Details

sample129.0ms

Algorithm

intervals

Results

74.0ms	849×	body	80	nan
35.0ms	256×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
3	20
2	18
1	14
0	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.0b	(sqrt (- 1 (* x x)))
0.0b	(/ (sqrt (- 1 (* x x))) x)
0.2b	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
59×	`times-frac`
50×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
31×	`sqrt-prod`
16×	`distribute-lft-out`
15×	`log-prod`
14×	`div-inv`
13×	`fma-def`
10×	`difference-of-squares`
8×	`associate-/l*`
7×	`add-exp-log`
6×	`pow1` `distribute-rgt-out` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`log-div` `associate-/r*`
2×	`flip3-+` `flip3--` `frac-add` `distribute-rgt1-in` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `log-pow`

Counts

4 → 142

Calls

4 calls:

26.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
9.0ms	(sqrt (- 1 (* x x)))
16.0ms	(/ (sqrt (- 1 (* x x))) x)
33.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
53.0ms	(sqrt (- 1 (* x x)))
114.0ms	(/ (sqrt (- 1 (* x x))) x)
229.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

simplify1.1s

Counts

154 → 154

Iterations

Iter	Nodes
done	2000
3	2000
2	1579
1	554
0	247

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (log (/ 1 (sqrt x))) (log (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x)))))
0.2b	(/ 1 (sqrt x))
0.2b	(/ 1 (sqrt x))
0.2b	(/ (sqrt (- 1 (* x x))) (sqrt x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

136×	`times-frac`
132×	`*-un-lft-identity`
120×	`sqrt-prod`
112×	`add-sqr-sqrt`
89×	`add-cube-cbrt`
48×	`log-prod`
26×	`associate-+r+`
22×	`associate-+l+` `distribute-lft-out`
18×	`associate-/r*`
15×	`pow1`
14×	`add-exp-log` `associate-/l*` `difference-of-squares`
11×	`div-inv`
10×	`add-cbrt-cube`
9×	`log-pow` `pow-flip`
8×	`fma-def`
5×	`div-exp`
4×	`expm1-log1p-u` `log-div` `distribute-rgt-out` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `inv-pow`
2×	`rec-exp` `flip3-+` `sqrt-div` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `sqrt-undiv` `sum-log` `flip3--` `frac-add` `distribute-rgt1-in` `associate-+l-` `flip--`

Counts

4 → 254

Calls

4 calls:

43.0ms	(+ (log (/ 1 (sqrt x))) (log (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x)))))
8.0ms	(/ 1 (sqrt x))
8.0ms	(/ 1 (sqrt x))
17.0ms	(/ (sqrt (- 1 (* x x))) (sqrt x))

series589.0ms

Counts

4 → 12

Calls

4 calls:

434.0ms	(+ (log (/ 1 (sqrt x))) (log (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x)))))
35.0ms	(/ 1 (sqrt x))
43.0ms	(/ 1 (sqrt x))
76.0ms	(/ (sqrt (- 1 (* x x))) (sqrt x))

simplify1.7s

Counts

266 → 266

Iterations

Iter	Nodes
done	2002
3	2002
2	1950
1	758
0	342

prune3.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes98.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	12

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.1s	24086×	body	80	nan
1.5s	8000×	body	80	valid