Details

sample93.0ms

Algorithm

intervals

Results

47.0ms	299×	body	80	valid
17.0ms	99×	body	80	nan

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	596
2	95
1	38
0	17

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))
3.5b	(sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l))))
6.5b	(/ (* M D) (* 2 d))
9.2b	(* (pow (/ (* M D) (* 2 d)) 2) (/ h l))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
38×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`*-un-lft-identity` `add-cube-cbrt`
15×	`times-frac`
13×	`associate-l`
10×	`pow-exp` `unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/` `div-inv` `unpow2` `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 → 128

Calls

4 calls:

23.0ms	(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))
6.0ms	(sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l))))
16.0ms	(/ (* M D) (* 2 d))
37.0ms	(* (pow (/ (* M D) (* 2 d)) 2) (/ h l))

series602.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))
154.0ms	(sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l))))
30.0ms	(/ (* M D) (* 2 d))
98.0ms	(* (pow (/ (* M D) (* 2 d)) 2) (/ h l))

simplify1.8s

Counts

140 → 140

Iterations

Iter	Nodes
done	5042
2	2464
1	600
0	233

prune971.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.7b

localize42.0ms

Local error

Found 4 expressions with local error:

4.2b	(* h (* (/ D 2) (/ M d)))
4.6b	(* (* (* h (* (/ D 2) (/ M d))) (* (/ D 2) (/ M d))) (/ 1 l))
5.5b	(* (/ D 2) (/ M d))
5.5b	(* (/ D 2) (/ M d))

rewrite666.0ms

Algorithm

rewrite-expression-head

Rules

897×	`add-exp-log`
537×	`prod-exp`
487×	`add-cbrt-cube`
277×	`cbrt-unprod`
250×	`div-exp`
131×	`cbrt-undiv`
64×	`add-sqr-sqrt`
53×	`times-frac` `associate-*r/`
52×	`frac-times`
42×	`pow1`
40×	`-un-lft-identity` `associate-r` `associate-l/` `add-cube-cbrt`
31×	`rec-exp` `1-exp`
30×	`associate-l`
27×	`pow-prod-down`
8×	`unswap-sqr`
5×	`div-inv`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`un-div-inv`

Counts

4 → 386

Calls

4 calls:

38.0ms	(* h (* (/ D 2) (/ M d)))
585.0ms	(* (* (* h (* (/ D 2) (/ M d))) (* (/ D 2) (/ M d))) (/ 1 l))
14.0ms	(* (/ D 2) (/ M d))
14.0ms	(* (/ D 2) (/ M d))

series257.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* h (* (/ D 2) (/ M d)))
128.0ms	(* (* (* h (* (/ D 2) (/ M d))) (* (/ D 2) (/ M d))) (/ 1 l))
31.0ms	(* (/ D 2) (/ M d))
28.0ms	(* (/ D 2) (/ M d))

simplify2.6s

Counts

398 → 398

Iterations

Iter	Nodes
done	5000
1	1587
0	531

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize76.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (/ D 2) (/ M d))
22.9b	(cbrt (* h (* (/ D 2) (/ M d))))
22.9b	(cbrt (* h (* (/ D 2) (/ M d))))
22.9b	(cbrt (* h (* (/ D 2) (/ M d))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`times-frac`
18×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r` `associate-l` `associate-*r/`
9×	`cbrt-div`
6×	`pow1`
4×	`expm1-log1p-u` `frac-times` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-prod` `pow1/3`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 98

Calls

4 calls:

27.0ms	(* (/ D 2) (/ M d))
19.0ms	(cbrt (* h (* (/ D 2) (/ M d))))
22.0ms	(cbrt (* h (* (/ D 2) (/ M d))))
39.0ms	(cbrt (* h (* (/ D 2) (/ M d))))

series561.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ D 2) (/ M d))
165.0ms	(cbrt (* h (* (/ D 2) (/ M d))))
173.0ms	(cbrt (* h (* (/ D 2) (/ M d))))
186.0ms	(cbrt (* h (* (/ D 2) (/ M d))))

simplify1.6s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	1568
1	451
0	175

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.7b

localize31.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* h (* (/ M (/ d D)) (/ M (/ d D)))) (* 4 l))
4.8b	(/ M (/ d D))
4.8b	(/ M (/ d D))
5.1b	(* h (* (/ M (/ d D)) (/ M (/ d D))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

190×	`add-cbrt-cube` `add-exp-log`
151×	`times-frac`
90×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
82×	`cbrt-undiv` `div-exp`
68×	`prod-exp` `cbrt-unprod`
27×	`associate-/r*`
11×	`div-inv`
9×	`pow1`
8×	`associate-*r/`
7×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down` `associate-/l/`
2×	`frac-times` `associate-*l/` `associate-/r/`
1×	`associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 250

Calls

4 calls:

50.0ms	(/ (* h (* (/ M (/ d D)) (/ M (/ d D)))) (* 4 l))
6.0ms	(/ M (/ d D))
19.0ms	(/ M (/ d D))
39.0ms	(* h (* (/ M (/ d D)) (/ M (/ d D))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (* h (* (/ M (/ d D)) (/ M (/ d D)))) (* 4 l))
38.0ms	(/ M (/ d D))
25.0ms	(/ M (/ d D))
139.0ms	(* h (* (/ M (/ d D)) (/ M (/ d D))))

simplify3.2s

Counts

262 → 262

Iterations

Iter	Nodes
done	5002
2	4780
1	919
0	310

prune1.8s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.7b

regimes3.0s

Accuracy

0% (2.0b remaining)

Error of 9.0b against oracle of 7.0b and baseline of 9.0b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	21

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.8s	9369×	body	80	valid
621.0ms	3123×	body	80	nan