Details

sample110.0ms

Algorithm

intervals

Results

59.0ms	374×	body	80	valid
24.0ms	157×	body	80	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
6	2053
5	653
4	215
3	97
2	52
1	26
0	12

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (pow k m) a)
2.6b	(/ (* (pow k m) a) (fma (+ k 10) k 1))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 54

Calls

2 calls:

18.0ms	(* (pow k m) a)
13.0ms	(/ (* (pow k m) a) (fma (+ k 10) k 1))

series279.0ms

Counts

2 → 6

Calls

2 calls:

134.0ms	(* (pow k m) a)
145.0ms	(/ (* (pow k m) a) (fma (+ k 10) k 1))

simplify2.3s

Counts

60 → 60

Iterations

Iter	Nodes
3	5273
2	1035
1	311
0	129

prune682.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (pow k (/ m 2)) a)
2.6b	(/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (fma (+ k 10) k 1))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 64

Calls

2 calls:

20.0ms	(* (pow k (/ m 2)) a)
45.0ms	(/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (fma (+ k 10) k 1))

series269.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(* (pow k (/ m 2)) a)
151.0ms	(/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (fma (+ k 10) k 1))

simplify3.3s

Counts

70 → 70

Iterations

Iter	Nodes
3	7814
2	1445
1	417
0	156

prune943.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (pow k (/ m 2)) a)
0.2b	(/ 1 (fma (+ k 10) k 1))
2.4b	(* (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (/ 1 (fma (+ k 10) k 1)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

185×	`add-exp-log`
139×	`prod-exp`
29×	`pow-to-exp` `pow-exp`
28×	`add-cbrt-cube` `div-exp`
26×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
16×	`associate-r`
14×	`rec-exp` `1-exp`
13×	`cbrt-unprod`
8×	`associate-l`
6×	`pow1`
4×	`cbrt-undiv` `unpow-prod-down`
3×	`expm1-log1p-u` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`*-commutative` `div-inv` `sqr-pow`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow`

Counts

3 → 148

Calls

3 calls:

9.0ms	(* (pow k (/ m 2)) a)
4.0ms	(/ 1 (fma (+ k 10) k 1))
106.0ms	(* (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (/ 1 (fma (+ k 10) k 1)))

series347.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(* (pow k (/ m 2)) a)
33.0ms	(/ 1 (fma (+ k 10) k 1))
153.0ms	(* (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (/ 1 (fma (+ k 10) k 1)))

simplify3.4s

Counts

157 → 157

Iterations

Iter	Nodes
3	7638
2	1888
1	619
0	232

prune1.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow k (/ m 2)) a)
0.1b	(/ (/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (sqrt (fma (+ k 10) k 1))) (sqrt (fma (+ k 10) k 1)))
16.9b	(sqrt (fma (+ k 10) k 1))
16.9b	(sqrt (fma (+ k 10) k 1))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
64×	`add-exp-log`
60×	`sqrt-prod`
59×	`add-sqr-sqrt`
52×	`*-un-lft-identity` `add-cube-cbrt`
27×	`div-exp`
24×	`prod-exp`
20×	`add-cbrt-cube`
10×	`associate-/l*`
8×	`pow-to-exp` `pow-exp` `div-inv`
7×	`cbrt-undiv` `associate-l`
6×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqr-pow`
1×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`

Counts

4 → 168

Calls

4 calls:

19.0ms	(* (pow k (/ m 2)) a)
19.0ms	(/ (/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (sqrt (fma (+ k 10) k 1))) (sqrt (fma (+ k 10) k 1)))
1.0ms	(sqrt (fma (+ k 10) k 1))
1.0ms	(sqrt (fma (+ k 10) k 1))

series419.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (pow k (/ m 2)) a)
175.0ms	(/ (/ (* (pow k (/ m 2)) (* (pow k (/ m 2)) a)) (sqrt (fma (+ k 10) k 1))) (sqrt (fma (+ k 10) k 1)))
53.0ms	(sqrt (fma (+ k 10) k 1))
60.0ms	(sqrt (fma (+ k 10) k 1))

simplify1.2s

Counts

180 → 180

Iterations

Iter	Nodes
2	2716
1	727
0	281

prune2.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes160.0ms

Accuracy

93.8% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 2.0b

bsearch123.0ms

Steps

Iters	Range		Point
9	1.2627758266903733e-06	227.73282802742628	224.30094724071168

simplify7.0ms

Iterations

Iter	Nodes
2	49
1	49
0	39

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.0s	11957×	body	80	valid
495.0ms	4159×	body	80	nan