Details

sample891.0ms

Algorithm

intervals

Results

184.0ms	313×	body	80	nan
152.0ms	32×	body	1280	valid
43.0ms	165×	body	80	valid
39.0ms	9×	body	320	nan
30.0ms	23×	body	1280	nan
25.0ms	25×	body	640	valid
20.0ms	17×	body	640	nan
14.0ms	17×	body	320	valid
9.0ms	17×	body	160	valid
2.0ms	4×	body	160	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2040
6	2040
5	1370
4	472
3	215
2	101
1	44
0	18

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.1b

localize78.0ms

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)))

rewrite166.0ms

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×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 94

Calls

4 calls:

60.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
15.0ms	(* (sqrt 2) t)
44.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
44.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.4s

Counts

4 → 12

Calls

4 calls:

481.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
75.0ms	(* (sqrt 2) t)
259.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.6s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	2000
3	2000
2	1605
1	483
0	181

prune838.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.8b

localize68.0ms

Local error

Found 4 expressions with local error:

4.8b	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
7.1b	(/ (* l l) x)
9.7b	(/ (* 4 (* t t)) x)
28.9b	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 77

Calls

4 calls:

0.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
18.0ms	(/ (* l l) x)
31.0ms	(/ (* 4 (* t t)) x)
2.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
22.0ms	(/ (* l l) x)
39.0ms	(/ (* 4 (* t t)) x)
413.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

simplify1.3s

Counts

89 → 89

Iterations

Iter	Nodes
done	2031
3	2031
2	1450
1	393
0	148

prune715.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize68.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma t t (* l (/ l x)))
4.8b	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x))
9.7b	(/ (* 4 (* t t)) x)
28.9b	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `times-frac` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`fma-udef`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l*`

Counts

4 → 64

Calls

4 calls:

1.0ms	(fma t t (* l (/ l x)))
0.0ms	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x))
36.0ms	(/ (* 4 (* t t)) x)
3.0ms	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x)))

series664.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma t t (* l (/ l x)))
112.0ms	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x))
43.0ms	(/ (* 4 (* t t)) x)
430.0ms	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 (* t t)) x)))

simplify1.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	2001
3	2001
2	949
1	298
0	127

prune728.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

localize81.0ms

Local error

Found 4 expressions with local error:

9.7b	(/ (* 4 (* t t)) x)
28.9b	(sqrt (fma t t (* l (/ l x))))
28.9b	(sqrt (fma t t (* l (/ l x))))
28.9b	(sqrt (fma 2 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (/ (* 4 (* t t)) x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
7×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `associate-/r*` `sqrt-pow1` `times-frac` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

30.0ms	(/ (* 4 (* t t)) x)
2.0ms	(sqrt (fma t t (* l (/ l x))))
2.0ms	(sqrt (fma t t (* l (/ l x))))
3.0ms	(sqrt (fma 2 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (/ (* 4 (* t t)) x)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* 4 (* t t)) x)
124.0ms	(sqrt (fma t t (* l (/ l x))))
116.0ms	(sqrt (fma t t (* l (/ l x))))
346.0ms	(sqrt (fma 2 (* (sqrt (fma t t (* l (/ l x)))) (sqrt (fma t t (* l (/ l x))))) (/ (* 4 (* t t)) x)))

simplify1.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	2003
3	2003
2	897
1	296
0	124

prune778.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

regimes904.0ms

Accuracy

77.3% (5.3b remaining)

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

bsearch221.0ms

Steps

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

simplify40.0ms

Iterations

Iter	Nodes
done	44
1	44
0	41

end0.0ms

sample10.2s

Algorithm

intervals

Results

2.4s	10197×	body	80	nan
1.4s	653×	body	320	valid
1.3s	5154×	body	80	valid
1.2s	558×	body	1280	nan
1.1s	896×	body	1280	valid
992.0ms	971×	body	640	valid
630.0ms	565×	body	640	nan
297.0ms	357×	body	320	nan
133.0ms	326×	body	160	valid
105.0ms	177×	body	160	nan