Details

sample302.0ms

Algorithm

intervals

Results

71.0ms	422×	body	80	nan
53.0ms	232×	body	80	valid
47.0ms	68×	body	5120	valid
32.0ms	54×	body	2560	valid
17.0ms	38×	body	1280	valid
9.0ms	11×	body	10240	exit
4.0ms	11×	body	640	valid
2.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	21	52
1	59	52
2	289	52
3	3334	52
done	5001	46

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.8b

localize39.0ms

Local error

Found 4 expressions with local error:

20.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
20.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
20.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
26.8b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.1s

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:

75.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
81.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
77.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
863.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series615.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
105.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
107.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
299.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify387.0ms

Counts

155 → 155

Iterations

Useful iterations: done (382.0ms)

Iter	Nodes	Cost
0	157	4688
1	602	4293
done	5000	3059

prune393.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.2b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite30.0ms

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:

29.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify1.4s

Counts

31 → 31

Iterations

Useful iterations: 2 (145.0ms)

Iter	Nodes	Cost
0	67	283
1	186	86
2	872	38
done	5000	38

prune170.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.6b	(* (cbrt c0) (cbrt c0))
0.6b	(cbrt c0)
0.6b	(cbrt c0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
21×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`add-exp-log`
4×	`unswap-sqr`
3×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 62

Calls

3 calls:

22.0ms	(* (cbrt c0) (cbrt c0))
2.0ms	(cbrt c0)
2.0ms	(cbrt c0)

series843.0ms

Counts

3 → 9

Calls

3 calls:

285.0ms	(* (cbrt c0) (cbrt c0))
287.0ms	(cbrt c0)
271.0ms	(cbrt c0)

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	61	459
1	139	360
2	735	342
done	5000	331

prune231.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 31.3b

localize44.0ms

Local error

Found 4 expressions with local error:

20.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
20.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
21.2b	(/ (* (* w h) (* D D)) (* d d))
33.2b	(+ (/ c0 (/ (* (* w h) (* D D)) (* 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

183×	`add-exp-log` `add-cbrt-cube`
99×	`prod-exp` `cbrt-unprod`
40×	`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 → 133

Calls

4 calls:

60.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
55.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
45.0ms	(/ (* (* w h) (* D D)) (* d d))
852.0ms	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series1.1s

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
160.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
121.0ms	(/ (* (* w h) (* D D)) (* d d))
683.0ms	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify602.0ms

Counts

145 → 145

Iterations

Useful iterations: done (594.0ms)

Iter	Nodes	Cost
0	195	4292
1	751	4076
done	5000	3046

prune579.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 30.3b

regimes784.0ms

Accuracy

0% (3.2b remaining)

Error of 33.9b against oracle of 30.7b and baseline of 33.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	8	9
done	8	9

end0.0ms

sample14.6s

Algorithm

intervals

Results

3.8s	2339×	body	5120	valid
2.7s	13266×	body	80	nan
2.3s	1674×	body	2560	valid
1.7s	6996×	body	80	valid
736.0ms	570×	body	10240	exit
613.0ms	903×	body	1280	valid
271.0ms	468×	body	640	valid
163.0ms	239×	body	320	valid
28.0ms	111×	body	160	valid