Details

sample91.0ms

Algorithm

intervals

Results

52.0ms	74×	body	1280	valid
13.0ms	35×	body	640	valid
5.0ms	29×	body	320	valid
4.0ms	105×	body	80	valid
2.0ms	90×	body	80	nan
1.0ms	13×	body	160	valid

simplify14.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize8.0ms

Local error

Found 1 expressions with local error:

3.7b	(log (+ 1.0 x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log-prod` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-div`
1×	`flip3-+` `rem-log-exp` `log-pow` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

6.0ms

(log (+ 1.0 x))

series73.0ms

Counts

1 → 3

Calls

1 calls:

72.0ms

(log (+ 1.0 x))

simplify516.0ms

Counts: 18 → 18

prune70.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
2×	`diff-log` `associate-*r/` `frac-sub`
1×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `sub-neg` `flip3--` `*-un-lft-identity` `flip3-+` `associate--l+` `sum-log` `add-cbrt-cube` `flip--` `flip-+`

Counts

1 → 16

Calls

1 calls:

83.0ms

(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

series67.0ms

Counts

1 → 3

Calls

1 calls:

67.0ms

(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

simplify487.0ms

Counts: 19 → 19

prune85.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(sqrt (+ 1.0 x))
3.8b	(log (sqrt (+ 1.0 x)))
3.8b	(log (sqrt (+ 1.0 x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

7.0ms	(sqrt (+ 1.0 x))
7.0ms	(sqrt (+ 1.0 x))
7.0ms	(log (sqrt (+ 1.0 x)))
11.0ms	(log (sqrt (+ 1.0 x)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (+ 1.0 x))
45.0ms	(sqrt (+ 1.0 x))
121.0ms	(log (sqrt (+ 1.0 x)))
140.0ms	(log (sqrt (+ 1.0 x)))

simplify732.0ms

Counts: 84 → 84

prune278.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ 1.0 x)))
0.2b	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))
3.8b	(log (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))))
3.8b	(log (sqrt (+ 1.0 x)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

98×	`sqrt-prod`
69×	`sqrt-pow1`
55×	`pow1`
54×	`sqrt-div`
52×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
35×	`pow1/2`
25×	`log-pow`
20×	`add-cube-cbrt`
18×	`swap-sqr` `pow-prod-up`
14×	`flip3-+` `flip-+`
10×	`add-exp-log` `log-div` `associate-r` `associate-l` `pow-prod-down` `pow-sqr`
9×	`unswap-sqr`
8×	`frac-times` `log-prod` `distribute-lft-out`
6×	`add-cbrt-cube`
4×	`associate-r/` `associate-l/` `add-log-exp`
3×	`rem-log-exp`
2×	`pow2` `rem-sqrt-square` `pow-plus` `prod-exp`
1×	`sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 170

Calls

4 calls:

17.0ms	(sqrt (sqrt (+ 1.0 x)))
80.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))
34.0ms	(log (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))))
6.0ms	(log (sqrt (+ 1.0 x)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (sqrt (+ 1.0 x)))
36.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))
101.0ms	(log (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))))
104.0ms	(log (sqrt (+ 1.0 x)))

simplify939.0ms

Counts: 182 → 182

prune603.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes111.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 22.0b

bsearch2.0ms

simplify668.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.6s	2248×	body	1280	valid
1.1s	1633×	body	640	valid
154.0ms	818×	body	320	valid
107.0ms	2881×	body	80	valid
67.0ms	2602×	body	80	nan
43.0ms	420×	body	160	valid