Details

sample119.0ms

Algorithm

intervals

Results

39.0ms	56×	body	1280	valid
20.0ms	246×	body	80	nan
18.0ms	39×	body	640	valid
15.0ms	128×	body	80	valid
7.0ms	20×	body	320	valid
3.0ms	13×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	13
2	13
1	11
0	6

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(log1p N)
3.8b	(- (log1p N) (log N))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 49

Calls

2 calls:

1.0ms	(log1p N)
12.0ms	(- (log1p N) (log N))

series476.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(log1p N)
453.0ms	(- (log1p N) (log N))

simplify4.6s

Counts

55 → 55

Iterations

Iter	Nodes
4	4832
3	1464
2	491
1	223
0	101

prune394.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
3.9b	(log (/ (+ 1 N) N))

rewrite31.0ms

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:

26.0ms	(/ (+ 1 N) N)
4.0ms	(log (/ (+ 1 N) N))

series100.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (+ 1 N) N)
48.0ms	(log (/ (+ 1 N) N))

simplify2.8s

Counts

72 → 72

Iterations

Iter	Nodes
4	5149
3	1527
2	507
1	232
0	106

prune515.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ 1 (sqrt N)))
0.3b	(/ 1 (sqrt N))
0.4b	(/ (+ 1 N) (sqrt N))
4.0b	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
102×	`times-frac`
78×	`add-sqr-sqrt` `add-cube-cbrt`
72×	`log-prod`
57×	`sqrt-prod`
28×	`associate-+r+`
22×	`associate-+l+`
17×	`distribute-lft-out`
16×	`pow1`
15×	`add-exp-log`
14×	`log-pow`
12×	`associate-/r*`
9×	`pow-flip`
8×	`fma-def` `add-cbrt-cube`
7×	`associate-/l*`
5×	`div-exp` `div-inv`
4×	`expm1-log1p-u` `rem-log-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `sqrt-pow1` `pow1/2` `inv-pow`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r-` `sum-log` `log-rec` `associate-+l-`

Counts

4 → 220

Calls

4 calls:

3.0ms	(log (/ 1 (sqrt N)))
5.0ms	(/ 1 (sqrt N))
15.0ms	(/ (+ 1 N) (sqrt N))
35.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(log (/ 1 (sqrt N)))
45.0ms	(/ 1 (sqrt N))
67.0ms	(/ (+ 1 N) (sqrt N))
224.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))

simplify4.0s

Counts

232 → 232

Iterations

Iter	Nodes
3	4860
2	1567
1	626
0	280

prune2.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (/ 1 (* N N)) -1/2 (/ 1 N))
0.5b	(/ 1 (* N N))
0.5b	(/ 1 (* N N))
11.3b	(fma 1/3 (/ (/ 1 (* N N)) N) (fma (/ 1 (* N N)) -1/2 (/ 1 N)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
20×	`pow1`
14×	`add-cbrt-cube`
12×	`pow-flip`
8×	`add-sqr-sqrt` `*-un-lft-identity` `div-exp` `add-cube-cbrt`
6×	`times-frac` `prod-exp` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `cbrt-unprod` `fma-udef` `div-inv` `inv-pow`

Counts

4 → 92

Calls

4 calls:

0.0ms	(fma (/ 1 (* N N)) -1/2 (/ 1 N))
14.0ms	(/ 1 (* N N))
14.0ms	(/ 1 (* N N))
0.0ms	(fma 1/3 (/ (/ 1 (* N N)) N) (fma (/ 1 (* N N)) -1/2 (/ 1 N)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(fma (/ 1 (* N N)) -1/2 (/ 1 N))
26.0ms	(/ 1 (* N N))
18.0ms	(/ 1 (* N N))
28.0ms	(fma 1/3 (/ (/ 1 (* N N)) N) (fma (/ 1 (* N N)) -1/2 (/ 1 N)))

simplify2.8s

Counts

104 → 104

Iterations

Iter	Nodes
4	4249
3	1429
2	385
1	179
0	91

prune901.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.8b

bsearch52.0ms

Steps

Iters	Range		Point
10	19.9847175368848	4649870806659.843	8114.657537075721

simplify4.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

892.0ms	1694×	body	1280	valid
839.0ms	1215×	body	640	valid
524.0ms	8213×	body	80	nan
381.0ms	4159×	body	80	valid
168.0ms	614×	body	320	valid
45.0ms	318×	body	160	valid