Details

sample1.3s

Algorithm

intervals

Results

1.2s

3359×

body

valid

simplify5.1s

Counts

1 → 1

Iterations

Iter	Nodes
4	8119
3	1785
2	390
1	93
0	31

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
0.3b	(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (/ 15/8 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) (+ (/ 3/4 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (/ (+ (/ 1/2 (* (fabs x) (fabs x))) 1) (fabs x)))))
0.4b	(/ (/ 15/8 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x)))
1.0b	(sqrt PI)

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

129×	`pow1`
114×	`add-cbrt-cube`
113×	`add-exp-log`
69×	`pow-prod-up`
55×	`prod-exp` `cbrt-unprod`
33×	`times-frac` `pow-plus`
32×	`add-sqr-sqrt`
31×	`cbrt-undiv` `div-exp`
28×	`*-un-lft-identity`
23×	`associate-l` `add-cube-cbrt`
17×	`pow2` `pow-sqr`
16×	`pow-prod-down`
13×	`sqrt-prod`
8×	`frac-add`
7×	`associate-/l*`
6×	`associate-r`
5×	`frac-times` `associate-*r/`
4×	`flip3-+` `pow3` `flip-+` `insert-posit16` `div-inv` `add-log-exp`
3×	`distribute-lft-out` `unswap-sqr`
2×	`*-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-l/` `associate-/l/`

Counts

4 → 195

Calls

4 calls:

89.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
2.6s	(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (/ 15/8 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) (+ (/ 3/4 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (/ (+ (/ 1/2 (* (fabs x) (fabs x))) 1) (fabs x)))))
122.0ms	(/ (/ 15/8 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x)))
2.0ms	(sqrt PI)

series610.0ms

Counts

4 → 10

Calls

4 calls:

44.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
480.0ms	(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (/ 15/8 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))) (+ (/ 3/4 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (/ (+ (/ 1/2 (* (fabs x) (fabs x))) 1) (fabs x)))))
86.0ms	(/ (/ 15/8 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x)))
0.0ms	(sqrt PI)

simplify2.9s

Counts

205 → 205

Iterations

Iter	Nodes
2	5181
1	1108
0	318

prune3.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize103.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (/ 1 PI)) (* (+ (+ (/ 15/8 (pow (fabs x) 7)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (/ 1 (fabs x)) (/ 3/4 (pow (fabs x) 5)))) (exp (* (fabs x) (fabs x)))))
0.3b	(/ 15/8 (pow (fabs x) 7))
0.3b	(/ 3/4 (pow (fabs x) 5))
0.3b	(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))

rewrite618.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
46×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
30×	`frac-add`
27×	`add-exp-log`
24×	`unpow-prod-down`
23×	`associate-*l/`
22×	`add-cbrt-cube`
16×	`associate-l`
15×	`associate-/r*`
14×	`flip3-+` `flip-+`
13×	`sqrt-prod`
12×	`sqrt-div`
11×	`frac-times` `associate-*r/`
9×	`pow1` `div-exp` `associate-/l*`
8×	`sqr-pow`
6×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`insert-posit16` `div-inv` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
2×	`pow-to-exp` `pow-exp`
1×	`associate-r` `*-commutative`

Counts

4 → 171

Calls

4 calls:

579.0ms	(* (sqrt (/ 1 PI)) (* (+ (+ (/ 15/8 (pow (fabs x) 7)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (/ 1 (fabs x)) (/ 3/4 (pow (fabs x) 5)))) (exp (* (fabs x) (fabs x)))))
5.0ms	(/ 15/8 (pow (fabs x) 7))
5.0ms	(/ 3/4 (pow (fabs x) 5))
26.0ms	(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

