Details

sample431.0ms

Algorithm

intervals

Results

100.0ms	399×	body	80	nan
76.0ms	67×	body	5120	valid
54.0ms	19×	body	10240	exit
39.0ms	43×	body	2560	valid
31.0ms	213×	body	80	valid
26.0ms	36×	body	1280	valid
9.0ms	16×	body	640	valid
4.0ms	9×	body	320	valid
1.0ms	3×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	21	52
1	60	52
2	303	50
3	3435	50
done	5000	45

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 55.7b

localize87.0ms

Local error

Found 4 expressions with local error:

17.7b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.7b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.7b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
25.3b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.4s

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:

86.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
87.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
82.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
1.2s	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series1.0s

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
178.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
189.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
485.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify737.0ms

Counts

168 → 168

Iterations

Useful iterations: done (727.0ms)

Iter	Nodes	Cost
0	161	4866
1	619	4432
done	5000	3209

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 34.4b

localize19.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ c0 (* 2.0 w))
5.4b	(* (/ c0 (* 2.0 w)) 0)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 53

Calls

2 calls:

16.0ms	(/ c0 (* 2.0 w))
50.0ms	(* (/ c0 (* 2.0 w)) 0)

series43.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ c0 (* 2.0 w))
3.0ms	(* (/ c0 (* 2.0 w)) 0)

simplify1.9s

Counts

59 → 59

Iterations

Useful iterations: 2 (234.0ms)

Iter	Nodes	Cost
0	85	496
1	213	284
2	914	206
done	5000	206

prune513.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.6b

localize5.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune111.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.6b

localize111.0ms

Local error

Found 4 expressions with local error:

23.0b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
23.0b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
23.0b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
33.7b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-log-exp`
5×	`fma-def`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `times-frac` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`cbrt-div` `pow1/3`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 69

Calls

4 calls:

61.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
62.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
59.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
2.0s	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))

series1.7s

Counts

4 → 12

Calls

4 calls:

355.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
343.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
344.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
623.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))

simplify1.9s

Counts

81 → 81

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	146	3599
1	379	3423
2	1998	2374
done	5002	2193

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.5b

regimes1.8s

Accuracy

0% (3.0b remaining)

Error of 34.4b against oracle of 31.4b and baseline of 34.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

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

end0.0ms

sample18.2s

Algorithm

intervals

Results

5.0s	2335×	body	5120	valid
3.5s	13180×	body	80	nan
2.9s	1619×	body	2560	valid
1.3s	566×	body	10240	exit
1.3s	6867×	body	80	valid
929.0ms	964×	body	1280	valid
393.0ms	441×	body	640	valid
176.0ms	257×	body	320	valid
36.0ms	120×	body	160	valid