Details

sample389.0ms

Algorithm

intervals

Results

309.0ms

4008×

body

valid

simplify65.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36
done	5001	36

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
120×	`times-frac`
89×	`add-cube-cbrt` `*-un-lft-identity`
40×	`add-exp-log` `add-cbrt-cube`
39×	`swap-sqr` `associate-r` `associate-l`
26×	`pow1`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `sqrt-prod` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 214

Calls

4 calls:

21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series78.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify70.0ms

Counts

224 → 224

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	426	1780
1	2077	1524
2	5002	1377
done	5002	1377

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite5.4s

Algorithm

rewrite-expression-head

Rules

3341×	`add-exp-log`
1930×	`prod-exp`
1241×	`div-exp`
1117×	`add-cbrt-cube`
618×	`cbrt-unprod`
361×	`cbrt-undiv`
131×	`frac-times` `associate-*l/`
112×	`1-exp`
96×	`pow-to-exp` `pow-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
39×	`pow1` `associate-r`
33×	`associate-*r/`
27×	`associate-l`
26×	`swap-sqr`
17×	`pow-prod-down`
9×	`div-inv`
8×	`unswap-sqr`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 729

Calls

4 calls:

5.0s	(* (* (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
227.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series186.0ms

Counts

4 → 10

Calls

4 calls:

137.0ms	(* (* (* (* (* (/ (sqrt 1.0) 1) (/ (* 1.0 (sqrt 1.0)) (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify182.0ms

Counts

739 → 739

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	4398	16140
1	5001	15671
done	5001	15671

prune1.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite627.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-exp-log` `add-cbrt-cube`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
62×	`pow-plus` `pow-prod-up`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
12×	`pow-prod-down`
10×	`pow2` `pow-sqr`
9×	`div-inv`
8×	`unswap-sqr`
4×	`pow3` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 332

Calls

4 calls:

555.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series108.0ms

Counts

4 → 10

Calls

4 calls:

51.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
32.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify61.0ms

Counts

342 → 342

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1372	4480
1	5002	2465
done	5002	2465

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))) (* (/ 3.0 4.0) (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

1217×	`frac-times`
937×	`associate-*r/`
679×	`associate-*l/`
434×	`frac-add`
99×	`add-sqr-sqrt`
90×	`times-frac`
69×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-l`
33×	`add-exp-log` `add-cbrt-cube`
29×	`associate-r`
26×	`swap-sqr`
21×	`pow1`
10×	`prod-exp` `cbrt-unprod` `unswap-sqr`
9×	`cbrt-undiv` `div-exp` `div-inv`
4×	`add-log-exp`
3×	`pow-prod-down` `sqrt-prod` `*-commutative`
2×	`pow2` `flip3-+` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 619

Calls

4 calls:

258.0ms	(* (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))) (* (/ 3.0 4.0) (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))))
21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series185.0ms

Counts

4 → 10

Calls

4 calls:

136.0ms	(* (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))) (* (/ 3.0 4.0) (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify135.0ms

Counts

629 → 629

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5001	13378
done	5001	13378

prune1.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.3b

regimes335.0ms

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	45
1	46	45
done	46	45

end0.0ms

sample5.1s

Algorithm

intervals

Results

4.2s

55664×

body

valid