Details

sample50.0ms

Algorithm

intervals

Results

25.0ms	837×	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

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	(- 1.0 (* x x))
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)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
27×	`times-frac`
23×	`add-cube-cbrt`
20×	`sqrt-prod`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1`
4×	`sqrt-div` `distribute-lft-out`
3×	`flip3--` `associate-/r*` `flip--` `div-inv`
2×	`associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `distribute-rgt-out` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-exp` `frac-add` `clear-num` `sum-log` `flip-+`

Counts

4 → 91

Calls

4 calls:

7.0ms	(- 1.0 (* x x))
3.0ms	(sqrt (- 1.0 (* x x)))
18.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms	(/ (sqrt (- 1.0 (* x x))) x)

series343.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- 1.0 (* x x))
63.0ms	(sqrt (- 1.0 (* x x)))
105.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
131.0ms	(/ (sqrt (- 1.0 (* x x))) x)

simplify45.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	409	777
1	1409	748
2	5001	730

prune467.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
16×	`sqrt-div`
12×	`frac-times`
10×	`flip3-+` `flip-+`
9×	`pow1` `flip3--` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
6×	`associate-r/` `associate-r` `associate-l/` `sqrt-prod` `add-log-exp`
5×	`distribute-lft-out`
4×	`associate-l` `associate-/l*`
3×	`associate-/r*` `div-inv`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `pow-prod-down` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-out` `frac-2neg` `pow1/2` `div-exp` `frac-add` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

13.0ms	(/ (sqrt (* (+ (sqrt 1.0) x) (- (sqrt 1.0) x))) x)
12.0ms	(sqrt (* (+ (sqrt 1.0) x) (- (sqrt 1.0) x)))
13.0ms	(+ (/ 1.0 x) (/ (sqrt (* (+ (sqrt 1.0) x) (- (sqrt 1.0) x))) x))
12.0ms	(* (+ (sqrt 1.0) x) (- (sqrt 1.0) x))

series657.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(/ (sqrt (* (+ (sqrt 1.0) x) (- (sqrt 1.0) x))) x)
137.0ms	(sqrt (* (+ (sqrt 1.0) x) (- (sqrt 1.0) x)))
170.0ms	(+ (/ 1.0 x) (/ (sqrt (* (+ (sqrt 1.0) x) (- (sqrt 1.0) x))) x))
116.0ms	(* (+ (sqrt 1.0) x) (- (sqrt 1.0) x))

simplify63.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	525	1271
1	2289	1196
2	5002	1192

prune383.0ms

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	10
1	14	10

end0.0ms

sample1.4s

Algorithm

intervals

Results

723.0ms	24046×	body	80	nan
295.0ms	8000×	body	80	valid