Details

sample122.0ms

Algorithm

intervals

Results

67.0ms	808×	body	80	nan
19.0ms	256×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
2	16
1	12
0	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`log-prod` `distribute-lft-out`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `sqrt-prod` `div-inv`
3×	`log-div` `add-cbrt-cube`
2×	`flip3-+` `distribute-rgt-out` `sqrt-div` `frac-add` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3--` `pow1/2` `rem-log-exp` `log-pow` `flip--` `difference-of-squares`

Counts

3 → 53

Calls

3 calls:

42.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
4.0ms	(sqrt (- 1.0 (* x x)))
52.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series691.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
80.0ms	(sqrt (- 1.0 (* x x)))
474.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.7s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
2	1911
1	446
0	180

prune346.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(sqrt (- 1.0 (* x x)))
0.1b	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.1b	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`sqrt-prod`
18×	`add-sqr-sqrt`
12×	`times-frac` `add-cube-cbrt`
10×	`sqrt-div`
8×	`pow1` `distribute-lft-out`
4×	`rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `div-inv` `add-log-exp`
2×	`flip3-+` `distribute-rgt-out` `flip3--` `frac-add` `flip-+` `flip--` `difference-of-squares`

Counts

4 → 74

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (* x x)))
4.0ms	(sqrt (- 1.0 (* x x)))
74.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
97.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(sqrt (- 1.0 (* x x)))
82.0ms	(sqrt (- 1.0 (* x x)))
302.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
239.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify982.0ms

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1860
1	446
0	186

prune706.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.2b	(/ 1.0 (sqrt x))
0.2b	(/ 1 (sqrt x))
0.4b	(* (sqrt (/ 1 (sqrt x))) (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

148×	`sqrt-prod`
123×	`add-sqr-sqrt`
120×	`times-frac`
106×	`*-un-lft-identity`
84×	`add-cube-cbrt`
25×	`associate-l`
18×	`associate-/r*`
16×	`associate-r`
14×	`add-exp-log`
13×	`associate-/l*`
12×	`add-cbrt-cube` `sqrt-div` `unswap-sqr`
10×	`pow1`
9×	`distribute-lft-out`
7×	`difference-of-squares`
6×	`div-inv`
4×	`div-exp` `add-log-exp`
3×	`frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-*r/` `pow-flip`
2×	`flip3-+` `frac-add` `flip-+` `associate-/l/`
1×	`rec-exp` `sqrt-undiv` `distribute-rgt-out` `flip3--` `sqrt-unprod` `1-exp` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `flip--` `inv-pow`

Counts

4 → 228

Calls

4 calls:

21.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
8.0ms	(/ 1.0 (sqrt x))
5.0ms	(/ 1 (sqrt x))
321.0ms	(* (sqrt (/ 1 (sqrt x))) (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
66.0ms	(/ 1.0 (sqrt x))
45.0ms	(/ 1 (sqrt x))
322.0ms	(* (sqrt (/ 1 (sqrt x))) (sqrt (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))

simplify1.7s

Counts

240 → 240

Iterations

Iter	Nodes
done	5000
2	3690
1	845
0	391

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes62.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.2s	24124×	body	80	nan
695.0ms	8000×	body	80	valid