Details

sample260.0ms

Algorithm

intervals

Results

57.0ms	158×	body	80	valid
35.0ms	349×	body	80	nan
13.0ms	32×	body	640	valid
11.0ms	25×	body	1280	valid
8.0ms	14×	body	1280	nan
7.0ms	25×	body	320	valid
7.0ms	20×	body	640	nan
3.0ms	16×	body	160	valid
3.0ms	10×	body	320	nan
1.0ms	8×	body	160	nan

simplify6.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	18	27
1	39	27
2	93	27
3	189	27
4	397	27
5	661	27
6	1122	27
7	2624	27
8	4131	27
done	5000	27

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
13.3b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

77.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
20.0ms	(* (sqrt 2.0) t)
58.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
59.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.9s

Counts

4 → 12

Calls

4 calls:

645.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
76.0ms	(* (sqrt 2.0) t)
330.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.4s

Counts

92 → 92

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	168	2472
1	414	2283
2	1552	2077
done	5000	2025

prune456.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.8b

localize38.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
5.4b	(/ (pow l 2) x)
9.8b	(/ (pow t 2) x)
27.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

32.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
9.0ms	(/ (pow l 2) x)
16.0ms	(/ (pow t 2) x)
40.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
36.0ms	(/ (pow l 2) x)
36.0ms	(/ (pow t 2) x)
219.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify1.4s

Counts

142 → 142

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	254	2317
1	535	2084
2	1725	1868
done	5001	1862

prune865.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
9.8b	(/ (pow t 2) x)
27.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-r/` `add-cbrt-cube` `associate-/l`
7×	`pow1` `sqrt-prod`
6×	`associate-l` `add-log-exp`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`associate-+r+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 103

Calls

4 calls:

20.0ms	(* (sqrt 2.0) t)
24.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
9.0ms	(/ (pow t 2) x)
20.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sqrt 2.0) t)
88.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
21.0ms	(/ (pow t 2) x)
237.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

simplify1.5s

Counts

115 → 115

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	214	2195
1	485	1872
2	1673	1601
done	5000	1587

prune739.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.9b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
9.8b	(/ (pow t 2) x)
27.5b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-r/` `associate-/l` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 92

Calls

4 calls:

69.0ms	(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
30.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
16.0ms	(/ (pow t 2) x)
34.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
102.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
21.0ms	(/ (pow t 2) x)
240.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

simplify1.3s

Counts

104 → 104

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	200	2320
1	467	1956
2	1616	1639
done	5000	1625

prune668.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.9b

regimes1.5s

Accuracy

77.8% (5.3b remaining)

Error of 9.2b against oracle of 3.9b and baseline of 27.8b

bsearch936.0ms

Steps

Iters	Range		Point
10	8.394896216821908e+49	9.623627385293308e+64	5.564919863052779e+60
10	1.5758220318623351e-174	8.046018310283969e-162	3.39285568249297e-169
7	1.04743012393885e-255	1.698545711080697e-253	1.2791561736442862e-253
7	-6.210081772932775e+49	-4.6782824394543606e+47	-1.670018113804049e+49

simplify35.0ms

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	50	182
1	63	143
2	68	115
3	71	115
done	71	115

end0.0ms

sample6.2s

Algorithm

intervals

Results

1.5s	5205×	body	80	valid
1.5s	10136×	body	80	nan
532.0ms	1006×	body	640	valid
475.0ms	805×	body	1280	valid
386.0ms	558×	body	1280	nan
244.0ms	614×	body	320	valid
232.0ms	609×	body	640	nan
215.0ms	362×	body	320	nan
127.0ms	370×	body	160	valid
39.0ms	190×	body	160	nan