Details

sample104.0ms

Algorithm

intervals

Results

53.0ms	302×	body	80	valid
8.0ms	68×	body	80	nan

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	2702
4	460
3	181
2	81
1	36
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize46.0ms

Local error

Found 4 expressions with local error:

2.6b	(* (sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)) w0)
4.5b	(sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0))
5.5b	(fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)
5.7b	(/ (* M D) (* 2.0 d))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `pow-prod-down` `-commutative` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 72

Calls

4 calls:

15.0ms	(* (sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)) w0)
2.0ms	(sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0))
0.0ms	(fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)
15.0ms	(/ (* M D) (* 2.0 d))

series1.8s

Counts

4 → 12

Calls

4 calls:

895.0ms	(* (sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)) w0)
397.0ms	(sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0))
479.0ms	(fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)
50.0ms	(/ (* M D) (* 2.0 d))

simplify1.5s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1813
1	416
0	176

prune806.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.2b

localize42.0ms

Local error

Found 4 expressions with local error:

2.6b	(* (sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0)) w0)
4.5b	(sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0))
5.7b	(/ (* M D) (* 2.0 d))
10.7b	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

651×	`times-frac`
304×	`add-sqr-sqrt`
282×	`*-un-lft-identity`
278×	`add-cube-cbrt`
177×	`unpow-prod-down`
90×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
67×	`add-exp-log`
47×	`div-inv`
37×	`sqr-pow`
35×	`associate-/r*`
33×	`div-exp`
30×	`neg-mul-1`
23×	`add-cbrt-cube`
13×	`prod-exp`
10×	`pow-exp` `associate-/l*`
9×	`sqrt-prod`
7×	`pow1` `cbrt-undiv` `associate-l` `hypot-def`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`pow-to-exp` `clear-num` `frac-2neg` `flip3-+` `associate-*l/` `flip-+` `distribute-lft-out` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-/r/` `*-commutative`

Counts

4 → 453

Calls

4 calls:

752.0ms	(* (sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0)) w0)
396.0ms	(sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0))
15.0ms	(/ (* M D) (* 2.0 d))
39.0ms	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h)))

series2.4s

Counts

4 → 12

Calls

4 calls:

741.0ms	(* (sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0)) w0)
563.0ms	(sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0))
47.0ms	(/ (* M D) (* 2.0 d))
1.1s	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h)))

simplify1.2s

Counts

465 → 465

Iterations

Iter	Nodes
done	5000
1	2244
0	824

prune4.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize111.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
5.1b	(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (- h))
5.7b	(/ (* M D) (* 2.0 d))
5.7b	(/ (* M D) (* 2.0 d))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-exp-log`
79×	`times-frac`
60×	`add-sqr-sqrt`
58×	`associate-l`
42×	`unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt`
41×	`div-exp`
35×	`add-cbrt-cube` `prod-exp`
30×	`cbrt-prod`
15×	`pow-exp`
12×	`div-inv`
11×	`cbrt-undiv` `cbrt-unprod` `associate-/l*`
10×	`associate-r` `sqr-pow`
7×	`unswap-sqr`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `pow-to-exp` `clear-num` `associate-/r*` `distribute-rgt-neg-in` `frac-2neg`
1×	`neg-mul-1` `pow-prod-down` `associate-l/` `-commutative` `distribute-rgt-neg-out`

Counts

4 → 191

Calls

4 calls:

37.0ms	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
59.0ms	(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (- h))
20.0ms	(/ (* M D) (* 2.0 d))
20.0ms	(/ (* M D) (* 2.0 d))

series1.9s

Counts

4 → 12

Calls

4 calls:

663.0ms	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
1.1s	(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (- h))
39.0ms	(/ (* M D) (* 2.0 d))
52.0ms	(/ (* M D) (* 2.0 d))

simplify1.4s

Counts

203 → 203

Iterations

Iter	Nodes
done	5000
2	3871
1	919
0	318

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize69.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (+ (* (/ (pow (* M D) (/ 2.0 2)) (/ (cbrt l) (/ (pow (/ (/ 1 2.0) d) (/ 2.0 2)) (cbrt l)))) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (- h))) 1.0))
5.1b	(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (- h))
5.7b	(/ (* M D) (* 2.0 d))
8.4b	(/ (pow (* M D) (/ 2.0 2)) (/ (cbrt l) (/ (pow (/ (/ 1 2.0) d) (/ 2.0 2)) (cbrt l))))

rewrite4.8s

Algorithm

rewrite-expression-head

Rules

43376×	`times-frac`
16414×	`add-sqr-sqrt`
16395×	`*-un-lft-identity` `add-cube-cbrt`
11042×	`unpow-prod-down`
10254×	`cbrt-prod`
1946×	`sqr-pow`
1722×	`associate-/r*`
915×	`div-inv`
194×	`add-exp-log`
135×	`div-exp`
58×	`associate-l`
43×	`pow-exp`
26×	`add-cbrt-cube`
25×	`prod-exp`
14×	`pow-to-exp`
11×	`cbrt-undiv`
10×	`associate-r`
7×	`pow1` `associate-/r/` `unswap-sqr`
6×	`cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `neg-mul-1` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 10521

Calls

4 calls:

1.6s	(sqrt (+ (* (/ (pow (* M D) (/ 2.0 2)) (/ (cbrt l) (/ (pow (/ (/ 1 2.0) d) (/ 2.0 2)) (cbrt l)))) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (- h))) 1.0))
67.0ms	(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (- h))
20.0ms	(/ (* M D) (* 2.0 d))
857.0ms	(/ (pow (* M D) (/ 2.0 2)) (/ (cbrt l) (/ (pow (/ (/ 1 2.0) d) (/ 2.0 2)) (cbrt l))))

series2.8s

Counts

4 → 12

Calls

4 calls:

656.0ms	(sqrt (+ (* (/ (pow (* M D) (/ 2.0 2)) (/ (cbrt l) (/ (pow (/ (/ 1 2.0) d) (/ 2.0 2)) (cbrt l)))) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (- h))) 1.0))
1.1s	(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (- h))
35.0ms	(/ (* M D) (* 2.0 d))
1.0s	(/ (pow (* M D) (/ 2.0 2)) (/ (cbrt l) (/ (pow (/ (/ 1 2.0) d) (/ 2.0 2)) (cbrt l))))

simplify6.5s

Counts

10533 → 10533

Iterations

Iter	Nodes
done	16017
0	16017

prune2.7m

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

regimes1.4s

Accuracy

-8.6% (4.2b remaining)

Error of 8.9b against oracle of 4.8b and baseline of 8.6b

bsearch299.0ms

Steps

Iters	Range		Point
10	8.12201969800172e+146	1.0328687671313965e+163	8.33046890233557e+146
9	4.201874675255858e-250	3.851983626193544e-241	6.742814395308296e-243
9	-9.83473179926482e-102	-3.0421930142797753e-109	-2.4004248004346256e-106
11	-1.7641631018079695e+126	-1.5320532078182614e+103	-1.6413070018908769e+106

simplify18.0ms

Iterations

Iter	Nodes
done	62
1	62
0	53

end0.0ms

sample1.5s

Algorithm

intervals

Results

755.0ms	9319×	body	80	valid
230.0ms	3144×	body	80	nan