Details

sample829.0ms

Algorithm

intervals

Results

458.0ms	54×	body	2560	valid
140.0ms	71×	body	5120	valid
79.0ms	382×	body	80	nan
43.0ms	219×	body	80	valid
29.0ms	18×	body	10240	exit
24.0ms	26×	body	1280	valid
11.0ms	14×	body	640	valid
6.0ms	10×	body	320	valid
1.0ms	3×	body	160	valid

simplify917.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

917.0ms

(* (/ 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)))))

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 49.5b

localize70.0ms

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))
14.7b	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
9.2b	(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)))
9.2b	(* (* (/ d D) (/ d D)) (/ c0 h))

rewrite6.6s

Algorithm

rewrite-expression-head

Rules

54×	`add-cbrt-cube` `add-exp-log`
23×	`add-sqr-sqrt`
22×	`prod-exp` `cbrt-unprod`
21×	`*-un-lft-identity`
17×	`associate-r` `add-cube-cbrt`
15×	`cbrt-undiv` `div-exp`
13×	`times-frac`
12×	`pow1`
9×	`frac-times`
8×	`sqrt-div` `associate-l` `sqrt-prod`
7×	`fma-def` `associate-*r/`
6×	`associate-*l/` `frac-add` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`flip3-+` `flip-+` `unswap-sqr`
2×	`*-commutative` `div-inv` `distribute-lft-out` `difference-of-squares`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 140

Calls

4 calls:

Slowest

4.2s	(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)))
1.9s	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
434.0ms	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
49.0ms	(* (* (/ d D) (/ d D)) (/ c0 h))

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

744.0ms	(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)))
296.0ms	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
295.0ms	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
59.0ms	(* (* (/ d D) (/ d D)) (/ c0 h))

simplify20.1s

Counts

114 → 152

Calls

114 calls:

Slowest

1.1s	(* (* (* (/ c0 (* w 2)) (/ c0 (* w 2))) (/ c0 (* w 2))) (* (* (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))))
719.0ms	(+ (* (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))))
696.0ms	(* c0 (+ (* (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)))))
563.0ms	(* (* (/ (* (* d d) d) (* (* D D) D)) (* (* (/ d D) (/ d D)) (/ d D))) (/ (* (* c0 c0) c0) (* (* h h) h)))
515.0ms	(* (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D))) (/ (* (* c0 c0) c0) (* (* h h) h)))

prune3.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.8b

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

prune91.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 23.8b

localize91.0ms

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))
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))
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))
14.7b	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))

rewrite5.7s

Algorithm

rewrite-expression-head

Rules

21×	`fma-def`
17×	`*-un-lft-identity`
16×	`sqrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
10×	`add-log-exp`
8×	`sqrt-div`
6×	`frac-add`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
3×	`+-commutative` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 91

Calls

4 calls:

Slowest

1.8s	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.8s	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.7s	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
502.0ms	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

324.0ms	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
311.0ms	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
298.0ms	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
285.0ms	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))

simplify9.3s

Counts

56 → 103

Calls

56 calls:

Slowest

699.0ms	(+ (* (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))))
657.0ms	(+ (* (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))))
581.0ms	(+ (* (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))))
450.0ms	(* (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))))) w)
392.0ms	(* (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))))) w)

prune2.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 23.8b

localize92.0ms

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))
14.7b	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
9.2b	(* (* (/ d D) (/ d D)) (/ c0 h))
9.2b	(* (* (/ d D) (/ d D)) (/ c0 h))

rewrite2.4s

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

1.9s	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
441.0ms	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
33.0ms	(* (* (/ d D) (/ d D)) (/ c0 h))
31.0ms	(* (* (/ d D) (/ d D)) (/ c0 h))

series770.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

341.0ms	(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
320.0ms	(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
67.0ms	(* (* (/ d D) (/ d D)) (/ c0 h))
42.0ms	(* (* (/ d D) (/ d D)) (/ c0 h))

simplify20.4s

Counts

130 → 167

Calls

130 calls:

Slowest

876.0ms	(* (* (/ (* (* d d) d) (* (* D D) D)) (* (* (/ d D) (/ d D)) (/ d D))) (* (* (/ c0 h) (/ c0 h)) (/ c0 h)))
657.0ms	(+ (* (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))))
588.0ms	(* (* (/ (* (* d d) d) (* (* D D) D)) (* (* (/ d D) (/ d D)) (/ d D))) (/ (* (* c0 c0) c0) (* (* h h) h)))
588.0ms	(* (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D))) (/ (* (* c0 c0) c0) (* (* h h) h)))
566.0ms	(* (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D))) (/ (* (* c0 c0) c0) (* (* h h) h)))

prune3.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 23.5b

regimes2.1s

Accuracy

17.9% (7.4b remaining)

Error of 32.5b against oracle of 25.1b and baseline of 34.2b

bsearch10.0ms

end0.0ms

sample19.9s

Algorithm

intervals

Results

5.7s	2242×	body	5120	valid
3.9s	13355×	body	80	nan
3.2s	1727×	body	2560	valid
2.2s	6772×	body	80	valid
1.7s	567×	body	10240	exit
1.3s	923×	body	1280	valid
443.0ms	442×	body	640	valid
212.0ms	250×	body	320	valid
76.0ms	102×	body	160	valid