Details

sample92.0ms

Algorithm

intervals

Results

41.0ms	724×	body	80	nan
18.0ms	256×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
12×	`times-frac`
8×	`log-prod` `distribute-lft-out`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`div-inv` `add-log-exp`
3×	`pow1` `add-exp-log` `log-div`
2×	`distribute-rgt-out` `flip3-+` `frac-add` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `rem-log-exp` `sum-log` `log-pow`

Counts

2 → 37

Calls

2 calls:

68.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
95.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series582.0ms

Counts

2 → 6

Calls

2 calls:

129.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
453.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify748.0ms

Counts

43 → 43

Iterations

Useful iterations: done (747.0ms)

Iter	Nodes	Cost
0	137	943
1	342	914
2	1330	822
done	5002	806

prune209.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize35.0ms

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))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
78×	`sqrt-prod`
76×	`times-frac`
69×	`add-sqr-sqrt`
58×	`add-cube-cbrt`
25×	`log-prod`
15×	`distribute-lft-out`
13×	`associate-+r+`
12×	`associate-/r*`
11×	`pow1`
10×	`associate-/l*`
9×	`add-exp-log`
8×	`log-pow` `add-cbrt-cube`
7×	`difference-of-squares`
6×	`associate-+l+` `distribute-neg-in`
5×	`add-log-exp`
4×	`distribute-rgt-neg-in` `div-inv`
3×	`associate-+r-` `log-div`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `sqrt-div` `div-exp` `clear-num` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sqrt-undiv` `distribute-rgt-out` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `neg-log` `frac-add` `flip--`

Counts

4 → 167

Calls

4 calls:

4.0ms	(log (sqrt x))
147.0ms	(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
32.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
12.0ms	(/ 1.0 (sqrt x))

series735.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(log (sqrt x))
500.0ms	(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
81.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
51.0ms	(/ 1.0 (sqrt x))

simplify1.5s

Counts

179 → 179

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	319	2911
1	725	2651
2	2766	2479
done	5001	2468

prune699.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.4b	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.4b	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
24×	`times-frac`
16×	`add-sqr-sqrt` `sqrt-prod` `distribute-lft-out`
14×	`add-cube-cbrt`
8×	`div-inv` `add-log-exp`
6×	`pow1` `sqrt-div`
4×	`add-exp-log` `distribute-rgt-out` `flip3-+` `frac-add` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 76

Calls

4 calls:

64.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
73.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
71.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
84.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series798.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
134.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
275.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
263.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify939.0ms

Counts

88 → 88

Iterations

Useful iterations: done (934.0ms)

Iter	Nodes	Cost
0	164	1926
1	396	1794
2	1596	1660
done	5002	1628

prune589.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.2s

Counts

4 → 12

Calls

4 calls:

282.0ms	(cbrt x)
237.0ms	(cbrt x)
334.0ms	(cbrt x)
312.0ms	(cbrt x)

simplify2.9s

Counts

56 → 56

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	24	260
1	45	244
2	116	220
3	342	208
4	935	208
5	3497	208
done	5001	208

prune228.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	15	20
done	15	20

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.4s	24347×	body	80	nan
659.0ms	8000×	body	80	valid