Details

sample834.0ms

Algorithm

intervals

Results

733.0ms

3624×

body

valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	2139
2	384
1	90
0	31

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize141.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(pow (/ 1.0 (fabs x)) 4)
1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) (+ 4 1))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

39×	`unpow-prod-down`
38×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
36×	`times-frac` `add-cube-cbrt`
13×	`cube-prod` `add-exp-log`
10×	`pow-unpow`
8×	`pow1`
7×	`add-cbrt-cube`
6×	`pow-exp`
4×	`div-inv` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-exp` `sqrt-prod` `sqr-pow`
2×	`rem-cube-cbrt`
1×	`cube-div` `cube-mult` `cbrt-undiv` `unpow-prod-up` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

6.0ms	(pow (/ 1.0 (fabs x)) 3)
5.0ms	(pow (/ 1.0 (fabs x)) 4)
1.0ms	(sqrt PI)
10.0ms	(pow (/ 1.0 (fabs x)) (+ 4 1))

series183.0ms

Counts

4 → 10

Calls

4 calls:

63.0ms	(pow (/ 1.0 (fabs x)) 3)
39.0ms	(pow (/ 1.0 (fabs x)) 4)
0.0ms	(sqrt PI)
81.0ms	(pow (/ 1.0 (fabs x)) (+ 4 1))

simplify2.0s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	3377
1	808
0	202

prune1.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.3b

localize99.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (pow (/ 1.0 (fabs x)) 3) (+ (/ 1.0 2.0) (* (/ 1.0 (pow (fabs x) 4)) (/ 15.0 8.0))))
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) (+ 4 1))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
47×	`times-frac`
46×	`*-un-lft-identity`
44×	`add-cube-cbrt`
41×	`unpow-prod-down`
32×	`associate-l`
28×	`cube-prod`
18×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`cube-div` `frac-times` `pow1` `pow-unpow` `associate-*r/`
6×	`frac-add` `pow-exp` `unswap-sqr`
5×	`div-inv`
4×	`prod-exp` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `div-exp` `associate-r` `associate-*l/` `sqrt-prod`
2×	`cube-mult` `pow-pow` `flip3-+` `unpow3` `flip-+` `rem-cube-cbrt`
1×	`distribute-rgt-in` `cbrt-undiv` `unpow-prod-up` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 156

Calls

4 calls:

73.0ms	(* (pow (/ 1.0 (fabs x)) 3) (+ (/ 1.0 2.0) (* (/ 1.0 (pow (fabs x) 4)) (/ 15.0 8.0))))
7.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)
9.0ms	(pow (/ 1.0 (fabs x)) (+ 4 1))

series363.0ms

Counts

4 → 10

Calls

4 calls:

228.0ms	(* (pow (/ 1.0 (fabs x)) 3) (+ (/ 1.0 2.0) (* (/ 1.0 (pow (fabs x) 4)) (/ 15.0 8.0))))
68.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)
67.0ms	(pow (/ 1.0 (fabs x)) (+ 4 1))

simplify595.0ms

Counts

166 → 166

Iterations

Iter	Nodes
done	5000
1	1005
0	245

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (/ 1.0 (fabs x)) (+ 4 1)) (/ 3.0 4.0))
0.3b	(/ (* 1.0 (+ (/ 1.875 (pow (fabs x) 4)) 0.5)) (pow (fabs x) 3))
1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) (+ 4 1))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
45×	`times-frac`
40×	`add-exp-log`
36×	`unpow-prod-down` `*-un-lft-identity`
34×	`add-cube-cbrt`
18×	`associate-l`
14×	`add-cbrt-cube`
13×	`div-exp` `associate-r`
12×	`associate-/r*`
11×	`prod-exp`
8×	`pow-exp` `unswap-sqr`
6×	`pow1` `cube-prod` `sqr-pow`
5×	`pow-to-exp`
4×	`pow-unpow` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `associate-*r/` `sqrt-prod` `cbrt-unprod`
2×	`cube-mult` `unpow-prod-up` `unpow3` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `-commutative` `flip-+` `distribute-lft-out` `associate-/l`

Counts

4 → 146

Calls

4 calls:

59.0ms	(* (pow (/ 1.0 (fabs x)) (+ 4 1)) (/ 3.0 4.0))
41.0ms	(/ (* 1.0 (+ (/ 1.875 (pow (fabs x) 4)) 0.5)) (pow (fabs x) 3))
1.0ms	(sqrt PI)
9.0ms	(pow (/ 1.0 (fabs x)) (+ 4 1))

series427.0ms

Counts

4 → 10

Calls

4 calls:

144.0ms	(* (pow (/ 1.0 (fabs x)) (+ 4 1)) (/ 3.0 4.0))
192.0ms	(/ (* 1.0 (+ (/ 1.875 (pow (fabs x) 4)) 0.5)) (pow (fabs x) 3))
0.0ms	(sqrt PI)
91.0ms	(pow (/ 1.0 (fabs x)) (+ 4 1))

simplify2.0s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	4717
1	833
0	279

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (pow (/ 1.0 (fabs x)) 5) (/ 4.0 3.0))
0.4b	(* (/ 1.0 (pow (fabs x) 3)) (+ (/ 1.875 (pow (fabs x) 4)) 0.5))
1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

558×	`times-frac`
288×	`add-sqr-sqrt`
276×	`*-un-lft-identity`
274×	`add-cube-cbrt`
205×	`unpow-prod-down`
40×	`associate-l`
37×	`add-exp-log`
35×	`div-inv`
19×	`sqr-pow`
18×	`div-exp`
17×	`associate-/l*`
14×	`add-cbrt-cube`
13×	`associate-/r*`
10×	`cube-prod`
8×	`pow1`
7×	`pow-exp`
5×	`unswap-sqr`
4×	`pow-to-exp` `cbrt-undiv` `associate-r` `prod-exp` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3` `sqrt-prod`
2×	`frac-times` `flip3-+` `associate-*r/` `cbrt-unprod` `flip-+`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `distribute-lft-out`

Counts

4 → 384

Calls

4 calls:

33.0ms	(/ (pow (/ 1.0 (fabs x)) 5) (/ 4.0 3.0))
132.0ms	(* (/ 1.0 (pow (fabs x) 3)) (+ (/ 1.875 (pow (fabs x) 4)) 0.5))
2.0ms	(sqrt PI)
18.0ms	(pow (/ 1.0 (fabs x)) 5)

series449.0ms

Counts

4 → 10

Calls

4 calls:

173.0ms	(/ (pow (/ 1.0 (fabs x)) 5) (/ 4.0 3.0))
205.0ms	(* (/ 1.0 (pow (fabs x) 3)) (+ (/ 1.875 (pow (fabs x) 4)) 0.5))
0.0ms	(sqrt PI)
71.0ms	(pow (/ 1.0 (fabs x)) 5)

simplify1.0s

Counts

394 → 394

Iterations

Iter	Nodes
done	5000
1	2044
0	708

prune4.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes540.0ms

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	36
1	36
0	31

end0.0ms

sample5.5s

Algorithm

intervals

Results

5.0s

19409×

body

valid