Details

sample55.0ms

Algorithm

intervals

Results

22.0ms	775×	body	80	nan
12.0ms	256×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	7
1	16	7
2	18	7
3	18	7
done	18	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

7.0ms	(sqrt (- 1.0 (* x x)))
31.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
39.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
13.0ms	(/ (sqrt (- 1.0 (* x x))) x)

series567.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt (- 1.0 (* x x)))
287.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
96.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
126.0ms	(/ (sqrt (- 1.0 (* x x))) x)

simplify52.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	537	1057
1	1921	1003
2	5001	992
done	5001	992

prune347.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
59×	`add-sqr-sqrt`
47×	`add-cube-cbrt` `*-un-lft-identity`
42×	`cbrt-prod`
36×	`associate-/r*` `sqrt-prod`
22×	`sqrt-div`
16×	`add-exp-log` `cbrt-div`
11×	`flip3--` `flip--`
10×	`add-cbrt-cube`
9×	`difference-of-squares`
8×	`associate-/l/`
7×	`pow1`
6×	`cbrt-undiv` `div-exp`
5×	`associate-/r/`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
2×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod`
1×	`frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 156

Calls

4 calls:

7.0ms	(sqrt (- 1.0 (* x x)))
7.0ms	(sqrt (- 1.0 (* x x)))
7.0ms	(sqrt (- 1.0 (* x x)))
36.0ms	(/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (/ x (cbrt (sqrt (- 1.0 (* x x))))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(sqrt (- 1.0 (* x x)))
60.0ms	(sqrt (- 1.0 (* x x)))
57.0ms	(sqrt (- 1.0 (* x x)))
129.0ms	(/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (/ x (cbrt (sqrt (- 1.0 (* x x))))))

simplify79.0ms

Counts

168 → 168

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	676	2416
1	3049	2302
2	5002	2224
done	5002	2224

prune583.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	13	18
done	13	18

end0.0ms

sample1.5s

Algorithm

intervals

Results

708.0ms	24216×	body	80	nan
289.0ms	8000×	body	80	valid