Details

sample1.3s

Algorithm

intervals

Results

1.2s

3576×

body

valid

simplify5.8s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 15/8 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x)))
0.3b	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
0.3b	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
1.0b	(sqrt PI)

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

249×	`pow1`
138×	`pow-prod-up`
130×	`add-cbrt-cube` `add-exp-log`
68×	`prod-exp` `cbrt-unprod`
66×	`pow-plus`
34×	`pow2` `pow-sqr`
30×	`cbrt-undiv` `div-exp` `pow-prod-down`
13×	`times-frac`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow3`
7×	`associate-/l*`
4×	`add-log-exp`
3×	`sqrt-prod` `div-inv`
2×	`associate-r` `associate-l` `*-commutative`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 199

Calls

4 calls:

67.0ms	(/ (/ 15/8 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x)))
73.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
49.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
1.0ms	(sqrt PI)

series223.0ms

Counts

4 → 10

Calls

4 calls:

86.0ms	(/ (/ 15/8 (* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))) (* (fabs x) (fabs x)))
69.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
67.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
0.0ms	(sqrt PI)

simplify2.0s

Counts

209 → 209

Iterations

Iter	Nodes
3	4335
2	1145
1	418
0	179

prune3.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.3b

localize97.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (/ 15/8 (pow (fabs x) 5)) (* (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)))))
0.3b	(/ (/ 15/8 (pow (fabs x) 5)) (* (fabs x) (fabs x)))
0.3b	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
1.0b	(sqrt PI)

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

129×	`pow1`
87×	`times-frac`
69×	`pow-prod-up`
56×	`add-sqr-sqrt`
53×	`add-exp-log`
52×	`*-un-lft-identity`
47×	`add-cube-cbrt`
42×	`add-cbrt-cube`
33×	`pow-plus`
25×	`associate-/l*`
23×	`associate-l`
21×	`prod-exp`
19×	`cbrt-unprod`
18×	`unpow-prod-down`
17×	`pow2` `pow-sqr`
16×	`pow-prod-down`
15×	`div-exp`
13×	`sqrt-prod`
8×	`frac-add`
7×	`cbrt-undiv`
6×	`associate-r` `sqr-pow`
5×	`frac-times` `associate-*r/`
4×	`flip3-+` `pow3` `flip-+` `div-inv` `add-log-exp`
3×	`distribute-lft-out` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `*-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 → 207

Calls

4 calls:

1.7s	(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (/ 15/8 (pow (fabs x) 5)) (* (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)))))
24.0ms	(/ (/ 15/8 (pow (fabs x) 5)) (* (fabs x) (fabs x)))
88.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
2.0ms	(sqrt PI)

series778.0ms

Counts

4 → 10

Calls

4 calls:

606.0ms	(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (/ 15/8 (pow (fabs x) 5)) (* (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)))))
102.0ms	(/ (/ 15/8 (pow (fabs x) 5)) (* (fabs x) (fabs x)))
71.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
0.0ms	(sqrt PI)

simplify2.7s

Counts

217 → 217

Iterations

Iter	Nodes
2	5000
1	1201
0	374

prune3.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
45×	`times-frac`
39×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`add-exp-log`
24×	`unpow-prod-down`
22×	`add-cbrt-cube`
18×	`frac-add`
15×	`associate-/r*`
9×	`pow1` `div-exp` `associate-l/` `distribute-lft-out` `associate-/l`
8×	`sqrt-div` `sqr-pow`
7×	`frac-times` `associate-r` `associate-*r/`
6×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
5×	`cbrt-undiv`
4×	`div-inv` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
2×	`pow-to-exp` `pow-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 152

Calls

4 calls:

7.0ms	(/ 3/4 (pow (fabs x) 5))
5.0ms	(/ 15/8 (pow (fabs x) 7))
11.0ms	(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
1.1s	(* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (/ 3/4 (pow (fabs x) 5))) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (/ 15/8 (pow (fabs x) 7))))

series744.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ 3/4 (pow (fabs x) 5))
79.0ms	(/ 15/8 (pow (fabs x) 7))
57.0ms	(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
528.0ms	(* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (/ 3/4 (pow (fabs x) 5))) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (/ 15/8 (pow (fabs x) 7))))

simplify3.4s

Counts

164 → 164

Iterations

Iter	Nodes
2	4660
1	1020
0	363

prune3.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 15/8 (pow (fabs x) 5)) (fabs x))
0.3b	(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (/ (/ 15/8 (pow (fabs x) 5)) (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)))))
0.3b	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
1.0b	(sqrt PI)

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

179×	`times-frac`
129×	`pow1`
110×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
101×	`add-cube-cbrt`
69×	`pow-prod-up`
39×	`add-exp-log`
36×	`unpow-prod-down`
35×	`add-cbrt-cube`
33×	`pow-plus`
25×	`associate-/l*`
23×	`associate-l`
17×	`pow2` `prod-exp` `pow-sqr` `cbrt-unprod`
16×	`pow-prod-down`
13×	`sqrt-prod`
12×	`sqr-pow`
8×	`div-exp` `frac-add`
6×	`associate-r` `div-inv`
5×	`frac-times` `associate-*r/`
4×	`cbrt-undiv` `flip3-+` `pow3` `flip-+` `add-log-exp`
3×	`associate-/r*` `distribute-lft-out` `unswap-sqr`
2×	`*-commutative`
1×	`distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-*l/` `pow-exp` `associate-/l/`

Counts

4 → 253

Calls

4 calls:

16.0ms	(/ (/ 15/8 (pow (fabs x) 5)) (fabs x))
1.8s	(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (/ (/ 15/8 (pow (fabs x) 5)) (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)))))
62.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
1.0ms	(sqrt PI)

series598.0ms

Counts

4 → 10

Calls

4 calls:

64.0ms	(/ (/ 15/8 (pow (fabs x) 5)) (fabs x))
468.0ms	(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (/ (/ 15/8 (pow (fabs x) 5)) (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)))))
65.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (* (fabs x) (fabs x)))
0.0ms	(sqrt PI)

simplify3.4s

Counts

263 → 263

Iterations

Iter	Nodes
2	4982
1	1364
0	465

prune4.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes295.0ms

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
2	31
1	31
0	25

end0.0ms

sample10.5s

Algorithm

intervals

Results

10.1s

25476×

body

valid