Details

sample736.0ms

Algorithm

intervals

Results

474.0ms	407×	body	80	nan
67.0ms	74×	body	5120	valid
43.0ms	218×	body	80	valid
35.0ms	49×	body	2560	valid
19.0ms	20×	body	10240	exit
17.0ms	28×	body	1280	valid
9.0ms	3×	body	160	valid
9.0ms	16×	body	640	valid
4.0ms	11×	body	320	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	21	567
1	60	567
2	295	527
3	3419	527
done	5000	527

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 54.5b

localize69.0ms

Local error

Found 4 expressions with local error:

15.1b	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
15.1b	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
15.1b	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
29.2b	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

211×	`add-cbrt-cube` `add-exp-log`
96×	`prod-exp` `cbrt-unprod`
66×	`cbrt-undiv` `div-exp`
25×	`frac-times` `associate-*l/`
21×	`associate-r`
19×	`pow1`
15×	`add-sqr-sqrt` `associate-*r/`
14×	`sqrt-div` `frac-add`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac` `pow-prod-down`
7×	`fma-def` `flip3--` `flip--`
6×	`add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`associate-l` `*-commutative` `div-inv` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `difference-of-squares`

Counts

4 → 208

Calls

4 calls:

59.0ms	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
61.0ms	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
55.0ms	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
2.7s	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))

series617.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
75.0ms	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
102.0ms	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
324.0ms	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))

simplify3.9s

Counts

220 → 220

Iterations

Useful iterations: 2 (1.6s)

Iter	Nodes	Cost
0	218	99828
1	734	81477
2	4373	69264
done	5000	69264

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 29.8b

localize7.0ms

Local error

Found 1 expressions with local error:

5.7b	(* (/ c0 (* 2.0 w)) 0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
7×	`associate-l`
6×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt` `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:

24.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify1.6s

Counts

33 → 33

Iterations

Useful iterations: 2 (141.0ms)

Iter	Nodes	Cost
0	69	5964
1	188	1363
2	863	554
done	5000	554

prune344.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.3b

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

prune96.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 28.3b

localize209.0ms

Local error

Found 4 expressions with local error:

15.1b	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
29.2b	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))
29.2b	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))
29.2b	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))

rewrite7.8s

Algorithm

rewrite-expression-head

Rules

73×	`add-cbrt-cube` `add-exp-log`
42×	`sqrt-div` `frac-add`
35×	`frac-times` `associate-*l/`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
21×	`fma-def` `flip3--` `associate-*r/` `flip--`
13×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
10×	`add-log-exp`
9×	`pow1`
7×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`+-commutative` `sum-log` `flip3-+` `times-frac` `pow-prod-down` `flip-+` `difference-of-squares`
1×	`associate-l` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 160

Calls

4 calls:

77.0ms	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
2.5s	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))
2.6s	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))
2.6s	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))

series1.2s

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (* (/ d D) (/ d D)) (/ c0 (* w h)))
343.0ms	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))
413.0ms	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))
355.0ms	(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))

simplify3.4s

Counts

172 → 172

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	218	110204
1	734	91103
2	4373	86792
done	5000	86792

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 28.3b

regimes1.5s

Accuracy

19.5% (5.9b remaining)

Error of 32.3b against oracle of 26.3b and baseline of 33.7b

bsearch4.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	25	699
1	31	699
done	31	699

end0.0ms

sample13.1s

Algorithm

intervals

Results

3.2s	2359×	body	5120	valid
2.8s	1701×	body	2560	valid
2.5s	12935×	body	80	nan
1.6s	6729×	body	80	valid
647.0ms	608×	body	10240	exit
580.0ms	877×	body	1280	valid
213.0ms	468×	body	640	valid
83.0ms	231×	body	320	valid
24.0ms	102×	body	160	valid