Details

sample921.0ms

Algorithm

intervals

Results

451.0ms	19×	body	640	valid
175.0ms	80×	body	5120	valid
83.0ms	60×	body	2560	valid
73.0ms	395×	body	80	nan
37.0ms	205×	body	80	valid
30.0ms	22×	body	10240	exit
21.0ms	24×	body	1280	valid
6.0ms	9×	body	320	valid
2.0ms	4×	body	160	valid

simplify864.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	2972
2	280
1	59
0	21

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.6b

localize92.0ms

Local error

Found 4 expressions with local error:

11.8b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
11.8b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
13.6b	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
29.3b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite207.0ms

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:

46.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
36.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
39.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
80.0ms	(+ (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:

99.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
99.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
735.0ms	(sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
906.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify1.2s

Counts

143 → 143

Iterations

Iter	Nodes
2	3560
1	668
0	224

prune2.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 46.7b

localize179.0ms

Local error

Found 4 expressions with local error:

10.3b	(/ (+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (+ (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)) (* (- (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))))
13.6b	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
13.6b	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
39.8b	(+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))))

rewrite4.0s

Algorithm

rewrite-expression-head

Rules

2650×	`frac-times`
1492×	`associate-*r/`
1310×	`associate-*l/`
1078×	`frac-add`
825×	`flip3--` `flip--`
808×	`sqrt-div`
506×	`associate-/l/`
72×	`associate-/r/`
48×	`frac-sub`
22×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`cube-unmult`
8×	`sqrt-prod`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`sum-cubes`
4×	`associate-+r+` `insert-posit16` `associate-/l*`
3×	`associate-/r*` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `rem-sqrt-square` `sub-neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 1165

Calls

4 calls:

2.8s	(/ (+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (+ (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)) (* (- (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))))
204.0ms	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
179.0ms	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
680.0ms	(+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))))

series3.7s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (+ (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)) (* (- (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))))
289.0ms	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
287.0ms	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
1.9s	(+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))))

simplify8.7s

Counts

1177 → 1177

Iterations

Iter	Nodes
1	8321
0	2501

prune39.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 21.0b

localize14.0ms

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

prune204.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 21.0b

localize184.0ms

Local error

Found 4 expressions with local error:

13.6b	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
13.6b	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
29.4b	(+ (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))))
44.5b	(/ (+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (- (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))))) (/ (+ (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)) (* (- (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (+ (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))))))

rewrite5.0s

Algorithm

rewrite-expression-head

Rules

3348×	`frac-times`
3094×	`sqrt-div`
2124×	`associate-*l/`
2064×	`associate-*r/`
1562×	`flip3--` `flip--`
1440×	`frac-add`
1412×	`associate-/l/`
1320×	`frac-sub`
99×	`times-frac`
60×	`sub-div`
58×	`add-sqr-sqrt`
56×	`*-un-lft-identity` `add-cube-cbrt`
33×	`associate-/r/`
21×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`sqrt-prod`
6×	`pow1` `flip3-+` `flip-+` `add-log-exp`
5×	`div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `difference-of-squares`
1×	`+-commutative` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `div-sub`

Counts

4 → 1568

Calls

4 calls:

288.0ms	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
181.0ms	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
317.0ms	(+ (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))))
4.0s	(/ (+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (- (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))))) (/ (+ (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)) (* (- (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (+ (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

281.0ms	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
290.0ms	(sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))
256.0ms	(+ (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))))
1.5s	(/ (+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (- (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))))) (/ (+ (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)) (* (- (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (+ (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))))))

simplify10.0s

Counts

1580 → 1580

Iterations

Iter	Nodes
1	7029
0	1936

prune1.1m

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 21.0b

regimes2.8s

Accuracy

-10% (11.1b remaining)

Error of 34.8b against oracle of 23.7b and baseline of 33.8b

bsearch1.6s

Steps

Iters	Range		Point
5	1.0737336719524054e+193	2.607252513265907e+193	1.0915833705181084e+193
10	3.057318762709241e+152	1.3631137907758233e+163	1.350659423435845e+163
8	1.3111129806904424e+89	8.255754215219532e+91	1.3340810790915187e+89
7	4.616964668353107e+42	5.2008845700897414e+44	5.1060876778360224e+44

simplify57.0ms

Iterations

Iter	Nodes
2	75
1	75
0	56

end0.0ms

sample17.2s

Algorithm

intervals

Results

4.7s	2243×	body	5120	valid
3.0s	13034×	body	80	nan
2.8s	1724×	body	2560	valid
2.5s	6690×	body	80	valid
1.5s	627×	body	10240	exit
1.1s	994×	body	1280	valid
399.0ms	451×	body	640	valid
173.0ms	227×	body	320	valid
38.0ms	99×	body	160	valid