Details

sample343.0ms

Algorithm

intervals

Results

268.0ms

3494×

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `times-frac`
63×	`add-cube-cbrt` `*-un-lft-identity`
26×	`unpow-prod-down` `cube-prod`
22×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
13×	`swap-sqr` `associate-r` `associate-l`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `div-exp`
4×	`pow-exp` `prod-exp` `cbrt-unprod` `add-log-exp` `rem-cube-cbrt` `unswap-sqr`
3×	`sqrt-prod`
2×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `sqr-pow`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 172

Calls

4 calls:

22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
7.0ms	(pow (/ 1.0 (fabs x)) 3)
7.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series95.0ms

Counts

4 → 10

Calls

4 calls:

28.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms	(pow (/ 1.0 (fabs x)) 3)
34.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify122.0ms

Counts

182 → 182

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	584	1144
1	3655	959
2	5003	912
done	5003	912

prune656.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
98×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
13×	`unpow-prod-down` `cube-prod`
10×	`div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`

Counts

4 → 193

Calls

4 calls:

22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
3.0ms	(sqrt PI)

series83.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify110.0ms

Counts

203 → 203

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	535	1298
1	3321	1112
2	5001	972
done	5001	972

prune909.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

202×	`times-frac`
194×	`add-exp-log`
161×	`associate-r`
134×	`add-sqr-sqrt`
121×	`add-cube-cbrt` `*-un-lft-identity`
94×	`prod-exp`
85×	`unpow-prod-down` `cube-prod`
80×	`div-exp`
42×	`pow-exp`
41×	`pow-to-exp`
40×	`add-cbrt-cube`
25×	`cube-mult` `unpow3` `sqr-pow`
18×	`pow1`
14×	`associate-l` `cbrt-unprod`
13×	`swap-sqr`
10×	`cbrt-undiv`
7×	`div-inv`
4×	`associate-*r/` `pow-prod-down` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `sqrt-prod`
2×	`frac-times` `associate-l/` `-commutative` `rem-cube-cbrt`
1×	`cube-div` `pow2` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up`

Counts

4 → 344

Calls

4 calls:

75.0ms	(* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series160.0ms

Counts

4 → 10

Calls

4 calls:

97.0ms	(* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
39.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify58.0ms

Counts

354 → 354

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1467	2952
1	5002	2014
done	5002	2014

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
0.3b	(* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

409×	`add-exp-log`
231×	`prod-exp`
162×	`times-frac`
151×	`div-exp` `associate-r`
95×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
85×	`unpow-prod-down` `cube-prod`
82×	`pow-exp`
81×	`pow-to-exp`
57×	`add-cbrt-cube`
30×	`associate-*r/`
27×	`cbrt-unprod`
26×	`frac-times`
25×	`cube-mult` `unpow3` `sqr-pow`
20×	`pow1`
14×	`associate-*l/`
12×	`frac-add`
11×	`cbrt-undiv`
9×	`pow-prod-down`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`pow-unpow` `sqrt-prod` `div-inv`
2×	`associate-l` `*-commutative` `rem-cube-cbrt`
1×	`cube-div` `distribute-rgt-in` `rem-sqrt-square` `pow-pow` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 375

Calls

4 calls:

200.0ms	(* (* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
74.0ms	(* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
6.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series299.0ms

Counts

4 → 10

Calls

4 calls:

163.0ms	(* (* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3))) (+ (/ 3.0 4.0) (* (/ (* 1.0 (/ 1.0 (fabs x))) (fabs x)) (/ 15.0 8.0))))
97.0ms	(* (* 1.0 (/ 1.0 (pow (fabs x) 2))) (/ (pow 1.0 3) (pow (fabs x) 3)))
39.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify83.0ms

Counts

385 → 385

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1760	4864
1	5001	4154
done	5001	4154

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

regimes423.0ms

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	40
1	48	40
done	48	40

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.8s

23012×

body

valid