Details

sample350.0ms

Algorithm

intervals

Results

291.0ms

3513×

body

valid

simplify729.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (148.0ms)

Iter	Nodes	Cost
0	31	103
1	90	103
2	364	66
3	1803	54
done	5001	54

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize34.0ms

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)

rewrite51.0ms

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:

13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series75.0ms

Counts

4 → 10

Calls

4 calls:

23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify709.0ms

Counts

224 → 224

Iterations

Useful iterations: done (703.0ms)

Iter	Nodes	Cost
0	146	3221
1	421	2898
2	1679	2387
done	5000	2378

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
44×	`unpow-prod-down`
43×	`add-sqr-sqrt`
42×	`add-cube-cbrt` `*-un-lft-identity`
38×	`cube-prod`
24×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`pow-exp`
9×	`pow-unpow`
8×	`pow1` `div-exp`
7×	`rem-cube-cbrt`
6×	`div-inv`
5×	`pow-to-exp` `sqr-pow`
4×	`cbrt-undiv` `add-log-exp`
3×	`cube-div` `cube-mult` `pow-pow` `unpow3` `prod-exp` `sqrt-prod`
2×	`unpow2`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `cbrt-unprod`

Counts

4 → 155

Calls

4 calls:

6.0ms	(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
4.0ms	(pow (/ 1.0 (fabs x)) 3)
4.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series124.0ms

Counts

4 → 10

Calls

4 calls:

53.0ms	(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
38.0ms	(pow (/ 1.0 (fabs x)) 3)
32.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify1.1s

Counts

165 → 165

Iterations

Useful iterations: 2 (297.0ms)

Iter	Nodes	Cost
0	188	2052
1	553	1821
2	2385	1480
done	5001	1480

prune619.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (/ 3.0 4.0) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3))
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

82×	`add-exp-log`
54×	`times-frac`
51×	`add-sqr-sqrt`
50×	`add-cube-cbrt` `*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
36×	`prod-exp`
32×	`associate-r`
28×	`add-cbrt-cube`
23×	`div-exp`
14×	`pow-exp`
9×	`cbrt-unprod`
7×	`pow1` `pow-to-exp`
6×	`cbrt-undiv` `cube-div` `pow-unpow` `div-inv`
5×	`frac-times` `associate-*l/`
4×	`add-log-exp` `rem-cube-cbrt`
3×	`cube-mult` `unpow3` `associate-*r/` `sqrt-prod` `sqr-pow`
2×	`pow-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 178

Calls

4 calls:

31.0ms	(* (* (/ 3.0 4.0) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3))
4.0ms	(pow (/ 1.0 (fabs x)) 3)
4.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series149.0ms

Counts

4 → 10

Calls

4 calls:

81.0ms	(* (* (/ 3.0 4.0) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3))
32.0ms	(pow (/ 1.0 (fabs x)) 3)
36.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify1.5s

Counts

188 → 188

Iterations

Useful iterations: 2 (446.0ms)

Iter	Nodes	Cost
0	214	2724
1	651	2387
2	3477	1848
done	5001	1848

prune714.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 (fabs x)) (+ (* (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0)) (/ (* (/ 15.0 8.0) (pow 1.0 6)) (pow (fabs x) 6))))
0.7b	(pow (/ 1.0 (fabs x)) 3)
0.9b	(pow (/ 1.0 (fabs x)) 4)
1.0b	(sqrt PI)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
26×	`unpow-prod-down`
15×	`add-exp-log`
13×	`cube-prod` `associate-l`
12×	`add-cbrt-cube`
9×	`pow1`
6×	`pow-unpow`
5×	`associate-*r/`
4×	`pow-exp` `div-inv` `add-log-exp`
3×	`frac-times` `div-exp` `associate-r` `sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `flip3-+` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`cube-div` `distribute-rgt-in` `cube-mult` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 127

Calls

4 calls:

52.0ms	(* (/ 1.0 (fabs x)) (+ (* (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0)) (/ (* (/ 15.0 8.0) (pow 1.0 6)) (pow (fabs x) 6))))
4.0ms	(pow (/ 1.0 (fabs x)) 3)
4.0ms	(pow (/ 1.0 (fabs x)) 4)
1.0ms	(sqrt PI)

series231.0ms

Counts

4 → 10

Calls

4 calls:

165.0ms	(* (/ 1.0 (fabs x)) (+ (* (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0)) (/ (* (/ 15.0 8.0) (pow 1.0 6)) (pow (fabs x) 6))))
32.0ms	(pow (/ 1.0 (fabs x)) 3)
33.0ms	(pow (/ 1.0 (fabs x)) 4)
0.0ms	(sqrt PI)

simplify1.5s

Counts

137 → 137

Iterations

Useful iterations: 2 (504.0ms)

Iter	Nodes	Cost
0	240	2661
1	779	2492
2	3629	2245
done	5001	2245

prune600.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

regimes198.0ms

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	55
1	45	55
done	45	55

end0.0ms

sample9.8s

Algorithm

intervals

Results

8.5s

103451×

body

valid