Details

sample168.0ms

Algorithm

intervals

Results

39.0ms	87×	body	5120	valid
25.0ms	430×	body	80	nan
19.0ms	51×	body	2560	valid
12.0ms	207×	body	80	valid
10.0ms	15×	body	10240	exit
8.0ms	27×	body	1280	valid
3.0ms	14×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: done (1.5s)

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 60.0b

localize19.0ms

Local error

Found 4 expressions with local error:

17.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
28.7b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite712.0ms

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:

41.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
41.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
40.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
581.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series574.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
101.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
103.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
271.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify1.4s

Counts

168 → 168

Iterations

Useful iterations: done (1.4s)

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

prune389.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 33.6b

localize5.0ms

Local error

Found 1 expressions with local error:

5.2b	(* (/ c0 (* 2.0 w)) 0)

rewrite24.0ms

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:

23.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify2.0s

Counts

33 → 33

Iterations

Useful iterations: 2 (80.0ms)

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

prune76.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 30.8b

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

prune24.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 30.8b

localize25.0ms

Local error

Found 4 expressions with local error:

29.8b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
29.8b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
29.8b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
33.8b	(+ (/ (* 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))))

rewrite1.0s

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:

27.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
28.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
27.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
938.0ms	(+ (/ (* 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))))

series892.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
191.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
193.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
322.0ms	(+ (/ (* 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))))

simplify850.0ms

Counts

81 → 81

Iterations

Useful iterations: done (847.0ms)

Iter	Nodes	Cost
0	146	3599
1	376	3423
2	1681	2374
done	5002	2193

prune448.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 30.6b

regimes415.0ms

Accuracy

0% (3.1b remaining)

Error of 33.3b against oracle of 30.2b and baseline of 33.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	6	5
done	6	5

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.1s	2303×	body	5120	valid
772.0ms	12953×	body	80	nan
638.0ms	1726×	body	2560	valid
411.0ms	6843×	body	80	valid
295.0ms	588×	body	10240	exit
265.0ms	882×	body	1280	valid
96.0ms	421×	body	640	valid
42.0ms	245×	body	320	valid
12.0ms	92×	body	160	valid