Details

sample111.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
11.0ms	271×	body	80	nan

simplify20.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 3 expressions with local error:

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

rewrite158.0ms

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:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
55.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
96.0ms	(/ (- 1.0 x) (+ 1.0 x))

series163.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
98.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
61.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify2.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	4272
2	1034
1	369
0	168

prune571.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (sqrt (expm1 (log1p (/ (- 1.0 x) (+ 1.0 x))))))
0.0b	(sqrt (expm1 (log1p (/ (- 1.0 x) (+ 1.0 x)))))
0.0b	(expm1 (log1p (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
20×	`times-frac`
16×	`add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
5×	`pow1` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `expm1-log1p` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `div-sub` `div-exp` `flip-+` `div-inv` `flip--` `expm1-udef`

Counts

4 → 83

Calls

4 calls:

0.0ms	(atan (sqrt (expm1 (log1p (/ (- 1.0 x) (+ 1.0 x))))))
1.0ms	(sqrt (expm1 (log1p (/ (- 1.0 x) (+ 1.0 x)))))
0.0ms	(expm1 (log1p (/ (- 1.0 x) (+ 1.0 x))))
20.0ms	(/ (- 1.0 x) (+ 1.0 x))

series597.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan (sqrt (expm1 (log1p (/ (- 1.0 x) (+ 1.0 x))))))
342.0ms	(sqrt (expm1 (log1p (/ (- 1.0 x) (+ 1.0 x)))))
201.0ms	(expm1 (log1p (/ (- 1.0 x) (+ 1.0 x))))
48.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify2.1s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1684
1	560
0	227

prune608.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 x))
0.0b	(sqrt (expm1 (log1p (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x))))))
0.0b	(expm1 (log1p (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))))
0.0b	(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

566×	`*-un-lft-identity`
472×	`times-frac`
325×	`add-sqr-sqrt`
324×	`prod-diff`
312×	`add-cube-cbrt`
119×	`distribute-lft-out`
80×	`associate-/r/`
40×	`flip3-+` `flip-+` `div-inv`
18×	`fma-neg`
7×	`distribute-lft-out--`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-rgt-out--` `sqrt-prod` `associate-/l*`
1×	`cbrt-undiv` `rem-sqrt-square` `expm1-log1p` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-exp` `frac-sub` `flip--` `expm1-udef` `sub-div`

Counts

4 → 433

Calls

4 calls:

18.0ms	(/ 1.0 (+ 1.0 x))
2.0ms	(sqrt (expm1 (log1p (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x))))))
1.0ms	(expm1 (log1p (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))))
148.0ms	(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))

series843.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1.0 (+ 1.0 x))
426.0ms	(sqrt (expm1 (log1p (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x))))))
290.0ms	(expm1 (log1p (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))))
95.0ms	(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))

simplify2.7s

Counts

445 → 445

Iterations

Iter	Nodes
done	5005
2	3490
1	1309
0	547

prune3.0s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample2.0s

Algorithm

intervals

Results

923.0ms	8157×	body	80	nan
726.0ms	8000×	body	80	valid