Details

sample81.0ms

Algorithm

intervals

Results

31.0ms	94×	body	10240	exit
23.0ms	80×	body	1280	valid
8.0ms	44×	body	640	valid
3.0ms	96×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	11×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	152
1	7	152
2	8	152
done	8	152

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
2.6b	(- (exp x) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 67

Calls

2 calls:

14.0ms	(/ (exp x) (- (exp x) 1.0))
9.0ms	(- (exp x) 1.0)

series50.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (exp x) (- (exp x) 1.0))
16.0ms	(- (exp x) 1.0)

simplify1.9s

Counts

73 → 73

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	117	21794
1	252	19567
2	672	17765
3	2050	17716
done	5001	17196

prune304.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (fma (* x x) (fma x 1/6 1/2) x))
0.0b	(fma (* x x) (fma x 1/6 1/2) x)
0.1b	(fma x 1/6 1/2)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 49

Calls

3 calls:

5.0ms	(/ (exp x) (fma (* x x) (fma x 1/6 1/2) x))
0.0ms	(fma (* x x) (fma x 1/6 1/2) x)
0.0ms	(fma x 1/6 1/2)

series125.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (exp x) (fma (* x x) (fma x 1/6 1/2) x))
35.0ms	(fma (* x x) (fma x 1/6 1/2) x)
48.0ms	(fma x 1/6 1/2)

simplify2.9s

Counts

58 → 58

Iterations

Useful iterations: 3 (802.0ms)

Iter	Nodes	Cost
0	98	19552
1	191	17494
2	586	17296
3	2404	17069
done	5023	17069

prune331.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/12 x (+ (/ 1 x) 1/2))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 1/12 x (+ (/ 1 x) 1/2))

series26.0ms

Counts

1 → 3

Calls

1 calls:

26.0ms

(fma 1/12 x (+ (/ 1 x) 1/2))

simplify4.8s

Counts

13 → 13

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	18	2445
1	29	2370
2	82	2370
3	387	2370
4	2688	2370
done	5000	2370

prune72.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma 1/12 x (+ (/ 1 x) 1/2)))
0.5b	(cbrt (fma 1/12 x (+ (/ 1 x) 1/2)))
0.5b	(cbrt (fma 1/12 x (+ (/ 1 x) 1/2)))
0.5b	(* (cbrt (fma 1/12 x (+ (/ 1 x) 1/2))) (cbrt (fma 1/12 x (+ (/ 1 x) 1/2))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

1.0ms	(cbrt (fma 1/12 x (+ (/ 1 x) 1/2)))
1.0ms	(cbrt (fma 1/12 x (+ (/ 1 x) 1/2)))
1.0ms	(cbrt (fma 1/12 x (+ (/ 1 x) 1/2)))
19.0ms	(* (cbrt (fma 1/12 x (+ (/ 1 x) 1/2))) (cbrt (fma 1/12 x (+ (/ 1 x) 1/2))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (fma 1/12 x (+ (/ 1 x) 1/2)))
125.0ms	(cbrt (fma 1/12 x (+ (/ 1 x) 1/2)))
104.0ms	(cbrt (fma 1/12 x (+ (/ 1 x) 1/2)))
99.0ms	(* (cbrt (fma 1/12 x (+ (/ 1 x) 1/2))) (cbrt (fma 1/12 x (+ (/ 1 x) 1/2))))

simplify133.0ms

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	127	37527