Details

sample49.0ms

Algorithm

intervals

Results

23.0ms	739×	body	80	nan
10.0ms	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

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 78

Calls

3 calls:

3.0ms	(sqrt (- 1.0 (* x x)))
6.0ms	(/ (sqrt (- 1.0 (* x x))) x)
26.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series503.0ms

Counts

3 → 9

Calls

3 calls:

263.0ms	(sqrt (- 1.0 (* x x)))
134.0ms	(/ (sqrt (- 1.0 (* x x))) x)
106.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify44.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	394	713
1	1359	689
2	5001	672

prune221.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

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))

rewrite70.0ms

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:

7.0ms	(sqrt (- (sqrt 1.0) x))
6.0ms	(sqrt (+ (sqrt 1.0) x))
9.0ms	(+ (/ 1.0 x) (* (sqrt (+ (sqrt 1.0) x)) (/ (sqrt (- (sqrt 1.0) x)) x)))
41.0ms	(* (sqrt (+ (sqrt 1.0) x)) (/ (sqrt (- (sqrt 1.0) x)) x))

series537.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (- (sqrt 1.0) x))
69.0ms	(sqrt (+ (sqrt 1.0) x))
163.0ms	(+ (/ 1.0 x) (* (sqrt (+ (sqrt 1.0) x)) (/ (sqrt (- (sqrt 1.0) x)) x)))
228.0ms	(* (sqrt (+ (sqrt 1.0) x)) (/ (sqrt (- (sqrt 1.0) x)) x))

simplify66.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (53.0ms)

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

prune332.0ms

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	15	11
1	15	11

end0.0ms

sample1.5s

Algorithm

intervals

Results

760.0ms	24242×	body	80	nan
313.0ms	8000×	body	80	valid