Details

sample108.0ms

Algorithm

intervals

Results

51.0ms	308×	body	80	valid
12.0ms	97×	body	80	nan

simplify7.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5017
6	4428
5	1433
4	379
3	165
2	79
1	36
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize70.0ms

Local error

Found 4 expressions with local error:

2.9b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.0b	(/ (* M D) (* 2.0 d))
10.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite127.0ms

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:

32.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
20.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
25.0ms	(/ (* M D) (* 2.0 d))
43.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series3.1s

Counts

4 → 12

Calls

4 calls:

943.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
738.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
68.0ms	(/ (* M D) (* 2.0 d))
1.4s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify2.9s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	2326
1	625
0	244

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.2b

localize61.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.0b	(/ (* M D) (* 2.0 d))
5.5b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.8b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite194.0ms

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:

14.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
27.0ms	(/ (* M D) (* 2.0 d))
88.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
51.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series3.6s

Counts

4 → 12

Calls

4 calls:

766.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
54.0ms	(/ (* M D) (* 2.0 d))
1.4s	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
1.4s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify3.4s

Counts

148 → 148

Iterations

Iter	Nodes
done	5293
2	2647
1	711
0	277

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.1b

localize112.0ms

Local error

Found 4 expressions with local error:

5.0b	(/ (* M D) (* 2.0 d))
5.0b	(/ (* M D) (* 2.0 d))
5.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

rewrite423.0ms

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:

30.0ms	(/ (* M D) (* 2.0 d))
24.0ms	(/ (* M D) (* 2.0 d))
34.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
251.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

series2.8s

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (* M D) (* 2.0 d))
55.0ms	(/ (* M D) (* 2.0 d))
1.4s	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
1.3s	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

simplify4.6s

Counts

352 → 352

Iterations

Iter	Nodes
done	5057
2	3345
1	1132
0	447

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize79.0ms

Local error

Found 4 expressions with local error:

5.0b	(/ (* M D) (* 2.0 d))
5.0b	(/ (* M D) (* 2.0 d))
5.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.9b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

177×	`add-exp-log`
95×	`prod-exp`
44×	`div-exp`
42×	`add-cbrt-cube`
25×	`pow-exp`
19×	`add-sqr-sqrt`
16×	`associate-r`
15×	`cbrt-unprod`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`cbrt-undiv` `associate-l`
8×	`rec-exp` `1-exp`
6×	`pow1` `unpow-prod-down`
5×	`pow-to-exp`
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 → 142

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
31.0ms	(/ (* M D) (* 2.0 d))
53.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
101.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

series2.8s

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (* M D) (* 2.0 d))
57.0ms	(/ (* M D) (* 2.0 d))
1.4s	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
1.3s	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

simplify3.0s

Counts

154 → 154

Iterations

Iter	Nodes
done	5000
2	2357
1	668
0	244

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

regimes4.4s

Accuracy

10.9% (1.4b remaining)

Error of 8.5b against oracle of 7.0b and baseline of 8.6b

bsearch2.0ms

simplify30.0ms

Iterations

Iter	Nodes
done	64
1	64
0	48

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	9324×	body	80	valid
683.0ms	3238×	body	80	nan