Details

sample86.0ms

Algorithm

intervals

Results

50.0ms	754×	body	80	nan
19.0ms	256×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

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:

24.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms	(/ (sqrt (- 1.0 (* x x))) x)
3.0ms	(sqrt (- 1.0 (* x x)))
30.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series594.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
136.0ms	(/ (sqrt (- 1.0 (* x x))) x)
63.0ms	(sqrt (- 1.0 (* x x)))
101.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify60.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	537	1057
1	1923	1003
2	5001	992

prune339.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

458×	`times-frac`
335×	`*-un-lft-identity`
316×	`sqrt-prod`
315×	`add-sqr-sqrt`
209×	`add-cube-cbrt`
50×	`difference-of-squares`
37×	`distribute-lft-out`
33×	`associate-/r*`
25×	`distribute-lft-out--`
22×	`sqrt-div`
17×	`associate-/r/`
13×	`fma-def`
10×	`div-inv`
9×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
7×	`associate-/l*`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def` `associate-/l/`
1×	`+-commutative` `frac-2neg` `frac-add` `clear-num` `sum-log`

Counts

4 → 359

Calls

4 calls:

7.0ms	(sqrt (+ (sqrt 1.0) x))
10.0ms	(sqrt (- (sqrt 1.0) x))
171.0ms	(+ (/ 1.0 x) (/ (sqrt (+ (sqrt 1.0) x)) (/ x (sqrt (- (sqrt 1.0) x)))))
28.0ms	(/ (sqrt (+ (sqrt 1.0) x)) (/ x (sqrt (- (sqrt 1.0) x))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (+ (sqrt 1.0) x))
63.0ms	(sqrt (- (sqrt 1.0) x))
174.0ms	(+ (/ 1.0 x) (/ (sqrt (+ (sqrt 1.0) x)) (/ x (sqrt (- (sqrt 1.0) x)))))
238.0ms	(/ (sqrt (+ (sqrt 1.0) x)) (/ x (sqrt (- (sqrt 1.0) x))))

simplify132.0ms

Algorithm

egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	991	5738
1	4255	5438
2	5002	5427

prune748.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	11
1	14	11

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.5s	24344×	body	80	nan
588.0ms	8000×	body	80	valid