504.0ms	(* (sqrt (/ 1 PI)) (* (+ (+ (/ 15/8 (pow (fabs x) 7)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (/ 1 (fabs x)) (/ 3/4 (pow (fabs x) 5)))) (exp (* (fabs x) (fabs x)))))
72.0ms	(/ 15/8 (pow (fabs x) 7))
58.0ms	(/ 3/4 (pow (fabs x) 5))
56.0ms	(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))

simplify4.1s

Counts

183 → 183

Iterations

Iter	Nodes
2	5120
1	1102
0	415

prune3.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 15/8 (pow (fabs x) 7))
0.3b	(* (sqrt (/ 1 PI)) (+ (+ (/ 15/8 (pow (fabs x) 7)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (/ 1 (fabs x)) (/ 3/4 (pow (fabs x) 5)))))
0.3b	(/ 3/4 (pow (fabs x) 5))
0.3b	(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))

rewrite838.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
56×	`add-sqr-sqrt` `times-frac`
47×	`add-cube-cbrt`
30×	`frac-add`
25×	`add-exp-log`
24×	`unpow-prod-down`
19×	`add-cbrt-cube`
16×	`associate-l` `sqrt-prod`
15×	`associate-/r*`
14×	`flip3-+` `flip-+`
13×	`distribute-lft-out`
12×	`sqrt-div`
11×	`frac-times` `associate-*r/`
9×	`div-exp` `associate-r` `associate-/l*`
8×	`sqr-pow`
6×	`pow1` `div-inv`
5×	`cbrt-undiv`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg`
2×	`pow-to-exp` `pow-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 182

Calls

4 calls:

6.0ms	(/ 15/8 (pow (fabs x) 7))
791.0ms	(* (sqrt (/ 1 PI)) (+ (+ (/ 15/8 (pow (fabs x) 7)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (/ 1 (fabs x)) (/ 3/4 (pow (fabs x) 5)))))
10.0ms	(/ 3/4 (pow (fabs x) 5))
27.0ms	(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ 15/8 (pow (fabs x) 7))
345.0ms	(* (sqrt (/ 1 PI)) (+ (+ (/ 15/8 (pow (fabs x) 7)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (/ 1 (fabs x)) (/ 3/4 (pow (fabs x) 5)))))
50.0ms	(/ 3/4 (pow (fabs x) 5))
34.0ms	(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))

simplify5.1s

Counts

194 → 194

Iterations

Iter	Nodes
2	5372
1	1202
0	402

prune3.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1 PI)) (+ (+ (+ (* (* 1/2 (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x)))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ 1 (fabs x))))
0.3b	(/ 3/4 (pow (fabs x) 5))
0.3b	(* (* 1/2 (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x))))
0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))

rewrite4.6s

Algorithm

rewrite-expression-head

Rules

426×	`add-exp-log`
250×	`prod-exp`
133×	`div-exp`
96×	`frac-add`
90×	`add-sqr-sqrt`
89×	`add-cbrt-cube`
80×	`times-frac`
74×	`*-un-lft-identity`
65×	`rec-exp` `1-exp`
57×	`associate-*r/` `add-cube-cbrt`
54×	`frac-times`
42×	`cbrt-unprod`
33×	`pow1`
30×	`associate-l`
25×	`un-div-inv`
22×	`cbrt-undiv`
21×	`sqrt-div` `associate-r`
17×	`associate-*l/`
16×	`sqrt-prod`
15×	`swap-sqr`
13×	`unswap-sqr`
12×	`unpow-prod-down` `pow-prod-down`
10×	`div-inv`
8×	`pow-flip` `inv-pow`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `distribute-lft-out`
5×	`pow-prod-up`
4×	`insert-posit16` `add-log-exp` `sqr-pow`
3×	`pow-sqr` `-commutative` `associate-/l`
1×	`pow2` `distribute-rgt-in` `pow-to-exp` `clear-num` `frac-2neg` `distribute-lft-in` `pow-plus` `pow-exp`

Counts

4 → 353

Calls

4 calls:

4.5s	(* (sqrt (/ 1 PI)) (+ (+ (+ (* (* 1/2 (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x)))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ 1 (fabs x))))
10.0ms	(/ 3/4 (pow (fabs x) 5))
62.0ms	(* (* 1/2 (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x))))
20.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

404.0ms	(* (sqrt (/ 1 PI)) (+ (+ (+ (* (* 1/2 (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x)))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ 1 (fabs x))))
50.0ms	(/ 3/4 (pow (fabs x) 5))
50.0ms	(* (* 1/2 (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x))))
30.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))

simplify6.1s

Counts

365 → 365

Iterations

Iter	Nodes
2	5642
1	1842
0	634

prune6.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes287.0ms

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	33
1	33
0	26

end0.0ms

sample4.5s

Algorithm

intervals

Results

4.4s

11107×

body

valid