Details

sample83.0ms

Algorithm

intervals

Results

27.0ms	80×	body	1280	valid
22.0ms	94×	body	10240	exit
14.0ms	44×	body	640	valid
4.0ms	96×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0ms

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)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

27.0ms	(/ (exp x) (- (exp x) 1.0))
8.0ms	(- (exp x) 1.0)

series91.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (exp x) (- (exp x) 1.0))
48.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

57 → 57

Iterations

Useful iterations: 3 (591.0ms)

Iter	Nodes	Cost
0	91	16288
1	191	14948
2	540	14868
3	1479	14828
done	5002	14828

prune271.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* x x) (+ (* x 1/6) 1/2)) x)
0.0b	(/ (exp x) (+ (* (* x x) (+ (* x 1/6) 1/2)) x))
0.1b	(* (* x x) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log`
11×	`pow1`
9×	`times-frac`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-r/` `associate-/r/` `-commutative` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 83

Calls

4 calls:

20.0ms	(+ (* (* x x) (+ (* x 1/6) 1/2)) x)
35.0ms	(/ (exp x) (+ (* (* x x) (+ (* x 1/6) 1/2)) x))
51.0ms	(* (* x x) (+ (* x 1/6) 1/2))
11.0ms	(* x 1/6)

series204.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* x x) (+ (* x 1/6) 1/2)) x)
53.0ms	(/ (exp x) (+ (* (* x x) (+ (* x 1/6) 1/2)) x))
101.0ms	(* (* x x) (+ (* x 1/6) 1/2))
16.0ms	(* x 1/6)

simplify2.1s

Counts

95 → 95

Iterations

Useful iterations: 2 (663.0ms)

Iter	Nodes	Cost
0	159	31034
1	456	27012
2	1847	26360
done	5006	26360

prune461.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.3b	(* 1/12 x)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 31

Calls

2 calls:

63.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
5.0ms	(* 1/12 x)

series53.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
28.0ms	(* 1/12 x)

simplify2.1s

Counts

37 → 37

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	58	6380
1	154	5678
2	477	5678
3	1810	5678
done	5002	5678

prune134.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
0.6b	(cbrt (* 1/12 x))
0.6b	(cbrt (* 1/12 x))
0.6b	(cbrt (* 1/12 x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

21.0ms	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
4.0ms	(cbrt (* 1/12 x))
3.0ms	(cbrt (* 1/12 x))
3.0ms	(cbrt (* 1/12 x))

series1.4s

Counts

4 → 12

Calls

4 calls:

384.0ms	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
379.0ms	(cbrt (* 1/12 x))
304.0ms	(cbrt (* 1/12 x))
323.0ms	(cbrt (* 1/12 x))

simplify27.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	55	15843