Details

sample110.0ms

Algorithm

intervals

Results

61.0ms	376×	body	80	valid
21.0ms	136×	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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize25.0ms

Local error

Found 1 expressions with local error:

1.5b	(/ (* (pow k m) a) (fma k (+ k 10) 1))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 26

Calls

1 calls:

19.0ms

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

series129.0ms

Counts

1 → 3

Calls

1 calls:

129.0ms

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

simplify1.7s

Counts

29 → 29

Iterations

Iter	Nodes
3	4400
2	887
1	261
0	100

prune356.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (pow k m) (/ (fma k (+ k 10) 1) a))
2.4b	(/ (fma k (+ k 10) 1) a)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
94×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
42×	`unpow-prod-down`
17×	`add-exp-log`
16×	`associate-/r*`
14×	`sqr-pow`
10×	`div-exp` `div-inv` `associate-/l*`
9×	`add-cbrt-cube`
4×	`cbrt-undiv`
2×	`expm1-log1p-u` `pow-to-exp` `pow1` `clear-num` `frac-2neg` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/`

Counts

2 → 163

Calls

2 calls:

17.0ms	(/ (pow k m) (/ (fma k (+ k 10) 1) a))
9.0ms	(/ (fma k (+ k 10) 1) a)

series579.0ms

Counts

2 → 6

Calls

2 calls:

534.0ms	(/ (pow k m) (/ (fma k (+ k 10) 1) a))
45.0ms	(/ (fma k (+ k 10) 1) a)

simplify860.0ms

Counts

169 → 169

Iterations

Iter	Nodes
2	2260
1	768
0	314

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (fma k (+ k 10) 1)) 1) (/ (sqrt (fma k (+ k 10) 1)) a))
0.1b	(/ (pow k m) (* (/ (sqrt (fma k (+ k 10) 1)) 1) (/ (sqrt (fma k (+ k 10) 1)) a)))
17.2b	(sqrt (fma k (+ k 10) 1))
17.2b	(sqrt (fma k (+ k 10) 1))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-exp-log`
84×	`add-sqr-sqrt`
65×	`times-frac`
49×	`div-exp`
42×	`*-un-lft-identity`
36×	`add-cube-cbrt`
35×	`sqrt-prod`
34×	`add-cbrt-cube`
24×	`prod-exp`
22×	`associate-r` `associate-l`
15×	`unswap-sqr`
13×	`cbrt-undiv`
8×	`pow1` `1-exp` `cbrt-unprod`
7×	`pow-to-exp` `pow-exp` `associate-/l*`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r/` `div-inv`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `sqr-pow`
1×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative`

Counts

4 → 173

Calls

4 calls:

31.0ms	(* (/ (sqrt (fma k (+ k 10) 1)) 1) (/ (sqrt (fma k (+ k 10) 1)) a))
35.0ms	(/ (pow k m) (* (/ (sqrt (fma k (+ k 10) 1)) 1) (/ (sqrt (fma k (+ k 10) 1)) a)))
2.0ms	(sqrt (fma k (+ k 10) 1))
2.0ms	(sqrt (fma k (+ k 10) 1))

series278.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ (sqrt (fma k (+ k 10) 1)) 1) (/ (sqrt (fma k (+ k 10) 1)) a))
131.0ms	(/ (pow k m) (* (/ (sqrt (fma k (+ k 10) 1)) 1) (/ (sqrt (fma k (+ k 10) 1)) a)))
57.0ms	(sqrt (fma k (+ k 10) 1))
53.0ms	(sqrt (fma k (+ k 10) 1))

simplify871.0ms

Counts

185 → 185

Iterations

Iter	Nodes
2	2108
1	801
0	273

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 a) (fma 10 (/ k a) (/ k (/ a k))))
0.1b	(/ (pow k m) (+ (/ 1 a) (fma 10 (/ k a) (/ k (/ a k)))))
0.1b	(/ k (/ a k))
3.0b	(fma 10 (/ k a) (/ k (/ a k)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

119×	`times-frac`
100×	`*-un-lft-identity`
73×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`associate-/r*` `unpow-prod-down` `distribute-lft-out`
16×	`div-inv`
14×	`add-exp-log`
13×	`fma-def`
11×	`add-cbrt-cube`
10×	`associate-/l*`
6×	`div-exp` `add-log-exp` `sqr-pow`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r/`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `fma-udef`
1×	`pow-to-exp` `+-commutative` `associate-+r+` `sum-log` `pow-exp`

Counts

4 → 180

Calls

4 calls:

20.0ms	(+ (/ 1 a) (fma 10 (/ k a) (/ k (/ a k))))
39.0ms	(/ (pow k m) (+ (/ 1 a) (fma 10 (/ k a) (/ k (/ a k)))))
12.0ms	(/ k (/ a k))
1.0ms	(fma 10 (/ k a) (/ k (/ a k)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (/ 1 a) (fma 10 (/ k a) (/ k (/ a k))))
132.0ms	(/ (pow k m) (+ (/ 1 a) (fma 10 (/ k a) (/ k (/ a k)))))
40.0ms	(/ k (/ a k))
42.0ms	(fma 10 (/ k a) (/ k (/ a k)))

simplify879.0ms

Counts

192 → 192

Iterations

Iter	Nodes
2	2173
1	679
0	301

prune1.9s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes163.0ms

Accuracy

98.1% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.9b

bsearch89.0ms

Steps

Iters	Range		Point
7	7.466180523549881e+118	1.459770704900975e+120	1.308663191510053e+120

simplify22.0ms

Iterations

Iter	Nodes
5	52
4	52
3	47
2	45
1	41
0	31

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.1s	11929×	body	80	valid
536.0ms	4259×	body	80	nan