Details

sample368.0ms

Algorithm

intervals

Results

114.0ms	83×	body	5120	valid
65.0ms	234×	body	80	valid
46.0ms	407×	body	80	nan
38.0ms	53×	body	2560	valid
24.0ms	24×	body	10240	exit
12.0ms	22×	body	1280	valid
7.0ms	14×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	3×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: done (1.8s)

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.0b

localize33.0ms

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:

67.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
54.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
44.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
854.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series715.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
137.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
106.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
324.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.1s

Counts

168 → 168

Iterations

Useful iterations: done (2.1s)

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

prune531.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 34.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite49.0ms

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:

48.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify3.6s

Counts

33 → 33

Iterations

Useful iterations: 2 (151.0ms)

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

prune108.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 32.3b

localize2.0ms

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

prune26.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 32.3b

localize65.0ms

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 (- (* (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.8s

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:

42.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
47.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
36.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
1.7s	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series1.3s

Counts

4 → 12

Calls

4 calls:

304.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
318.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
279.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
420.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (/ (* 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	1684	2374
done	5000	2166

prune735.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 32.2b

regimes665.0ms

Accuracy

0% (2.7b remaining)

Error of 33.9b against oracle of 31.2b and baseline of 33.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	3	3
1	5	1
done	5	1

end0.0ms

sample14.2s

Algorithm

intervals

Results

3.2s	2332×	body	5120	valid
3.2s	12850×	body	80	nan
2.1s	6866×	body	80	valid
2.0s	1672×	body	2560	valid
1.1s	894×	body	1280	valid
614.0ms	539×	body	10240	exit
255.0ms	448×	body	640	valid
120.0ms	224×	body	320	valid
24.0ms	98×	body	160	valid