Details

sample69.0ms

Algorithm

intervals

Results

32.0ms	720×	body	80	nan
14.0ms	256×	body	80	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	18
3	18
2	16
1	12
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
36×	`times-frac`
35×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
20×	`sqrt-prod`
13×	`fma-def`
7×	`associate-/l*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp` `difference-of-squares`
4×	`pow1` `sqrt-div` `div-inv` `distribute-lft-out`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out` `pow1/2` `div-exp` `frac-add` `flip-+`

Counts

3 → 97

Calls

3 calls:

8.0ms	(sqrt (- 1.0 (* x x)))
61.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
20.0ms	(/ (sqrt (- 1.0 (* x x))) x)

series418.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(sqrt (- 1.0 (* x x)))
141.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
187.0ms	(/ (sqrt (- 1.0 (* x x))) x)

simplify1.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1263
1	415
0	181

prune630.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (- 1.0 (* x x))) x)
0.1b	(fma (sqrt (/ 1.0 x)) (sqrt (/ 1.0 x)) (/ (sqrt (- 1.0 (* x x))) x))
0.1b	(sqrt (/ 1.0 x))
0.1b	(sqrt (/ 1.0 x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
42×	`sqrt-prod`
41×	`times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-/l*`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-div` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`associate-/r*` `div-inv`
2×	`sqrt-pow1` `pow1/2` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `fma-udef` `flip--`

Counts

4 → 111

Calls

4 calls:

10.0ms	(/ (sqrt (- 1.0 (* x x))) x)
0.0ms	(fma (sqrt (/ 1.0 x)) (sqrt (/ 1.0 x)) (/ (sqrt (- 1.0 (* x x))) x))
3.0ms	(sqrt (/ 1.0 x))
3.0ms	(sqrt (/ 1.0 x))

series627.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (sqrt (- 1.0 (* x x))) x)
293.0ms	(fma (sqrt (/ 1.0 x)) (sqrt (/ 1.0 x)) (/ (sqrt (- 1.0 (* x x))) x))
80.0ms	(sqrt (/ 1.0 x))
71.0ms	(sqrt (/ 1.0 x))

simplify1.5s

Counts

123 → 123

Iterations

Iter	Nodes
done	5004
2	1434
1	475
0	228

prune718.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Iter	Nodes
done	10
0	10

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.1s	24045×	body	80	nan
717.0ms	8000×	body	80	valid