Details

sample101.0ms

Algorithm

intervals

Results

51.0ms	816×	body	80	nan
19.0ms	256×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	16	13
3	18	13
done	18	13

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
42×	`times-frac`
39×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
20×	`sqrt-prod`
13×	`fma-def`
8×	`log-prod` `distribute-lft-out`
7×	`add-exp-log` `associate-/l*`
6×	`pow1` `add-cbrt-cube` `div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`log-div` `associate-/r*`
2×	`distribute-rgt-out` `flip3--` `flip3-+` `frac-add` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 119

Calls

4 calls:

8.0ms	(sqrt (- 1.0 (* x x)))
39.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
18.0ms	(/ (sqrt (- 1.0 (* x x))) x)
45.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series871.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (- 1.0 (* x x)))
446.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
202.0ms	(/ (sqrt (- 1.0 (* x x))) x)
147.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify1.2s

Counts

131 → 131

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	234	2010
1	535	1867
2	1540	1735
done	5000	1712

prune463.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `sqrt-prod`
17×	`add-cube-cbrt`
16×	`sqrt-div`
13×	`fma-def`
10×	`pow1`
9×	`times-frac` `associate-r`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `frac-times` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `log1p-expm1-u` `difference-of-squares` `unswap-sqr`
3×	`pow-prod-down` `div-inv` `distribute-lft-out`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `hypot-def` `distribute-lft-out--`
1×	`+-commutative` `distribute-rgt-out` `sqrt-unprod` `frac-add` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 113

Calls

4 calls:

16.0ms	(sqrt (- (sqrt 1.0) x))
25.0ms	(sqrt (+ (sqrt 1.0) x))
31.0ms	(+ (/ 1.0 x) (/ (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- (sqrt 1.0) x))) x))
74.0ms	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- (sqrt 1.0) x)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (- (sqrt 1.0) x))
73.0ms	(sqrt (+ (sqrt 1.0) x))
233.0ms	(+ (/ 1.0 x) (/ (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- (sqrt 1.0) x))) x))
164.0ms	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- (sqrt 1.0) x)))

simplify1.3s

Counts

125 → 125

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	195	1862
1	476	1639
2	1406	1528
done	5001	1490

prune615.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt x))
0.2b	(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
0.3b	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.3b	(/ 1.0 (sqrt x))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
78×	`sqrt-prod`
76×	`times-frac`
72×	`add-sqr-sqrt`
61×	`add-cube-cbrt`
25×	`log-prod`
16×	`fma-def`
15×	`pow1` `distribute-lft-out`
14×	`log-pow`
13×	`associate-+r+`
12×	`associate-/r*`
10×	`distribute-rgt-neg-in` `associate-/l*`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`difference-of-squares`
6×	`distribute-lft-neg-in` `associate-+l+` `distribute-neg-in`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-+r-` `log-div` `sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `sqrt-div` `div-exp` `clear-num` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sqrt-undiv` `distribute-rgt-out` `flip3--` `rem-log-exp` `neg-log` `frac-add` `flip--`

Counts

4 → 191

Calls

4 calls:

4.0ms	(log (sqrt x))
117.0ms	(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
29.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
13.0ms	(/ 1.0 (sqrt x))

series748.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(log (sqrt x))
484.0ms	(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
97.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
47.0ms	(/ 1.0 (sqrt x))

simplify2.2s

Counts

203 → 203

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	339	3023
1	745	2756
2	1875	2563
done	5000	2540

prune842.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	18
1	15	18
done	15	18

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.3s	23585×	body	80	nan
669.0ms	8000×	body	80	valid