Details

sample1.8s

Algorithm

intervals

Results

1.7s

3623×

body

valid

simplify6.8s

Counts

1 → 1

Iterations

Iter	Nodes
4	8828
3	1935
2	407
1	93
0	31

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize106.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.5b	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0b	(sqrt PI)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
144×	`times-frac`
124×	`add-exp-log`
113×	`*-un-lft-identity`
89×	`add-cube-cbrt`
50×	`pow1`
48×	`div-exp` `prod-exp`
45×	`swap-sqr`
40×	`add-cbrt-cube`
39×	`associate-r` `associate-l`
27×	`unswap-sqr`
24×	`rec-exp` `1-exp` `pow-flip` `inv-pow`
18×	`div-inv`
15×	`pow-prod-up`
12×	`cbrt-undiv` `cbrt-unprod`
9×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 310

Calls

4 calls:

29.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
29.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
24.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
1.0ms	(sqrt PI)

series70.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
24.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
22.0ms	(* (/ 1 (fabs x)) (/ 1 (fabs x)))
0.0ms	(sqrt PI)

simplify4.0s

Counts

320 → 320

Iterations

Iter	Nodes
3	3491
2	1249
1	485
0	168

prune2.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.5b

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
0.5b	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.5b	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

738×	`add-exp-log`
663×	`times-frac`
465×	`add-sqr-sqrt`
412×	`div-exp`
333×	`*-un-lft-identity`
300×	`add-cube-cbrt`
254×	`prod-exp`
180×	`add-cbrt-cube`
114×	`pow1`
99×	`associate-l`
98×	`swap-sqr`
87×	`associate-r`
86×	`rec-exp` `1-exp`
82×	`cbrt-undiv`
65×	`div-inv`
56×	`cbrt-unprod` `pow-div`
53×	`unswap-sqr`
34×	`pow-flip` `inv-pow`
30×	`pow-prod-up`
10×	`pow-sqr`
9×	`pow-prod-down`
7×	`frac-times` `associate-*r/`
5×	`associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sqrt-prod`
2×	`pow2` `pow-plus`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 631

Calls

4 calls:

80.0ms	(* (/ 1 (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
25.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
56.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series171.0ms

Counts

4 → 10

Calls

4 calls:

59.0ms	(* (/ 1 (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
60.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
53.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify2.1s

Counts

641 → 641

Iterations

Iter	Nodes
2	3854
1	1629
0	538

prune4.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.2b

localize93.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (pow (fabs x) 5)) (/ (/ 1 (fabs x)) (fabs x)))
0.4b	(* (/ 1 (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
0.5b	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

788×	`add-exp-log`
489×	`times-frac`
442×	`div-exp`
386×	`add-sqr-sqrt`
279×	`prod-exp`
244×	`*-un-lft-identity`
205×	`add-cube-cbrt`
165×	`add-cbrt-cube`
101×	`rec-exp` `1-exp`
88×	`pow1`
87×	`associate-r`
81×	`associate-l`
73×	`cbrt-undiv`
63×	`unswap-sqr`
53×	`cbrt-unprod`
49×	`swap-sqr`
45×	`div-inv`
42×	`pow-div`
29×	`pow-flip`
27×	`pow-prod-up` `inv-pow`
19×	`unpow-prod-down`
15×	`pow-to-exp` `pow-exp`
13×	`sqr-pow`
7×	`frac-times` `pow-prod-down` `associate-*r/` `pow-sqr`
5×	`associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sqrt-prod`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2`

Counts

4 → 586

Calls

4 calls:

32.0ms	(* (/ 1 (pow (fabs x) 5)) (/ (/ 1 (fabs x)) (fabs x)))
70.0ms	(* (/ 1 (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
50.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
2.0ms	(sqrt PI)

series209.0ms

Counts

4 → 10

Calls

4 calls:

82.0ms	(* (/ 1 (pow (fabs x) 5)) (/ (/ 1 (fabs x)) (fabs x)))
72.0ms	(* (/ 1 (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
54.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify1.6s

Counts

596 → 596

Iterations

Iter	Nodes
1	2400
0	721

prune3.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.1b

localize94.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma (/ (/ 1 (fabs x)) (fabs x)) 1/2 1) (/ 1 (fabs x)))
0.4b	(* (/ 1 (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
0.5b	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

647×	`add-exp-log`
354×	`div-exp`
348×	`times-frac`
256×	`add-sqr-sqrt`
233×	`prod-exp`
182×	`*-un-lft-identity`
164×	`add-cube-cbrt`
149×	`add-cbrt-cube`
85×	`pow1`
77×	`rec-exp` `1-exp`
65×	`cbrt-undiv`
59×	`associate-l`
57×	`associate-r`
49×	`swap-sqr` `cbrt-unprod`
40×	`pow-div`
34×	`div-inv`
31×	`unswap-sqr`
26×	`pow-flip` `inv-pow`
25×	`pow-prod-up`
7×	`pow-prod-down` `associate-*r/` `pow-sqr`
6×	`frac-times`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sqrt-prod`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `un-div-inv`

Counts

4 → 449

Calls

4 calls:

11.0ms	(* (fma (/ (/ 1 (fabs x)) (fabs x)) 1/2 1) (/ 1 (fabs x)))
55.0ms	(* (/ 1 (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
32.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series175.0ms

Counts

4 → 10

Calls

4 calls:

67.0ms	(* (fma (/ (/ 1 (fabs x)) (fabs x)) 1/2 1) (/ 1 (fabs x)))
57.0ms	(* (/ 1 (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
50.0ms	(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify2.6s

Counts

459 → 459

Iterations

Iter	Nodes
2	4839
1	1736
0	582

prune2.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.1b

regimes496.0ms

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
2	29
1	29
0	25

end0.0ms

sample4.0s

Algorithm

intervals

Results

3.8s

9605×

body

valid