Details

sample111.0ms

Algorithm

intervals

Results

58.0ms	862×	body	80	nan
19.0ms	256×	body	80	valid

simplify12.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

9.0ms	(- 1.0 (* x x))
24.0ms	(/ (sqrt (- 1.0 (* x x))) x)
36.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
72.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series896.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- 1.0 (* x x))
233.0ms	(/ (sqrt (- 1.0 (* x x))) x)
131.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
455.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.5s

Counts

134 → 134

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	239	1985
1	568	1856
2	2623	1720
done	5001	1714

prune706.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize39.0ms

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)))))
0.2b	(/ 1.0 (sqrt x))
0.2b	(/ (sqrt (- 1.0 (* x x))) (sqrt x))

rewrite200.0ms

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×	`log-div` `associate-+r-` `sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `clear-num` `sum-log` `frac-2neg` `flip3-+` `sqrt-div` `div-exp` `flip-+` `associate-/l/`
1×	`neg-sub0` `+-commutative` `sqrt-undiv` `neg-mul-1` `distribute-rgt-out` `flip3--` `rem-log-exp` `neg-log` `frac-add` `associate-+l-` `flip--`

Counts

4 → 191

Calls

4 calls:

5.0ms	(log (sqrt x))
148.0ms	(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
10.0ms	(/ 1.0 (sqrt x))
23.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))

series684.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(log (sqrt x))
441.0ms	(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
52.0ms	(/ 1.0 (sqrt x))
95.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))

simplify2.2s

Counts

203 → 203

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	323	2993
1	739	2727
2	2853	2542
done	5002	2535

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ 1 (sqrt x)) (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) x))
0.2b	(/ 1 (sqrt x))
0.2b	(/ 1.0 (sqrt x))
0.2b	(log (fma (/ 1 (sqrt x)) (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
24×	`sqrt-prod`
12×	`associate-/r*`
11×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `div-exp` `pow-flip`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-inv`
1×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `rem-log-exp` `log-pow` `fma-udef` `inv-pow`

Counts

4 → 112

Calls

4 calls:

0.0ms	(fma (/ 1 (sqrt x)) (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms	(/ 1 (sqrt x))
5.0ms	(/ 1.0 (sqrt x))
1.0ms	(log (fma (/ 1 (sqrt x)) (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) x)))

series800.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(fma (/ 1 (sqrt x)) (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) x))
32.0ms	(/ 1 (sqrt x))
53.0ms	(/ 1.0 (sqrt x))
461.0ms	(log (fma (/ 1 (sqrt x)) (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.2s

Counts

124 → 124

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	233	1663
1	509	1496
2	2135	1316
done	5001	1313

prune608.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes23.0ms

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

sample4.1s

Algorithm

intervals

Results

2.7s	24038×	body	80	nan
665.0ms	8000×	body	80	valid