Details

sample655.0ms

Algorithm

intervals

Results

418.0ms	84×	body	5120	valid
58.0ms	43×	body	2560	valid
40.0ms	373×	body	80	nan
22.0ms	214×	body	80	valid
16.0ms	31×	body	1280	valid
14.0ms	15×	body	10240	exit
8.0ms	17×	body	640	valid
3.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	21	52
1	60	52
2	303	50
3	3435	50
done	5000	45

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.9b

localize64.0ms

Local error

Found 4 expressions with local error:

16.7b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.7b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.7b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
28.8b	(+ (/ (* 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`
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:

70.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
70.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
60.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
914.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series793.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
131.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
131.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
353.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify530.0ms

Counts

168 → 168

Iterations

Useful iterations: done (523.0ms)

Iter	Nodes	Cost
0	161	4866
1	619	4432
done	5000	3209

prune735.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.8b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite40.0ms

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:

39.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify1.1s

Counts

33 → 33

Iterations

Useful iterations: 2 (140.0ms)

Iter	Nodes	Cost
0	69	299
1	188	90
2	873	42
done	5000	42

prune215.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 29.9b

localize8.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune88.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 29.9b

localize101.0ms

Local error

Found 4 expressions with local error:

25.7b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
25.7b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
25.7b	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
34.8b	(+ (/ (* 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))))

rewrite1.4s

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:

32.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
36.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
31.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
1.3s	(+ (/ (* 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))))

series1.0s

Counts

4 → 12

Calls

4 calls:

225.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
207.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
230.0ms	(cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))
351.0ms	(+ (/ (* 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))))

simplify1.3s

Counts

81 → 81

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	146	3599
1	379	3423
2	1998	2374
done	5002	2193

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 29.7b

regimes1.6s

Accuracy

0% (2.5b remaining)

Error of 33.2b against oracle of 30.7b and baseline of 33.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

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

end0.0ms

sample13.3s

Algorithm

intervals

Results

3.3s	2301×	body	5120	valid
2.2s	13094×	body	80	nan
1.5s	1744×	body	2560	valid
1.5s	945×	body	1280	valid
1.0s	574×	body	10240	exit
1.0s	6739×	body	80	valid
634.0ms	462×	body	640	valid
75.0ms	228×	body	320	valid
20.0ms	91×	body	160	valid