Details

sample898.0ms

Algorithm

intervals

Results

771.0ms

3611×

body

valid

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	1493
2	392
1	95
0	31

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize87.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b	(sqrt PI)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
144×	`times-frac`
124×	`add-exp-log`
113×	`*-un-lft-identity`
89×	`add-cube-cbrt`
50×	`pow1`
48×	`div-exp` `prod-exp`
45×	`swap-sqr`
40×	`add-cbrt-cube`
39×	`associate-r` `associate-l`
27×	`unswap-sqr`
24×	`rec-exp` `1-exp` `pow-flip` `inv-pow`
18×	`div-inv`
15×	`pow-prod-up`
12×	`cbrt-undiv` `cbrt-unprod`
9×	`pow-prod-down` `pow-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 302

Calls

4 calls:

46.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
32.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
46.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
2.0ms	(sqrt PI)

series107.0ms

Counts

4 → 10

Calls

4 calls:

36.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
23.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
47.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms	(sqrt PI)

simplify3.2s

Counts

312 → 312

Iterations

Iter	Nodes
done	5003
3	2638
2	975
1	446
0	157

prune1.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.4b

localize72.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (+ 3/4 (* 15/8 (/ 1 (* (fabs x) (fabs x))))))
0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b	(sqrt PI)

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-exp-log`
112×	`add-sqr-sqrt`
96×	`times-frac`
78×	`*-un-lft-identity`
65×	`prod-exp`
62×	`add-cube-cbrt`
48×	`div-exp`
46×	`add-cbrt-cube`
40×	`pow1`
30×	`swap-sqr`
29×	`associate-r`
27×	`associate-l`
24×	`rec-exp` `1-exp`
19×	`unswap-sqr`
17×	`cbrt-unprod`
16×	`pow-flip` `inv-pow`
13×	`frac-times`
12×	`cbrt-undiv` `div-inv`
10×	`pow-prod-up`
9×	`pow-prod-down` `associate-*l/`
7×	`associate-*r/`
6×	`pow-sqr`
5×	`flip3-+` `un-div-inv` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`*-commutative` `sqrt-prod`
2×	`pow2` `pow-plus`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 260

Calls

4 calls:

76.0ms	(* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (+ 3/4 (* 15/8 (/ 1 (* (fabs x) (fabs x))))))
46.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
24.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0ms	(sqrt PI)

series158.0ms

Counts

4 → 10

Calls

4 calls:

87.0ms	(* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (+ 3/4 (* 15/8 (/ 1 (* (fabs x) (fabs x))))))
36.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
35.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms	(sqrt PI)

simplify2.1s

Counts

270 → 270

Iterations

Iter	Nodes
done	5001
2	2172
1	778
0	234

prune1.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite617.0ms

Algorithm

rewrite-expression-head

Rules

47×	`times-frac`
39×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
31×	`add-cube-cbrt`
29×	`add-cbrt-cube`
27×	`add-exp-log`
17×	`associate-l`
15×	`sqrt-prod`
9×	`cbrt-undiv` `div-exp` `associate-/l/`
8×	`prod-exp` `cbrt-unprod`
7×	`pow1` `associate-/r` `associate-/l`
6×	`flip3-+` `flip-+`
5×	`frac-add`
4×	`frac-times` `associate-r` `associate-*r/` `insert-posit16` `div-inv` `add-log-exp`
3×	`distribute-lft-out` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-*l/`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative`

Counts

4 → 138

Calls

4 calls:

57.0ms	(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (* (fabs x) (fabs x)))
289.0ms	(/ (+ (* (/ (/ (exp (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x))) (+ 1/2 (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))))) (/ (exp (* (fabs x) (fabs x))) (fabs x))) (sqrt PI))
265.0ms	(* (/ (/ (exp (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x))) (+ 1/2 (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (* (fabs x) (fabs x)))))
1.0ms	(sqrt PI)

series1.1s

Counts

4 → 10

Calls

4 calls:

112.0ms	(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (* (fabs x) (fabs x)))
710.0ms	(/ (+ (* (/ (/ (exp (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x))) (+ 1/2 (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (* (fabs x) (fabs x))))) (/ (exp (* (fabs x) (fabs x))) (fabs x))) (sqrt PI))
324.0ms	(* (/ (/ (exp (* (fabs x) (fabs x))) (fabs x)) (* (fabs x) (fabs x))) (+ 1/2 (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (* (fabs x) (fabs x)))))
0.0ms	(sqrt PI)

simplify3.3s

Counts

148 → 148

Iterations

Iter	Nodes
done	5013
2	4564
1	912
0	289

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

269×	`pow1`
114×	`pow-prod-up`
64×	`pow-plus`
54×	`pow-sqr`
40×	`add-sqr-sqrt`
38×	`add-cbrt-cube` `add-exp-log`
37×	`pow-prod-down`
36×	`*-un-lft-identity`
33×	`pow2`
32×	`times-frac`
30×	`frac-add` `add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
18×	`associate-l`
17×	`associate-*r/`
16×	`sqrt-prod`
14×	`flip3-+` `flip-+`
12×	`unpow-prod-down` `sqrt-div`
11×	`frac-times`
9×	`associate-r`
7×	`associate-/r*`
6×	`unswap-sqr`
4×	`insert-posit16` `add-log-exp` `sqr-pow`
3×	`div-exp` `-commutative` `distribute-lft-out` `associate-/l`
2×	`div-inv`
1×	`distribute-rgt-in` `pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `swap-sqr` `associate-*l/` `pow-exp`

Counts

4 → 245

Calls

4 calls:

148.0ms	(* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x))
2.9s	(* (sqrt (/ 1 PI)) (+ (+ (/ (exp (* (fabs x) (fabs x))) (fabs x)) (/ (* (exp (* (fabs x) (fabs x))) 1/2) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ (* (exp (* (fabs x) (fabs x))) 3/4) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x))) (* 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))))))
14.0ms	(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
47.0ms	(* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x))
726.0ms	(* (sqrt (/ 1 PI)) (+ (+ (/ (exp (* (fabs x) (fabs x))) (fabs x)) (/ (* (exp (* (fabs x) (fabs x))) 1/2) (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ (* (exp (* (fabs x) (fabs x))) 3/4) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (fabs x))) (* 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))))))
188.0ms	(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
46.0ms	(* (* (fabs x) (fabs x)) (* (fabs x) (fabs x)))

simplify3.1s

Counts

257 → 257

Iterations

Iter	Nodes
done	5001
1	1237
0	367

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes272.0ms

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	38
1	38
0	27

end0.0ms

sample2.2s

Algorithm

intervals

Results

2.0s

7407×

body

valid