Details

sample79.0ms

Algorithm

intervals

Results

43.0ms	375×	body	80	valid
14.0ms	133×	body	80	nan

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	2068
5	649
4	212
3	94
2	50
1	24
0	12

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma k (+ k 10) 1)
0.2b	(* (pow k m) a)
1.9b	(/ (* (pow k m) a) (fma k (+ k 10) 1))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

0.0ms	(fma k (+ k 10) 1)
17.0ms	(* (pow k m) a)
21.0ms	(/ (* (pow k m) a) (fma k (+ k 10) 1))

series319.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(fma k (+ k 10) 1)
142.0ms	(* (pow k m) a)
146.0ms	(/ (* (pow k m) a) (fma k (+ k 10) 1))

simplify3.8s

Counts

74 → 74

Iterations

Iter	Nodes
3	6093
2	1082
1	325
0	137

prune935.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma k (+ k 10) 1)
1.9b	(/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (fma k (+ k 10) 1))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-exp-log`
21×	`prod-exp`
13×	`div-exp`
11×	`add-cbrt-cube`
7×	`pow-to-exp` `pow-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`cbrt-undiv` `associate-/r*` `times-frac` `cbrt-unprod`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`clear-num` `frac-2neg` `fma-udef` `div-inv` `associate-/l*`

Counts

2 → 47

Calls

2 calls:

0.0ms	(fma k (+ k 10) 1)
46.0ms	(/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (fma k (+ k 10) 1))

series215.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(fma k (+ k 10) 1)
182.0ms	(/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (fma k (+ k 10) 1))

simplify4.9s

Counts

53 → 53

Iterations

Iter	Nodes
3	8697
2	1339
1	370
0	131

prune783.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (sqrt (fma k (+ k 10) 1)))
0.0b	(/ (/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (sqrt (fma k (+ k 10) 1))) (sqrt (fma k (+ k 10) 1)))
17.1b	(sqrt (fma k (+ k 10) 1))
17.1b	(sqrt (fma k (+ k 10) 1))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
99×	`add-exp-log`
66×	`sqrt-prod`
55×	`add-sqr-sqrt`
53×	`*-un-lft-identity` `add-cube-cbrt`
42×	`prod-exp`
40×	`div-exp`
27×	`add-cbrt-cube`
14×	`pow-to-exp` `pow-exp`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`cbrt-undiv`
9×	`div-inv`
6×	`pow1` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 182

Calls

4 calls:

55.0ms	(/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (sqrt (fma k (+ k 10) 1)))
38.0ms	(/ (/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (sqrt (fma k (+ k 10) 1))) (sqrt (fma k (+ k 10) 1)))
2.0ms	(sqrt (fma k (+ k 10) 1))
3.0ms	(sqrt (fma k (+ k 10) 1))

series530.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (sqrt (fma k (+ k 10) 1)))
171.0ms	(/ (/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (sqrt (fma k (+ k 10) 1))) (sqrt (fma k (+ k 10) 1)))
41.0ms	(sqrt (fma k (+ k 10) 1))
54.0ms	(sqrt (fma k (+ k 10) 1))

simplify1.6s

Counts

194 → 194

Iterations

Iter	Nodes
2	2730
1	728
0	268

prune2.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma k (+ k 10) 1)
0.3b	(/ (pow k (/ m 2)) (/ (fma k (+ k 10) 1) (* (pow k (/ m 2)) a)))
1.7b	(/ (fma k (+ k 10) 1) (* (pow k (/ m 2)) a))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
56×	`add-exp-log`
37×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
31×	`div-exp`
24×	`unpow-prod-down`
17×	`add-cbrt-cube`
12×	`prod-exp`
10×	`div-inv` `associate-/l*`
9×	`pow-to-exp` `pow-exp`
8×	`associate-/r*` `sqr-pow`
7×	`cbrt-undiv`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`associate-/r/` `fma-udef`

Counts

3 → 132

Calls

3 calls:

0.0ms	(fma k (+ k 10) 1)
15.0ms	(/ (pow k (/ m 2)) (/ (fma k (+ k 10) 1) (* (pow k (/ m 2)) a)))
17.0ms	(/ (fma k (+ k 10) 1) (* (pow k (/ m 2)) a))

series349.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma k (+ k 10) 1)
185.0ms	(/ (pow k (/ m 2)) (/ (fma k (+ k 10) 1) (* (pow k (/ m 2)) a)))
125.0ms	(/ (fma k (+ k 10) 1) (* (pow k (/ m 2)) a))

simplify1.1s

Counts

141 → 141

Iterations

Iter	Nodes
2	2240
1	674
0	271

prune1.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes226.0ms

Accuracy

89% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 2.0b

bsearch76.0ms

Steps

Iters	Range		Point
7	1.7315262087807526e-20	3.2346546672740204e-18	2.2584134818398895e-19

simplify32.0ms

Iterations

Iter	Nodes
5	76
4	76
3	72
2	63
1	54
0	35

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.9s	11902×	body	80	valid
963.0ms	4255×	body	80	nan