Details

sample568.0ms

Algorithm

intervals

Results

126.0ms	71×	body	5120	valid
96.0ms	66×	body	2560	valid
95.0ms	186×	body	80	valid
91.0ms	398×	body	80	nan
46.0ms	18×	body	640	valid
33.0ms	18×	body	10240	exit
25.0ms	21×	body	1280	valid
3.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid

simplify633.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	3014
2	286
1	60
0	21

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.1b

localize58.0ms

Local error

Found 4 expressions with local error:

16.8b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
16.8b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
16.8b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
23.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite1.9s

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:

46.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
57.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
40.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
1.8s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series966.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
123.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
152.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
587.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify1.2s

Counts

228 → 228

Iterations

Iter	Nodes
2	2885
1	696
0	217

prune4.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.9b

localize17.0ms

Local error

Found 1 expressions with local error:

6.9b	(* (/ c0 w) (/ 0 2))

rewrite27.0ms

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:

26.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify21.7s

Counts

56 → 56

Iterations

Iter	Nodes
4	5936
3	1055
2	469
1	277
0	112

prune562.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.4b

localize24.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
1	0
0	0

prune71.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 25.4b

localize87.0ms

Local error

Found 4 expressions with local error:

16.8b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
16.8b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
23.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
23.2b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

116×	`add-cbrt-cube` `add-exp-log`
48×	`cbrt-undiv` `div-exp`
46×	`add-sqr-sqrt`
40×	`prod-exp` `cbrt-unprod`
32×	`times-frac`
26×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
14×	`fma-def` `associate-r`
12×	`sqrt-div` `frac-add`
8×	`pow1` `sqrt-prod` `add-log-exp` `unswap-sqr`
6×	`frac-times` `flip3--` `associate-l/` `associate-r/` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv`
2×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+` `difference-of-squares`

Counts

4 → 180

Calls

4 calls:

42.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
43.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
1.3s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.4s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series1.3s

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
117.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
580.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
526.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify926.0ms

Counts

192 → 192

Iterations

Iter	Nodes
2	2885
1	696
0	217

prune3.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 25.3b

regimes1.4s

Accuracy

19% (6.4b remaining)

Error of 31.9b against oracle of 25.5b and baseline of 33.4b

bsearch7.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	33
1	33
0	27

end0.0ms

sample20.8s

Algorithm

intervals

Results

6.5s	2337×	body	5120	valid
3.9s	13274×	body	80	nan
3.1s	1761×	body	2560	valid
1.9s	6806×	body	80	valid
1.7s	900×	body	1280	valid
1.2s	603×	body	10240	exit
948.0ms	427×	body	640	valid
206.0ms	230×	body	320	valid
99.0ms	109×	body	160	valid