Details

sample924.0ms

Algorithm

intervals

Results

490.0ms	313×	body	80	nan
72.0ms	32×	body	1280	valid
61.0ms	165×	body	80	valid
43.0ms	17×	body	640	nan
43.0ms	17×	body	320	valid
34.0ms	9×	body	320	nan
18.0ms	23×	body	1280	nan
18.0ms	25×	body	640	valid
6.0ms	17×	body	160	valid
1.0ms	4×	body	160	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
6	2002
5	1119
4	393
3	181
2	93
1	42
0	18

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize81.0ms

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)
14.8b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
22.7b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite226.0ms

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:

84.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
14.0ms	(* (sqrt 2) t)
48.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
76.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.5s

Counts

4 → 12

Calls

4 calls:

514.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
52.0ms	(* (sqrt 2) t)
235.0ms	(- (* (/ (+ 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	2022
3	2022
2	1525
1	458
0	170

prune705.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.8b

localize57.0ms

Local error

Found 4 expressions with local error:

4.8b	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
7.1b	(/ (* l l) x)
9.8b	(/ (* t t) x)
28.9b	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

rewrite117.0ms

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:

35.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
15.0ms	(/ (* l l) x)
15.0ms	(/ (* t t) x)
50.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
24.0ms	(/ (* l l) x)
38.0ms	(/ (* t t) x)
372.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify1.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	2000
2	2000
1	536
0	172

prune610.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2) t)
4.8b	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
9.8b	(/ (* t t) x)
28.9b	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

15.0ms	(* (sqrt 2) t)
32.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
18.0ms	(/ (* t t) x)
43.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sqrt 2) t)
100.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
35.0ms	(/ (* t t) x)
414.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

simplify1.2s

Counts

91 → 91

Iterations

Iter	Nodes
done	2003
2	2003
1	499
0	171

prune630.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* t t) (* l (/ l x)))
4.8b	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
9.8b	(/ (* t t) x)
28.9b	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

rewrite71.0ms

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:

7.0ms	(+ (* t t) (* l (/ l x)))
18.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
13.0ms	(/ (* t t) x)
31.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* t t) (* l (/ l x)))
76.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
22.0ms	(/ (* t t) x)
358.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

simplify1.7s

Counts

80 → 80

Iterations

Iter	Nodes
done	2003
3	2003
2	1889
1	465
0	155

prune587.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.1b

regimes1.1s

Accuracy

77.2% (5.3b remaining)

Error of 9.2b against oracle of 3.8b and baseline of 27.3b

bsearch168.0ms

Steps

Iters	Range		Point
0	1.7049261699089995e+93	1.7482309059034422e+93	1.7265785379062208e+93
7	-21713105135126.78	-922935609835.4889	-16678696720617.19

simplify43.0ms

Iterations

Iter	Nodes
done	76
3	76
2	75
1	61
0	45

end0.0ms

sample10.3s

Algorithm

intervals

Results

3.0s	10197×	body	80	nan
1.8s	971×	body	640	valid
1.3s	5154×	body	80	valid
1.1s	896×	body	1280	valid
727.0ms	558×	body	1280	nan
541.0ms	565×	body	640	nan
508.0ms	653×	body	320	valid
302.0ms	357×	body	320	nan
206.0ms	326×	body	160	valid
138.0ms	177×	body	160	nan