbrt` `pow-exp`
9×	`cbrt-unprod`
8×	`cbrt-undiv`
6×	`div-inv`
5×	`pow1` `rec-exp` `1-exp` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `*-commutative` `flip--`

Counts

4 → 124

Calls

4 calls:

12.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
93.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
24.0ms	(/ (* 2.0 d) (* M D))
26.0ms	(/ (* M D) (* 2.0 d))

series1.7s

Counts

4 → 12

Calls

4 calls:

561.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
1.0s	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
41.0ms	(/ (* 2.0 d) (* M D))
37.0ms	(/ (* M D) (* 2.0 d))

simplify1.4s

Counts

136 → 136

Iterations

Useful iterations: 2 (444.0ms)

Iter	Nodes	Cost
0	287	2660
1	666	2420
2	2750	1837
done	5002	1837

prune970.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.5b

regimes1.4s

Accuracy

39.2% (1.2b remaining)

Error of 8.6b against oracle of 7.4b and baseline of 9.4b

bsearch1.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	84
1	51	84
done	51	84

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	9307×	body	80	valid
339.0ms	3114×	body	80	nan