Details

sample46.0ms

Algorithm

intervals

Results

30.0ms

422×

body

valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	28	67
1	69	67
2	221	48
3	795	37
4	2607	37
done	5000	37

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite5.3s

Algorithm

rewrite-expression-head

Rules

147×	`add-exp-log` `add-cbrt-cube`
98×	`prod-exp` `cbrt-unprod`
69×	`pow1`
49×	`pow-prod-down`
39×	`associate-l`
27×	`add-sqr-sqrt` `times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
15×	`cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`associate-r` `associate-l/` `sqrt-prod` `-commutative` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 157

Calls

4 calls:

4.9s	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
325.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
26.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series188.0ms

Counts

4 → 10

Calls

4 calls:

76.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
64.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
48.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify1.5s

Counts

167 → 167

Iterations

Useful iterations: 2 (342.0ms)

Iter	Nodes	Cost
0	297	4429
1	945	3002
2	3432	1751
done	5000	1751

prune515.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (fabs x) (fabs x)) (fabs x))
0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-exp-log` `add-cbrt-cube`
53×	`pow1`
45×	`prod-exp` `cbrt-unprod`
27×	`associate-l`
24×	`pow-prod-down`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`cbrt-undiv` `div-exp`
6×	`pow-plus` `pow-prod-up`
5×	`associate-r`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow2` `associate-*l/` `pow-sqr` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow3` `unswap-sqr`

Counts

4 → 127

Calls

4 calls:

8.0ms	(* (* (fabs x) (fabs x)) (fabs x))
326.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
26.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series140.0ms

Counts

4 → 10

Calls

4 calls:

30.0ms	(* (* (fabs x) (fabs x)) (fabs x))
60.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
50.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify893.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (206.0ms)

Iter	Nodes	Cost
0	217	2435
1	630	1711
2	2252	1163
done	5001	1163

prune448.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) (+ (* 1.0 (/ (pow (fabs x) 7) 21.0)) (/ (* (pow (fabs x) 4) 1.0) (/ 5.0 (fabs x))))) (/ 1.0 (sqrt PI)))
0.1b	(/ (* (pow (fabs x) 4) 1.0) (/ 5.0 (fabs x)))
0.2b	(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0b	(sqrt PI)

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
64×	`times-frac`
46×	`add-exp-log`
45×	`*-un-lft-identity`
43×	`add-cube-cbrt`
34×	`associate-r`
26×	`add-cbrt-cube`
17×	`associate-l`
16×	`div-exp` `frac-add`
14×	`prod-exp`
13×	`associate-/r*` `sqrt-prod`
12×	`flip3-+` `flip-+`
11×	`unswap-sqr`
9×	`associate-*l/`
8×	`cbrt-undiv` `frac-times`
7×	`pow1`
6×	`cbrt-unprod`
5×	`unpow-prod-down` `cube-prod` `associate-*r/` `div-inv`
4×	`pow-to-exp` `pow-exp` `add-log-exp`
3×	`sqr-pow`
2×	`*-commutative`
1×	`cube-mult` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down` `clear-num` `associate-/r/` `distribute-lft-out` `associate-/l*`

Counts

4 → 172

Calls

4 calls:

167.0ms	(* (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) (+ (* 1.0 (/ (pow (fabs x) 7) 21.0)) (/ (* (pow (fabs x) 4) 1.0) (/ 5.0 (fabs x))))) (/ 1.0 (sqrt PI)))
6.0ms	(/ (* (pow (fabs x) 4) 1.0) (/ 5.0 (fabs x)))
14.0ms	(* (/ 2.0 3.0) (pow (fabs x) 3))
1.0ms	(sqrt PI)

series441.0ms

Counts

4 → 10

Calls

4 calls:

332.0ms	(* (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (pow (fabs x) 3))) (+ (* 1.0 (/ (pow (fabs x) 7) 21.0)) (/ (* (pow (fabs x) 4) 1.0) (/ 5.0 (fabs x))))) (/ 1.0 (sqrt PI)))
59.0ms	(/ (* (pow (fabs x) 4) 1.0) (/ 5.0 (fabs x)))
49.0ms	(* (/ 2.0 3.0) (pow (fabs x) 3))
0.0ms	(sqrt PI)

simplify93.0ms

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	392	5886