Details

sample967.0ms

Algorithm

intervals

Results

858.0ms

3860×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	31	103
1	90	103
2	401	65
3	2023	51
done	5001	49

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize103.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 222

Calls

4 calls:

27.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
36.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
31.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(sqrt PI)

series107.0ms

Counts

4 → 10

Calls

4 calls:

38.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
31.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify1.8s

Counts

232 → 232

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	150	3287
1	407	2964
2	1497	2446
done	5000	2298

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.4b

localize72.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite1.0s

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×	`expm1-log1p-u` `pow3` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 340

Calls

4 calls:

939.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
38.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(sqrt PI)

series165.0ms

Counts

4 → 10

Calls

4 calls:

71.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
43.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
51.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify3.2s

Counts

350 → 350

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	398	8746
1	1043	7693
2	3101	3956
done	5000	3433

prune2.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.3b

localize127.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fabs x))
0.6b	(cbrt (fabs x))
0.7b	(pow (/ (cbrt 1.0) (cbrt (fabs x))) 3)
1.0b	(sqrt PI)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

78×	`cbrt-prod`
72×	`times-frac`
59×	`add-sqr-sqrt`
58×	`add-cube-cbrt` `*-un-lft-identity`
40×	`unpow-prod-down` `cube-prod`
7×	`add-exp-log`
6×	`pow1`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`pow1/3` `pow-exp` `div-inv` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow3` `div-exp` `sqr-pow`

Counts

4 → 143

Calls

4 calls:

1.0ms	(cbrt (fabs x))
1.0ms	(cbrt (fabs x))
13.0ms	(pow (/ (cbrt 1.0) (cbrt (fabs x))) 3)
2.0ms	(sqrt PI)

series598.0ms

Counts

4 → 10

Calls

4 calls:

158.0ms	(cbrt (fabs x))
140.0ms	(cbrt (fabs x))
299.0ms	(pow (/ (cbrt 1.0) (cbrt (fabs x))) 3)
0.0ms	(sqrt PI)

simplify1.9s

Counts

153 → 153

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	213	2205
1	684	1867
2	2360	1348
done	5001	1335

prune1.2s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.3b

localize80.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (* (/ (sqrt 1.0) (sqrt (fabs x))) (/ 1.0 (fabs x))) (/ (sqrt 1.0) (sqrt (fabs x)))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite6.0s

Algorithm

rewrite-expression-head

Rules

781×	`add-exp-log` `add-cbrt-cube`
426×	`prod-exp` `cbrt-unprod`
249×	`cbrt-undiv` `div-exp`
131×	`frac-times` `associate-*l/`
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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 433

Calls

4 calls:

5.8s	(* (* (* (* (* (/ (sqrt 1.0) (sqrt (fabs x))) (/ 1.0 (fabs x))) (/ (sqrt 1.0) (sqrt (fabs x)))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
39.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
47.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(sqrt PI)

series285.0ms

Counts

4 → 10

Calls

4 calls:

217.0ms	(* (* (* (* (* (/ (sqrt 1.0) (sqrt (fabs x))) (/ 1.0 (fabs x))) (/ (sqrt 1.0) (sqrt (fabs x)))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
35.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify2.7s

Counts

443 → 443

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	689	18452
1	2009	16460
done	5001	6143

prune2.1s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.2b

regimes308.0ms

bsearch0.0ms

simplify18.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	87
1	48	87
done	48	87

end0.0ms

sample4.4s

Algorithm

intervals

Results

4.1s

14908×

body

valid