Details

sample284.0ms

Algorithm

intervals

Results

80.0ms	412×	body	80	nan
57.0ms	64×	body	2560	valid
53.0ms	65×	body	5120	valid
21.0ms	196×	body	80	valid
15.0ms	18×	body	10240	exit
13.0ms	24×	body	1280	valid
5.0ms	9×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5011
3	3014
2	286
1	60
0	21

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.8b

localize69.0ms

Local error

Found 4 expressions with local error:

17.4b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
17.4b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
17.4b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
25.4b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

172×	`add-cbrt-cube` `add-exp-log`
72×	`cbrt-undiv` `div-exp`
63×	`add-sqr-sqrt`
60×	`prod-exp` `cbrt-unprod`
48×	`times-frac`
39×	`associate-l`
33×	`*-un-lft-identity` `add-cube-cbrt`
21×	`associate-r`
12×	`unswap-sqr`
10×	`pow1`
7×	`fma-def`
6×	`sqrt-div` `frac-add` `div-inv` `add-log-exp`
5×	`frac-times` `associate-l/` `associate-r/`
4×	`expm1-log1p-u` `sqrt-prod` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `pow-prod-down` `*-commutative` `flip--`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `difference-of-squares`

Counts

4 → 216

Calls

4 calls:

54.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
52.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
57.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
2.4s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series968.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
127.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
112.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
619.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify2.4s

Counts

228 → 228

Iterations

Iter	Nodes
done	5007
2	3007
1	697
0	217

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.7b

localize14.0ms

Local error

Found 1 expressions with local error:

5.7b	(* (/ c0 w) (/ 0 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`times-frac`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`pow1`
2×	`div-inv`
1×	`expm1-log1p-u` `frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 53

Calls

1 calls:

21.0ms

(* (/ c0 w) (/ 0 2))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(* (/ c0 w) (/ 0 2))

simplify14.4s

Counts

56 → 56

Iterations

Iter	Nodes
done	5015
3	1300
2	492
1	278
0	112

prune366.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.2b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune106.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 26.2b

localize130.0ms

Local error

Found 4 expressions with local error:

12.3b	(/ (fma (sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M))) (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))))) (fma (- (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M))))
13.1b	(sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)))
13.1b	(sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)))
40.9b	(fma (sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M))) (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`sqrt-prod`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 79

Calls

4 calls:

9.0ms	(/ (fma (sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M))) (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))))) (fma (- (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M))))
493.0ms	(sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)))
615.0ms	(sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)))
1.0ms	(fma (sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M))) (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))))

series5.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (fma (sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M))) (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))))) (fma (- (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)))) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M))))
325.0ms	(sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)))
318.0ms	(sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)))
3.5s	(fma (sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M))) (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))))

simplify2.1s

Counts

91 → 91

Iterations

Iter	Nodes
done	5007
2	1508
1	369
0	151

prune878.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 26.1b

regimes1.7s

Accuracy

-6.5% (9.4b remaining)

Error of 34.3b against oracle of 25.0b and baseline of 33.8b

bsearch521.0ms

Steps

Iters	Range		Point
8	4.784085916088698e-179	1.140447742874278e-175	2.3691491374921303e-177
5	-2.9600966421999986e-115	-1.4111306252012167e-115	-1.428069600682858e-115

simplify17.0ms

Iterations

Iter	Nodes
done	38
1	38
0	30

end0.0ms

sample14.5s

Algorithm

intervals

Results

3.8s	2275×	body	5120	valid
2.7s	13051×	body	80	nan
2.3s	1728×	body	2560	valid
1.7s	893×	body	1280	valid
1.4s	6780×	body	80	valid
883.0ms	600×	body	10240	exit
371.0ms	475×	body	640	valid
145.0ms	255×	body	320	valid
27.0ms	100×	body	160	valid