Details

sample592.0ms

Algorithm

intervals

Results

157.0ms	71×	body	5120	valid
119.0ms	66×	body	2560	valid
92.0ms	398×	body	80	nan
62.0ms	186×	body	80	valid
32.0ms	18×	body	10240	exit
24.0ms	21×	body	1280	valid
17.0ms	18×	body	640	valid
3.0ms	5×	body	320	valid
2.0ms	4×	body	160	valid

simplify808.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	2972
2	280
1	59
0	21

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 48.8b

localize86.0ms

Local error

Found 4 expressions with local error:

13.7b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
13.7b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
16.8b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
23.2b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-cbrt-cube` `add-exp-log`
54×	`prod-exp` `cbrt-unprod`
48×	`cbrt-undiv` `div-exp`
16×	`sqrt-div`
10×	`frac-times` `associate-*r/`
8×	`frac-add`
7×	`pow1` `flip3-+` `flip-+`
6×	`-un-lft-identity` `flip3--` `associate-l/` `flip--` `add-log-exp` `associate-/l/`
4×	`add-sqr-sqrt` `add-cube-cbrt` `insert-posit16`
2×	`clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `times-frac` `div-inv` `associate-/l`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

4 → 131

Calls

4 calls:

29.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
42.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
44.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
66.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series1.8s

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
79.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
765.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
826.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify1.3s

Counts

143 → 143

Iterations

Iter	Nodes
2	3570
1	670
0	224

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 46.2b

localize96.0ms

Local error

Found 4 expressions with local error:

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

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-div`
24×	`frac-add`
16×	`frac-times`
15×	`flip3-+` `flip-+`
12×	`flip3--` `flip--`
10×	`*-un-lft-identity` `add-log-exp`
8×	`associate-l/` `associate-r/`
7×	`pow1`
4×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`+-commutative` `sum-log` `distribute-lft-out`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 83

Calls

4 calls:

54.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
64.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
58.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
58.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series3.4s

Counts

4 → 12

Calls

4 calls:

1.0s	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
753.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
803.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
825.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify4.0s

Counts

95 → 95

Iterations

Iter	Nodes
3	10020
2	1534
1	372
0	133

prune2.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 46.2b

localize153.0ms

Local error

Found 4 expressions with local error:

23.2b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
23.2b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
25.0b	(log (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))))
44.3b	(+ (exp (log (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite658.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-div`
24×	`frac-add`
16×	`frac-times` `log-div`
15×	`flip3-+` `flip-+`
12×	`flip3--` `flip--`
11×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`pow1` `exp-diff` `associate-l/` `associate-r/`
5×	`add-sqr-sqrt` `add-exp-log` `add-cube-cbrt`
4×	`log-prod` `add-cbrt-cube` `log-pow` `insert-posit16`
3×	`+-commutative` `sum-log` `distribute-lft-out`
2×	`sqrt-pow1`
1×	`pow1/2` `rem-log-exp` `pow-prod-down` `sqrt-prod`

Counts

4 → 88

Calls

4 calls:

56.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
56.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
59.0ms	(log (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))))
485.0ms	(+ (exp (log (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series2.8s

Counts

4 → 12

Calls

4 calls:

901.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
938.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
211.0ms	(log (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))))
776.0ms	(+ (exp (log (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify4.8s

Counts

100 → 100

Iterations

Iter	Nodes
3	10433
2	1827
1	570
0	246

prune2.9s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 46.2b

localize117.0ms

Local error

Found 4 expressions with local error:

16.8b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
21.7b	(cbrt (/ (* 2 (/ (* c0 (/ d D)) (/ w (/ d D)))) h))
23.2b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
23.2b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-div`
16×	`frac-add`
12×	`frac-times`
11×	`flip3-+` `flip-+`
10×	`*-un-lft-identity`
9×	`flip3--` `flip--`
8×	`add-log-exp`
7×	`cbrt-prod` `pow1`
6×	`add-sqr-sqrt` `associate-l/` `associate-r/` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`times-frac`
2×	`+-commutative` `sum-log` `sqrt-pow1` `distribute-lft-out`
1×	`cbrt-div` `pow1/2` `pow1/3` `pow-prod-down` `sqrt-prod` `div-inv`

Counts

4 → 79

Calls

4 calls:

34.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
15.0ms	(cbrt (/ (* 2 (/ (* c0 (/ d D)) (/ w (/ d D)))) h))
43.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
56.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series2.9s

Counts

4 → 12

Calls

4 calls:

723.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
300.0ms	(cbrt (/ (* 2 (/ (* c0 (/ d D)) (/ w (/ d D)))) h))
963.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
874.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify8.2s

Counts

91 → 91

Iterations

Iter	Nodes
3	12376
2	1969
1	547
0	223

prune2.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 46.2b

regimes1.5s

Accuracy

0% (3.7b remaining)

Error of 52.1b against oracle of 48.4b and baseline of 52.1b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
2	36
1	36
0	27

end0.0ms

sample19.9s

Algorithm

intervals

Results

6.5s	2337×	body	5120	valid
3.8s	13274×	body	80	nan
3.0s	1761×	body	2560	valid
1.8s	6806×	body	80	valid
1.7s	603×	body	10240	exit
1.2s	900×	body	1280	valid
366.0ms	427×	body	640	valid
185.0ms	230×	body	320	valid
49.0ms	109×	body	160	valid