Details

sample51.0ms

Algorithm

intervals

Results

25.0ms	757×	body	80	nan
9.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 1

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
33×	`times-frac`
32×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
20×	`sqrt-prod`
8×	`log-prod` `distribute-lft-out`
7×	`add-exp-log` `associate-/l*`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`div-inv` `difference-of-squares`
4×	`sqrt-div`
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 → 98

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (* x x)))
20.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
5.0ms	(/ (sqrt (- 1.0 (* x x))) x)
18.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series580.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (- 1.0 (* x x)))
286.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
128.0ms	(/ (sqrt (- 1.0 (* x x))) x)
103.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	512	1017
1	1798	965
2	5001	961

prune235.0ms

Filtered

110 candidates to 88 candidates (80.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	1	111

Merged error: 0b

Counts

111 → 1

localize12.0ms

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
41×	`sqrt-prod`
36×	`*-un-lft-identity`
31×	`times-frac` `associate-r`
24×	`add-cube-cbrt`
12×	`sqrt-div`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `difference-of-squares`
7×	`associate-l`
6×	`flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
5×	`frac-add`
4×	`frac-times` `associate-*l/` `distribute-lft-out--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `prod-exp` `cbrt-unprod` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `flip3--` `div-exp` `pow-prod-down` `sum-log` `*-commutative` `flip--` `div-inv`

Counts

4 → 112

Calls

4 calls:

4.0ms	(sqrt (- (sqrt 1.0) x))
4.0ms	(sqrt (+ (sqrt 1.0) x))
6.0ms	(+ (/ 1.0 x) (* (sqrt (+ (sqrt 1.0) x)) (/ (sqrt (- (sqrt 1.0) x)) x)))
19.0ms	(* (sqrt (+ (sqrt 1.0) x)) (/ (sqrt (- (sqrt 1.0) x)) x))

series551.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (- (sqrt 1.0) x))
70.0ms	(sqrt (+ (sqrt 1.0) x))
177.0ms	(+ (/ 1.0 x) (* (sqrt (+ (sqrt 1.0) x)) (/ (sqrt (- (sqrt 1.0) x)) x)))
234.0ms	(* (sqrt (+ (sqrt 1.0) x)) (/ (sqrt (- (sqrt 1.0) x)) x))

simplify66.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	585	1363
1	2360	1290
2	5001	1274

prune288.0ms

Filtered

124 candidates to 86 candidates (69.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	124	1	125

Merged error: 0b

Counts

125 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	11
1	15	11

end0.0ms

sample1.4s

Algorithm

intervals

Results

743.0ms	23971×	body	80	nan
301.0ms	8000×	body	80	valid