Details

sample318.0ms

Algorithm

intervals

Results

119.0ms	88×	body	1280	valid
116.0ms	30×	body	2560	valid
36.0ms	53×	body	640	valid
14.0ms	102×	body	80	valid
7.0ms	63×	body	80	nan
6.0ms	13×	body	320	valid
4.0ms	14×	body	160	valid

simplify5.0s

Counts: 1 → 1

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.9b

localize26.0ms

Local error

Found 3 expressions with local error:

10.2b	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
7.8b	(pow (+ 1 (/ i n)) n)
1.2b	(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
49×	`*-un-lft-identity`
47×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube`
5×	`div-inv`
4×	`pow1` `unpow-prod-down`
3×	`expm1-log1p-u` `cbrt-undiv` `pow-unpow` `div-exp` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
1×	`pow-to-exp` `clear-num` `pow-pow` `frac-2neg` `pow-exp` `associate-/r/` `fma-udef` `distribute-lft-out` `sqr-pow`

Counts

3 → 105

Calls

3 calls:

Slowest

9.0ms	(pow (+ 1 (/ i n)) n)
6.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
0.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)

series878.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

378.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
260.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
240.0ms	(pow (+ 1 (/ i n)) n)

simplify2.0s

Counts: 114 → 114

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.4b

localize21.0ms

Local error

Found 4 expressions with local error:

10.4b	(* n (log1p (/ i n)))
10.2b	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
6.6b	(log1p (/ i n))
2.8b	(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`expm1-log1p-u` `div-inv`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `associate-/l*`
1×	`log1p-udef` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `log1p-expm1` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

Slowest

6.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
6.0ms	(* n (log1p (/ i n)))
0.0ms	(log1p (/ i n))
0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)

series970.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

469.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
318.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
100.0ms	(log1p (/ i n))
83.0ms	(* n (log1p (/ i n)))

simplify840.0ms

Counts: 129 → 129

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize22.0ms

Local error

Found 4 expressions with local error:

10.4b	(* n (log1p (/ i n)))
9.2b	(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
6.6b	(log1p (/ i n))
2.8b	(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`expm1-log1p-u` `div-inv`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `div-exp` `associate-r` `associate-l*`
1×	`log1p-udef` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

Slowest

8.0ms	(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
6.0ms	(* n (log1p (/ i n)))
0.0ms	(log1p (/ i n))
0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

922.0ms	(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
265.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
74.0ms	(* n (log1p (/ i n)))
58.0ms	(log1p (/ i n))

simplify760.0ms

Counts: 129 → 129

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize25.0ms

Local error

Found 4 expressions with local error:

2.6b	(+ (- (/ 1/100 n) (* 1/200 (/ i n))) (/ (* 1/200 (/ i n)) n))
0.4b	(* 1/200 (/ i n))
0.4b	(* 1/200 (/ i n))
0.3b	(/ 1 (+ (- (/ 1/100 n) (* 1/200 (/ i n))) (/ (* 1/200 (/ i n)) n)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
41×	`times-frac`
37×	`add-cube-cbrt`
26×	`associate-r`
18×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`associate-+l+`
13×	`prod-diff`
9×	`pow1` `add-log-exp`
8×	`frac-add`
6×	`associate-l` `associate-*r/` `associate-/r/`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `associate-/r*` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`cbrt-undiv` `fma-def` `associate-/l*`
2×	`sum-log` `flip3-+` `flip3--` `pow-prod-down` `*-commutative` `frac-sub` `flip-+` `flip--` `sub-div`
1×	`+-commutative` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `diff-log` `1-exp` `associate-+l-` `pow-flip` `inv-pow`

Counts

4 → 153

Calls

4 calls:

Slowest

50.0ms	(/ 1 (+ (- (/ 1/100 n) (* 1/200 (/ i n))) (/ (* 1/200 (/ i n)) n)))
44.0ms	(+ (- (/ 1/100 n) (* 1/200 (/ i n))) (/ (* 1/200 (/ i n)) n))
11.0ms	(* 1/200 (/ i n))
9.0ms	(* 1/200 (/ i n))

series144.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

72.0ms	(/ 1 (+ (- (/ 1/100 n) (* 1/200 (/ i n))) (/ (* 1/200 (/ i n)) n)))
33.0ms	(+ (- (/ 1/100 n) (* 1/200 (/ i n))) (/ (* 1/200 (/ i n)) n))
20.0ms	(* 1/200 (/ i n))
19.0ms	(* 1/200 (/ i n))

simplify1.9s

Counts: 165 → 165

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 1.5b

regimes257.0ms

Accuracy

52.2% (9.6b remaining)

Error of 12.5b against oracle of 2.9b and baseline of 23.0b

bsearch174.0ms

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.8s	2499×	body	1280	valid
2.6s	989×	body	2560	valid
890.0ms	1591×	body	640	valid
346.0ms	3083×	body	80	valid
296.0ms	847×	body	320	valid
235.0ms	2267×	body	80	nan
108.0ms	436×	body	160	valid
49.0ms	12×	body	5120	valid