Details

sample318.0ms

Algorithm

intervals

Results

67.0ms	83×	body	5120	valid
58.0ms	234×	body	80	valid
47.0ms	53×	body	2560	valid
42.0ms	407×	body	80	nan
20.0ms	24×	body	10240	exit
11.0ms	22×	body	1280	valid
6.0ms	14×	body	640	valid
2.0ms	5×	body	320	valid
1.0ms	3×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: done (2.3s)

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.0b

localize30.0ms

Local error

Found 4 expressions with local error:

16.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
28.9b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.0s

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:

75.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
53.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
51.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
812.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series749.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
127.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
118.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
362.0ms	(+ (/ (* 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

prune631.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 34.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite43.0ms

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:

41.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify3.0s

Counts

33 → 33

Iterations

Useful iterations: 2 (127.0ms)

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

prune113.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 32.3b

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

prune47.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 32.3b

localize64.0ms

Local error

Found 4 expressions with local error:

27.7b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
27.7b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
27.7b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
34.6b	(+ (/ (* 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))))

rewrite1.7s

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:

45.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
38.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
57.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
1.5s	(+ (/ (* 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))))

series1.4s

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
329.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
288.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
463.0ms	(+ (/ (* 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))))

simplify1.4s

Counts

81 → 81

Iterations

Useful iterations: done (1.4s)

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

prune634.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 32.1b

regimes713.0ms

Accuracy

0% (2.9b remaining)

Error of 33.9b against oracle of 31.0b and baseline of 33.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	3	4
1	4	1
done	4	1

end0.0ms

sample15.0s

Algorithm

intervals

Results

3.5s	2332×	body	5120	valid
2.8s	1672×	body	2560	valid
2.8s	12850×	body	80	nan
1.6s	6866×	body	80	valid
1.1s	539×	body	10240	exit
707.0ms	894×	body	1280	valid
317.0ms	448×	body	640	valid
88.0ms	224×	body	320	valid
25.0ms	98×	body	160	valid