Details

sample47.0ms

Algorithm

intervals

Results

13.0ms	580×	body	80	nan
12.0ms	256×	body	160	nan
7.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
31.4b	(sqrt (- (* x x) 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 28

Calls

2 calls:

7.0ms	(+ x (sqrt (- (* x x) 1.0)))
5.0ms	(sqrt (- (* x x) 1.0))

series117.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(+ x (sqrt (- (* x x) 1.0)))
50.0ms	(sqrt (- (* x x) 1.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	217	221
1	657	211
2	2555	205
3	5001	204

prune85.0ms

Filtered

34 candidates to 29 candidates (85.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
10×	`*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `frac-times` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 53

Calls

2 calls:

3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series338.0ms

Counts

2 → 6

Calls

2 calls:

142.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
195.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	656
1	1271	612
2	5002	600

prune161.0ms

Filtered

59 candidates to 44 candidates (74.6%)

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	13	9
1	13	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

369.0ms	7827×	body	160	nan
360.0ms	16399×	body	80	nan
223.0ms	8000×	body	80	valid