Details

sample400.0ms

Algorithm

intervals

Results

97.0ms	77×	body	5120	valid
96.0ms	454×	body	80	nan
55.0ms	62×	body	2560	valid
28.0ms	231×	body	80	valid
24.0ms	24×	body	10240	exit
15.0ms	26×	body	1280	valid
4.0ms	9×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: done (1.9s)

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.3b

localize54.0ms

Local error

Found 4 expressions with local error:

18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
26.5b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.1s

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:

67.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
73.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
56.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
890.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series773.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
147.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
163.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
344.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify488.0ms

Counts

155 → 155

Iterations

Useful iterations: done (482.0ms)

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

prune447.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 31.3b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite51.0ms

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:

49.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify1.2s

Counts

31 → 31

Iterations

Useful iterations: 2 (138.0ms)

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

prune134.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 29.0b

localize1.0ms

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

prune35.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 29.0b

localize42.0ms

Local error

Found 4 expressions with local error:

18.0b	(* (* c0 (* d d)) (/ 1 (* (* w h) (* D D))))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
31.3b	(+ (* (* c0 (* d d)) (/ 1 (* (* w h) (* D D)))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

373×	`add-exp-log`
246×	`prod-exp`
235×	`add-cbrt-cube`
138×	`cbrt-unprod`
60×	`div-exp`
45×	`cbrt-undiv`
15×	`rec-exp` `1-exp`
13×	`pow1`
7×	`associate-r`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `add-log-exp`
5×	`times-frac`
4×	`sqrt-div` `frac-add`
3×	`associate-*r/` `un-div-inv` `div-inv`
2×	`flip3--` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l`
1×	`+-commutative` `flip3-+` `associate-l` `sum-log` `*-commutative` `flip-+`

Counts

4 → 188

Calls

4 calls:

306.0ms	(* (* c0 (* d d)) (/ 1 (* (* w h) (* D D))))
64.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
80.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
980.0ms	(+ (* (* c0 (* d d)) (/ 1 (* (* w h) (* D D)))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series799.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (* c0 (* d d)) (/ 1 (* (* w h) (* D D))))
159.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
145.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
339.0ms	(+ (* (* c0 (* d d)) (/ 1 (* (* w h) (* D D)))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify883.0ms

Counts

200 → 200

Iterations

Useful iterations: done (871.0ms)

Iter	Nodes	Cost
0	277	6099
1	1104	5584
done	5000	4117

prune540.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 29.0b

regimes524.0ms

Accuracy

0% (2.1b remaining)

Error of 33.3b against oracle of 31.2b and baseline of 33.3b

bsearch0.0ms

simplify0.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
done	1	1

end0.0ms

sample13.2s

Algorithm

intervals

Results

3.1s	2319×	body	5120	valid
2.8s	12671×	body	80	nan
1.5s	6805×	body	80	valid
1.4s	906×	body	1280	valid
1.2s	1716×	body	2560	valid
720.0ms	571×	body	10240	exit
384.0ms	462×	body	640	valid
107.0ms	228×	body	320	valid
28.0ms	114×	body	160	valid