Details

sample176.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
16.0ms	248×	body	80	nan

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	19	11
3	21	11
done	21	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `div-exp` `flip--`

Counts

3 → 97

Calls

3 calls:

21.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
40.0ms	(/ (- 1.0 x) (+ 1.0 x))

series183.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
6.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
72.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	168	1479
1	364	1398
2	1318	1313
done	5000	1311

prune537.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
0.0b	(/ (- 1.0 x) (+ x 1.0))
0.0b	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))
0.0b	(pow (/ (- 1.0 x) (+ x 1.0)) 3)

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
100×	`times-frac`
99×	`add-sqr-sqrt`
58×	`cbrt-prod`
57×	`add-cube-cbrt`
52×	`unpow-prod-down` `cube-prod`
26×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `cbrt-undiv` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow` `associate-/l/`
1×	`pow-to-exp` `cbrt-div` `clear-num` `pow-pow` `frac-2neg` `flip3--` `pow1/3` `div-sub` `rem-cbrt-cube` `flip--`

Counts

4 → 201

Calls

4 calls:

1.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
37.0ms	(/ (- 1.0 x) (+ x 1.0))
40.0ms	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))
33.0ms	(pow (/ (- 1.0 x) (+ x 1.0)) 3)

series182.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))))
44.0ms	(/ (- 1.0 x) (+ x 1.0))
50.0ms	(cbrt (pow (/ (- 1.0 x) (+ x 1.0)) 3))
86.0ms	(pow (/ (- 1.0 x) (+ x 1.0)) 3)

simplify1.9s

Counts

213 → 213

Iterations

Useful iterations: 2 (741.0ms)

Iter	Nodes	Cost
0	219	3706
1	755	3076
2	4176	2841
done	5001	2841

prune682.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(* (- 1.0 x) (/ 1 (+ x 1.0)))
0.0b	(cbrt (pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3))
0.0b	(pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3)

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
27×	`add-exp-log`
26×	`times-frac`
24×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-cbrt-cube`
12×	`cube-div`
10×	`pow1`
8×	`cbrt-prod` `prod-exp`
7×	`distribute-lft-out`
6×	`frac-times` `cbrt-div` `flip3--` `div-exp` `associate-*l/` `flip--`
5×	`associate-l` `pow-exp`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `pow-unpow` `1-exp` `associate-r/` `un-div-inv` `associate-/l` `rem-cube-cbrt` `unswap-sqr`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `flip3-+` `unpow3` `cube-prod` `pow-prod-down` `flip-+` `div-inv` `sqr-pow`
1×	`pow-to-exp` `clear-num` `frac-2neg` `pow1/3` `*-commutative` `rem-cbrt-cube` `pow-flip` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 147

Calls

4 calls:

20.0ms	(/ 1 (+ x 1.0))
45.0ms	(* (- 1.0 x) (/ 1 (+ x 1.0)))
7.0ms	(cbrt (pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3))
26.0ms	(pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3)

series218.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1 (+ x 1.0))
46.0ms	(* (- 1.0 x) (/ 1 (+ x 1.0)))
50.0ms	(cbrt (pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3))
83.0ms	(pow (* (- 1.0 x) (/ 1 (+ x 1.0))) 3)

simplify2.1s

Counts

159 → 159

Iterations

Useful iterations: 2 (716.0ms)

Iter	Nodes	Cost
0	208	2088
1	618	1706
2	3706	1447
done	5001	1447

prune746.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	16
1	19	16
done	19	16

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
460.0ms	7876×	body	80	nan