Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

279×

body

valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	11
1	21	11
2	36	11
3	57	11
4	85	11
5	100	11
done	100	11

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 2 expressions with local error:

3.5b	(* y (+ 1.0 (* z z)))
4.3b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 70

Calls

2 calls:

7.0ms	(* y (+ 1.0 (* z z)))
8.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series117.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* y (+ 1.0 (* z z)))
58.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify469.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (121.0ms)

Iter	Nodes	Cost
0	156	1062
1	410	1035
2	1488	887
done	5001	887

prune184.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
4.3b	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
14.7b	(sqrt (+ 1.0 (* z z)))
14.7b	(sqrt (+ 1.0 (* z z)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-div`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-*r/`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
8×	`frac-times` `associate-/r/`
6×	`associate-r`
4×	`associate-*l/` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

19.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
20.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms	(sqrt (+ 1.0 (* z z)))
3.0ms	(sqrt (+ 1.0 (* z z)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
57.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
49.0ms	(sqrt (+ 1.0 (* z z)))
48.0ms	(sqrt (+ 1.0 (* z z)))

simplify794.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (197.0ms)

Iter	Nodes	Cost
0	217	2776
1	610	2090
2	2627	1728
done	5000	1728

prune342.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ 1.0 (* x (* y (+ (* z z) 1.0))))
3.5b	(* y (+ (* z z) 1.0))
4.1b	(* x (* y (+ (* z z) 1.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `add-sqr-sqrt` `associate-*r/`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down`
3×	`cbrt-undiv` `flip3-+` `times-frac` `div-exp` `flip-+` `associate-/l*` `add-log-exp`
2×	`associate-/r/` `*-commutative`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`

Counts

3 → 71

Calls

3 calls:

13.0ms	(/ 1.0 (* x (* y (+ (* z z) 1.0))))
10.0ms	(* y (+ (* z z) 1.0))
13.0ms	(* x (* y (+ (* z z) 1.0)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ 1.0 (* x (* y (+ (* z z) 1.0))))
51.0ms	(* y (+ (* z z) 1.0))
65.0ms	(* x (* y (+ (* z z) 1.0)))

simplify98.0ms

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	124	1034
1	341	1010