Details

sample110.0ms

Algorithm

intervals

Results

29.0ms	48×	body	1280	valid
22.0ms	128×	body	80	valid
19.0ms	50×	body	640	valid
19.0ms	274×	body	80	nan
6.0ms	21×	body	320	valid
1.0ms	9×	body	160	valid

simplify20.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

20.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize17.0ms

Local error

Found 1 expressions with local error:

2.5b	(- (log1p N) (log N))

rewrite13.0ms

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

12.0ms

(- (log1p N) (log N))

series100.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

100.0ms

(- (log1p N) (log N))

simplify2.9s

Counts

55 → 40

Calls

55 calls:

Slowest

344.0ms	(* (* (- (log1p N) (log N)) (- (log1p N) (log N))) (- (log1p N) (log N)))
234.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
180.0ms	(fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))
174.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
160.0ms	(fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))

prune351.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

2.4b	(log (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite18.0ms

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

14.0ms	(/ (+ 1 N) N)
4.0ms	(log (/ (+ 1 N) N))

series128.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

79.0ms	(/ (+ 1 N) N)
49.0ms	(log (/ (+ 1 N) N))

simplify4.1s

Counts

100 → 72

Calls

100 calls:

Slowest

512.0ms	(* (* (/ (+ 1 N) N) (/ (+ 1 N) N)) (/ (+ 1 N) N))
456.0ms	(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
342.0ms	(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
214.0ms	(- (+ (* 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))))

prune504.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 3 expressions with local error:

2.9b	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))
0.4b	(/ (+ 1 N) (sqrt N))
0.2b	(/ 1 (sqrt N))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

94×	`*-un-lft-identity`
84×	`times-frac`
64×	`add-sqr-sqrt` `add-cube-cbrt`
50×	`log-prod`
48×	`sqrt-prod`
28×	`associate-+r+`
22×	`associate-+l+`
17×	`distribute-lft-out`
12×	`pow1` `associate-/r*`
9×	`add-exp-log` `log-pow`
8×	`fma-def`
7×	`add-cbrt-cube` `associate-/l*`
6×	`pow-flip`
4×	`div-inv`
3×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `inv-pow` `associate-/l/`
1×	`+-commutative` `rec-exp` `associate-+r-` `sum-log` `1-exp` `associate-+l-`

Counts

3 → 177

Calls

3 calls:

Slowest

34.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))
27.0ms	(/ (+ 1 N) (sqrt N))
10.0ms	(/ 1 (sqrt N))

series419.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

301.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))
69.0ms	(/ (+ 1 N) (sqrt N))
50.0ms	(/ 1 (sqrt N))

simplify14.5s

Counts

222 → 186

Calls

222 calls:

Slowest

889.0ms	(* (* (+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N)))) (+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))) (+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N)))))
520.0ms	(+ (* (log (/ 1 (sqrt N))) (log (/ 1 (sqrt N)))) (- (* (log (/ (+ 1 N) (sqrt N))) (log (/ (+ 1 N) (sqrt N)))) (* (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))))
395.0ms	(* (* (/ (+ 1 N) (sqrt N)) (/ (+ 1 N) (sqrt N))) (/ (+ 1 N) (sqrt N)))
387.0ms	(* (sqrt N) (+ (* 1 1) (- (* N N) (* 1 N))))
368.0ms	(+ (pow (log (/ 1 (sqrt N))) 3) (pow (log (/ (+ 1 N) (sqrt N))) 3))

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

2.7b	(log (/ (sqrt (+ 1 N)) 1))
2.7b	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))
0.2b	(/ (sqrt (+ 1 N)) N)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
84×	`times-frac`
75×	`log-prod`
62×	`add-sqr-sqrt` `add-cube-cbrt`
52×	`sqrt-prod`
25×	`associate-+l+` `associate-+r+`
17×	`distribute-lft-out`
9×	`pow1` `add-exp-log`
7×	`associate-/l*`
6×	`log-pow`
5×	`add-cbrt-cube`
4×	`fma-def` `div-inv`
3×	`expm1-log1p-u` `log-div` `associate-/r*` `div-exp` `rem-log-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `sqrt-div` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `1-exp` `associate-+l-`

Counts

3 → 162

Calls

3 calls:

Slowest

19.0ms	(/ (sqrt (+ 1 N)) N)
17.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))
4.0ms	(log (/ (sqrt (+ 1 N)) 1))

series388.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

235.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))
82.0ms	(log (/ (sqrt (+ 1 N)) 1))
70.0ms	(/ (sqrt (+ 1 N)) N)

simplify15.9s

Counts

213 → 171

Calls

213 calls:

Slowest

785.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (sqrt (+ 1 N))) (* (cbrt N) (cbrt N)))))
613.0ms	(* (* (+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N))) (+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))) (+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N))))
533.0ms	(+ (* (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) 1))) (- (* (log (/ (sqrt (+ 1 N)) N)) (log (/ (sqrt (+ 1 N)) N))) (* (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))))
420.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (sqrt (+ 1 N))) (* (cbrt N) (cbrt N)))))
349.0ms	(/ (* (* (sqrt (+ 1 N)) (sqrt (+ 1 N))) (sqrt (+ 1 N))) (* (* N N) N))

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.7b

bsearch55.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.0s	1697×	body	1280	valid
549.0ms	8167×	body	80	nan
546.0ms	1216×	body	640	valid
496.0ms	4173×	body	80	valid
186.0ms	632×	body	320	valid
44.0ms	282×	body	160	valid