Details

sample227.0ms

Algorithm

intervals

Results

67.0ms	341×	body	80	nan
17.0ms	168×	body	80	valid
14.0ms	35×	body	640	valid
10.0ms	24×	body	1280	valid
8.0ms	23×	body	640	nan
7.0ms	23×	body	320	valid
6.0ms	14×	body	1280	nan
1.0ms	6×	body	160	valid
1.0ms	5×	body	320	nan
0.0ms	3×	body	160	nan

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4473
5	1119
4	393
3	181
2	93
1	42
0	18

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.5b	(* (sqrt 2) t)
11.9b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.3b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`sqrt-div` `insert-posit16`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

83.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
19.0ms	(* (sqrt 2) t)
50.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
84.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.5s

Counts

4 → 12

Calls

4 calls:

497.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
49.0ms	(* (sqrt 2) t)
255.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.7s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1525
1	458
0	170

prune601.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.3b

localize53.0ms

Local error

Found 4 expressions with local error:

3.2b	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
5.9b	(/ (* l l) x)
8.8b	(/ (* t t) x)
26.7b	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `associate-l/` `frac-add` `associate-r/` `flip-+` `insert-posit16`
3×	`sqrt-prod`
2×	`associate-+l+` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 78

Calls

4 calls:

46.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
22.0ms	(/ (* l l) x)
11.0ms	(/ (* t t) x)
34.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
20.0ms	(/ (* l l) x)
34.0ms	(/ (* t t) x)
416.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify1.6s

Counts

90 → 90

Iterations

Iter	Nodes
done	5004
2	2246
1	536
0	172

prune464.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))
3.2b	(+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4))
8.8b	(/ (* t t) x)
26.7b	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `associate-l/` `frac-add` `associate-r/` `insert-posit16`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+l+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

10.0ms	(+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))
19.0ms	(+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4))
10.0ms	(/ (* t t) x)
37.0ms	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

series608.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))
142.0ms	(+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4))
38.0ms	(/ (* t t) x)
347.0ms	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

simplify1.8s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1927
1	471
0	156

prune582.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.1b

localize80.0ms

Local error

Found 4 expressions with local error:

8.8b	(/ (* t t) x)
8.8b	(/ (* t t) x)
26.7b	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))
26.7b	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
6×	`pow1` `associate-/r*` `times-frac` `sqrt-prod`
4×	`cbrt-undiv` `flip3-+` `div-exp` `associate-l/` `frac-add` `associate-r/` `flip-+` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

11.0ms	(/ (* t t) x)
10.0ms	(/ (* t t) x)
40.0ms	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))
32.0ms	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

series877.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (* t t) x)
25.0ms	(/ (* t t) x)
389.0ms	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))
437.0ms	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

simplify2.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1622
1	380
0	125

prune886.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.1b

regimes835.0ms

Accuracy

77.5% (5.2b remaining)

Error of 8.9b against oracle of 3.7b and baseline of 26.7b

bsearch385.0ms

Steps

Iters	Range		Point
8	2.0215799830271626e+96	1.863612731888614e+99	1.4235245726759946e+99
7	-8.62882115661326e+99	-1.9133687329772835e+98	-1.178101575424767e+99

simplify15.0ms

Iterations

Iter	Nodes
done	52
1	52
0	41

end0.0ms

sample5.9s

Algorithm

intervals

Results

1.4s	10091×	body	80	nan
1.1s	5042×	body	80	valid
927.0ms	903×	body	1280	valid
646.0ms	661×	body	320	valid
485.0ms	1038×	body	640	valid
306.0ms	627×	body	640	nan
289.0ms	607×	body	1280	nan
163.0ms	335×	body	320	nan
70.0ms	356×	body	160	valid
34.0ms	186×	body	160	nan