Details

sample503.0ms

Algorithm

intervals

Results

104.0ms	73×	body	5120	valid
93.0ms	56×	body	2560	valid
78.0ms	411×	body	80	nan
75.0ms	28×	body	10240	exit
52.0ms	231×	body	80	valid
30.0ms	8×	body	640	valid
28.0ms	26×	body	1280	valid
3.0ms	5×	body	320	valid
3.0ms	7×	body	160	valid

simplify948.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

947.0ms

(* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 49.7b

localize80.0ms

Local error

Found 4 expressions with local error:

26.8b	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
13.4b	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
12.0b	(* (* (/ d D) (/ d D)) (/ c0 h))
12.0b	(* (* (/ d D) (/ d D)) (/ c0 h))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

86×	`add-cbrt-cube` `add-exp-log`
36×	`prod-exp` `cbrt-unprod`
28×	`add-sqr-sqrt`
26×	`cbrt-undiv` `div-exp` `associate-r`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`times-frac`
15×	`pow1`
10×	`frac-times` `associate-*l/`
8×	`sqrt-prod`
7×	`fma-def`
6×	`pow-prod-down` `associate-*r/` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`flip3--` `associate-l` `frac-add` `*-commutative` `div-inv` `flip--` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`

Counts

4 → 155

Calls

4 calls:

Slowest

1.6s	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
460.0ms	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
60.0ms	(* (* (/ d D) (/ d D)) (/ c0 h))
37.0ms	(* (* (/ d D) (/ d D)) (/ c0 h))

series749.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

337.0ms	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
309.0ms	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
60.0ms	(* (* (/ d D) (/ d D)) (/ c0 h))
42.0ms	(* (* (/ d D) (/ d D)) (/ c0 h))

simplify21.1s

Counts

130 → 167

Calls

130 calls:

Slowest

655.0ms	(+ (* (sqrt (- (pow (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) 3) (pow (* M M) 3))) w) (* (sqrt (+ (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))) (+ (* (* M M) (* M M)) (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))) (* (* (/ d D) (/ d D)) (/ c0 h))))
631.0ms	(* (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D))) (/ (* (* c0 c0) c0) (* (* h h) h)))
617.0ms	(* (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D))) (/ (* (* c0 c0) c0) (* (* h h) h)))
537.0ms	(+ (+ (log (/ d D)) (- (log d) (log D))) (log (/ c0 h)))
511.0ms	(* (* (/ (* (* d d) d) (* (* D D) D)) (* (* (/ d D) (/ d D)) (/ d D))) (/ (* (* c0 c0) c0) (* (* h h) h)))

prune3.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 24.0b

localize17.0ms

Local error

Found 1 expressions with local error:

4.4b	(* (/ c0 (* w 2)) 0)

rewrite40.0ms

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` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`

Counts

1 → 31

Calls

1 calls:

Slowest

39.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

4.0ms

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

simplify1.5s

Counts

20 → 34

Calls

20 calls:

Slowest

352.0ms	(* (* (* (/ c0 (* w 2)) (/ c0 (* w 2))) (/ c0 (* w 2))) (* (* 0 0) 0))
286.0ms	(+ (- (log c0) (+ (log w) (log 2))) (log 0))
250.0ms	(+ (- (log c0) (log (* w 2))) (log 0))
198.0ms	(+ (log (/ c0 (* w 2))) (log 0))
106.0ms	(* (/ (* (* c0 c0) c0) (* (* (* w 2) (* w 2)) (* w 2))) (* (* 0 0) 0))

prune540.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 22.6b

localize1.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

Calls

0 calls:

Slowest

series0.0ms

Counts

0 → 0

Calls

0 calls:

Slowest

simplify0.0ms

Counts

0 → 0

Calls

0 calls:

Slowest

prune113.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 22.6b

localize90.0ms

Local error

Found 4 expressions with local error:

33.7b	(+ (* (sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))) (sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
17.7b	(sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))
17.7b	(sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))
13.4b	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-div`
28×	`sqrt-prod`
14×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `sqrt-pow1` `flip3--` `add-cube-cbrt` `flip--`
8×	`frac-add`
6×	`add-log-exp`
5×	`rem-sqrt-square` `pow1/2`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`associate-l/` `associate-r/`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 92

Calls

4 calls:

Slowest

470.0ms	(sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))
442.0ms	(+ (* (sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))) (sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
427.0ms	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
392.0ms	(sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

316.0ms	(+ (* (sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))) (sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
262.0ms	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
257.0ms	(sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))
240.0ms	(sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))

simplify15.0s

Counts

66 → 104

Calls

66 calls:

Slowest

857.0ms	(exp (* 1/4 (+ (* 2 (log M)) (log -1))))
771.0ms	(+ (* (* (sqrt (sqrt (- (pow (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) 3) (pow (* M M) 3)))) (sqrt (sqrt (- (pow (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) 3) (pow (* M M) 3))))) w) (* (* (sqrt (sqrt (+ (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))) (+ (* (* M M) (* M M)) (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))))) (sqrt (sqrt (+ (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))) (+ (* (* M M) (* M M)) (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))))) (* (* (/ d D) (/ d D)) (/ c0 h))))
744.0ms	(+ (* (* (sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))) (sqrt (sqrt (- (pow (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) 3) (pow (* M M) 3))))) w) (* (sqrt (sqrt (+ (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))) (+ (* (* M M) (* M M)) (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))))) (* (* (/ d D) (/ d D)) (/ c0 h))))
726.0ms	(+ (* (* (sqrt (sqrt (- (pow (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) 3) (pow (* M M) 3)))) (sqrt (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))) w) (* (sqrt (sqrt (+ (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))) (+ (* (* M M) (* M M)) (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))))) (* (* (/ d D) (/ d D)) (/ c0 h))))
454.0ms	(exp (* 1/4 (+ (* 2 (log M)) (log -1))))

prune1.9s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 22.6b

regimes2.0s

Accuracy

1.4% (7.4b remaining)

Error of 33.9b against oracle of 26.5b and baseline of 34.0b

bsearch872.0ms

end0.0ms

sample19.6s

Algorithm

intervals

Results

5.0s	2254×	body	5120	valid
4.8s	13036×	body	80	nan
3.9s	1746×	body	2560	valid
2.0s	6757×	body	80	valid
1.2s	867×	body	1280	valid
1.2s	552×	body	10240	exit
512.0ms	519×	body	640	valid
134.0ms	210×	body	320	valid
57.0ms	131×	body	160	valid