Details

sample155.0ms

Algorithm

intervals

Results

30.0ms	70×	body	5120	valid
22.0ms	394×	body	80	nan
18.0ms	53×	body	2560	valid
12.0ms	209×	body	80	valid
10.0ms	17×	body	640	valid
9.0ms	17×	body	10240	exit
7.0ms	23×	body	1280	valid
1.0ms	9×	body	320	valid
0.0ms	1×	body	160	valid

simplify105.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	26
1	298	26
2	3398	26
3	5002	26
done	5002	26

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.6b

localize19.0ms

Local error

Found 4 expressions with local error:

17.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
24.5b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite761.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 143

Calls

4 calls:

43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
44.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
620.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series768.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
98.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
102.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
471.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify118.0ms

Counts

155 → 155

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	579	2159
1	3786	1523
2	5001	1523
done	5001	1523

prune287.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 36.3b

localize7.0ms

Local error

Found 1 expressions with local error:

6.4b	(* (/ c0 (* 2.0 w)) 0)

rewrite27.0ms

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×	`mul0` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `add-log-exp` `unswap-sqr`

Counts

1 → 28

Calls

1 calls:

26.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

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

simplify286.0ms

Counts

31 → 31

Iterations

Useful iterations: 2 (283.0ms)

Iter	Nodes	Cost
0	176	32
1	1859	16
2	5001	6
done	5001	6

prune61.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 34.8b

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune11.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 34.8b

localize29.0ms

Local error

Found 4 expressions with local error:

17.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
24.5b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
24.5b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

142×	`add-exp-log` `add-cbrt-cube`
78×	`prod-exp` `cbrt-unprod`
30×	`cbrt-undiv` `div-exp`
8×	`*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `sqrt-div` `frac-add`
2×	`+-commutative` `flip3--` `frac-2neg` `flip3-+` `times-frac` `clear-num` `associate-/r` `sum-log` `flip--` `flip-+` `div-inv` `distribute-lft-out` `associate-/l`

Counts

4 → 114

Calls

4 calls:

43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
619.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
622.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series706.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
97.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
253.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
257.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify121.0ms

Counts

126 → 126

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	579	2274
1	3786	1782
2	5001	1782
done	5001	1782

prune333.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 34.8b

regimes392.0ms

Accuracy

56.1% (1.1b remaining)

Error of 33.0b against oracle of 31.9b and baseline of 34.4b

bsearch3.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	78
1	42	78
2	42	78
done	42	78

end0.0ms

sample4.7s

Algorithm

intervals

Results

985.0ms	2212×	body	5120	valid
758.0ms	12997×	body	80	nan
629.0ms	1747×	body	2560	valid
393.0ms	6774×	body	80	valid
281.0ms	565×	body	10240	exit
249.0ms	862×	body	1280	valid
97.0ms	421×	body	640	valid
39.0ms	238×	body	320	valid
16.0ms	142×	body	160	valid