Details

sample95.0ms

Algorithm

intervals

Results

35.0ms	54×	body	1280	valid
14.0ms	247×	body	80	nan
13.0ms	131×	body	80	valid
12.0ms	34×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	17×	body	160	valid

simplify15.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

15.0ms

(- (log (+ N 1)) (log N))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize9.0ms

Local error

Found 1 expressions with local error:

4.9b	(- (log1p N) (log N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-diff`
10×	`add-cube-cbrt`
5×	`pow1`
4×	`log-pow`
3×	`log-prod` `fma-neg` `associate--r+`
2×	`diff-log` `distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `log1p-udef` `sub-neg` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`

Counts

1 → 37

Calls

1 calls:

Slowest

6.0ms

(- (log1p N) (log N))

series91.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

91.0ms

(- (log1p N) (log N))

simplify2.7s

Counts

38 → 40

Calls

38 calls:

Slowest

452.0ms	(fma (- (log N)) 1 (* (log N) 1))
213.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
206.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
181.0ms	(fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))
175.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune328.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

5.1b	(log (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`expm1-log1p-u` `div-exp` `rem-log-exp` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 66

Calls

2 calls:

Slowest

29.0ms	(/ (+ 1 N) N)
9.0ms	(log (/ (+ 1 N) N))

series124.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

66.0ms	(/ (+ 1 N) N)
57.0ms	(log (/ (+ 1 N) N))

simplify2.0s

Counts

57 → 72

Calls

57 calls:

Slowest

319.0ms	(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
242.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
204.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
176.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))
158.0ms	(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))

prune552.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

5.2b	(log (sqrt (/ (+ 1 N) N)))
5.2b	(log (sqrt (/ (+ 1 N) N)))
0.1b	(sqrt (/ (+ 1 N) N))
0.1b	(sqrt (/ (+ 1 N) N))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
38×	`log-prod` `add-cube-cbrt`
12×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `sqrt-div` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 130

Calls

4 calls:

Slowest

12.0ms	(sqrt (/ (+ 1 N) N))
11.0ms	(sqrt (/ (+ 1 N) N))
8.0ms	(log (sqrt (/ (+ 1 N) N)))
8.0ms	(log (sqrt (/ (+ 1 N) N)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

123.0ms	(log (sqrt (/ (+ 1 N) N)))
105.0ms	(log (sqrt (/ (+ 1 N) N)))
60.0ms	(sqrt (/ (+ 1 N) N))
49.0ms	(sqrt (/ (+ 1 N) N))

simplify2.7s

Counts

96 → 142

Calls

96 calls:

Slowest

219.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
212.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
208.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
190.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
140.0ms	(- (+ (* 1/2 (/ 1 N)) 1) (* 1/8 (/ 1 (pow N 2))))

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

5.2b	(log (sqrt (/ (+ 1 N) N)))
5.1b	(log (/ (+ 1 N) N))
0.1b	(sqrt (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
49×	`times-frac`
41×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
35×	`log-prod`
32×	`sqrt-prod`
13×	`distribute-lft-out`
10×	`add-exp-log`
8×	`pow1`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log-pow` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`associate-/r*` `rem-log-exp`
2×	`rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip-+`

Counts

4 → 131

Calls

4 calls:

Slowest

27.0ms	(/ (+ 1 N) N)
11.0ms	(sqrt (/ (+ 1 N) N))
8.0ms	(log (/ (+ 1 N) N))
7.0ms	(log (sqrt (/ (+ 1 N) N)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(log (sqrt (/ (+ 1 N) N)))
79.0ms	(/ (+ 1 N) N)
60.0ms	(log (/ (+ 1 N) N))
45.0ms	(sqrt (/ (+ 1 N) N))

simplify3.5s

Counts

105 → 143

Calls

105 calls:

Slowest

371.0ms	(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
261.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
226.0ms	(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
202.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
200.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.5b

bsearch85.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1793×	body	1280	valid
672.0ms	7957×	body	80	nan
490.0ms	1203×	body	640	valid
436.0ms	4072×	body	80	valid
184.0ms	618×	body	320	valid
53.0ms	314×	body	160	valid