Details

sample304.0ms

Algorithm

intervals

Results

64.0ms	52×	body	2560	valid
62.0ms	80×	body	5120	valid
59.0ms	209×	body	80	valid
38.0ms	395×	body	80	nan
14.0ms	17×	body	10240	exit
12.0ms	27×	body	1280	valid
5.0ms	14×	body	640	valid
3.0ms	11×	body	320	valid
0.0ms	2×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	21	52
1	60	52
2	295	50
3	3269	50
done	5000	45

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.5b

localize34.0ms

Local error

Found 4 expressions with local error:

19.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
19.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
19.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
25.9b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
7×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
4×	`pow1` `expm1-log1p-u` `times-frac` `log1p-expm1-u` `div-inv`
3×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 156

Calls

4 calls:

79.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
82.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
54.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
937.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series807.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
125.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
125.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
415.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.0s

Counts

168 → 168

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	161	4866
1	484	4432
2	3124	2971
done	5002	2933

prune452.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 32.0b

localize6.0ms

Local error

Found 1 expressions with local error:

4.7b	(* (/ c0 (* 2.0 w)) 0)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
3×	`pow1` `times-frac` `associate-r`
2×	`cbrt-undiv` `div-exp`
1×	`expm1-log1p-u` `mul0` `pow-prod-down` `associate-l/` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`

Counts

1 → 30

Calls

1 calls:

38.0ms

(* (/ c0 (* 2.0 w)) 0)

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* (/ c0 (* 2.0 w)) 0)

simplify2.7s

Counts

33 → 33

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	69	299
1	160	78
2	472	42
3	2122	42
done	5001	42

prune157.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 29.7b

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune52.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 29.7b

localize55.0ms

Local error

Found 4 expressions with local error:

11.9b	(/ (* c0 d) (* w h))
15.2b	(sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M))))
23.5b	(fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))
46.6b	(fma (/ (* c0 d) (* w h)) (/ d (* D D)) (sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`fma-udef`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 58

Calls

4 calls:

22.0ms	(/ (* c0 d) (* w h))
3.0ms	(sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M))))
0.0ms	(fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))
1.0ms	(fma (/ (* c0 d) (* w h)) (/ d (* D D)) (sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (* c0 d) (* w h))
314.0ms	(sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M))))
396.0ms	(fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))
336.0ms	(fma (/ (* c0 d) (* w h)) (/ d (* D D)) (sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))))

simplify1.2s

Counts

70 → 70

Iterations

Useful iterations: 2 (296.0ms)

Iter	Nodes	Cost
0	127	1651
1	313	1583
2	1403	1217
done	5000	1217

prune454.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 29.1b

regimes1.3s

Accuracy

0% (3.2b remaining)

Error of 33.8b against oracle of 30.6b and baseline of 33.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	2	2
1	4	1
done	4	1

end0.0ms

sample12.7s

Algorithm

intervals

Results

3.3s	2295×	body	5120	valid
3.1s	12800×	body	80	nan
1.6s	1751×	body	2560	valid
1.2s	6565×	body	80	valid
1.0s	924×	body	1280	valid
737.0ms	581×	body	10240	exit
221.0ms	465×	body	640	valid
76.0ms	227×	body	320	valid
30.0ms	117×	body	160	valid