Details

sample49.0ms

Algorithm

intervals

Results

13.0ms	298×	body	160	nan
12.0ms	571×	body	80	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: 31.4b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(- (* x x) 1.0)
0.0b	(+ x (sqrt (- (* x x) 1.0)))
29.2b	(sqrt (- (* x x) 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
5×	`add-exp-log`
4×	`log-prod` `sqrt-prod` `add-cbrt-cube`
2×	`log-div` `flip3--` `flip3-+` `sqrt-div` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `rem-log-exp` `sum-log` `log-pow`

Counts

4 → 56

Calls

4 calls:

12.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
3.0ms	(- (* x x) 1.0)
8.0ms	(+ x (sqrt (- (* x x) 1.0)))
5.0ms	(sqrt (- (* x x) 1.0))

series363.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
44.0ms	(- (* x x) 1.0)
69.0ms	(+ x (sqrt (- (* x x) 1.0)))
52.0ms	(sqrt (- (* x x) 1.0))

simplify136.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	327	471
1	1087	435
2	4892	422
3	5001	422

prune196.0ms

Filtered

68 candidates to 55 candidates (80.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

3.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
52.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series649.0ms

Counts

3 → 9

Calls

3 calls:

285.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
148.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
216.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify50.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	440	941
1	1553	864
2	5001	848

prune202.0ms

Filtered

76 candidates to 58 candidates (76.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (- x (sqrt 1.0))))
0.1b	(sqrt (sqrt (- x (sqrt 1.0))))
0.3b	(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0))))) (sqrt (sqrt (- x (sqrt 1.0)))))
0.3b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0)))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

116×	`sqrt-div`
79×	`sqrt-prod`
48×	`add-sqr-sqrt`
32×	`frac-times`
26×	`*-un-lft-identity`
24×	`associate-r`
23×	`flip3--` `flip--`
20×	`pow1`
16×	`add-cube-cbrt` `associate-*l/`
13×	`sqrt-pow1`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*r/` `pow-prod-down`
9×	`pow1/2`
8×	`associate-l` `difference-of-squares`
6×	`unswap-sqr`
4×	`rem-sqrt-square` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`
1×	`distribute-lft-out`

Counts

4 → 151

Calls

4 calls:

7.0ms	(sqrt (sqrt (- x (sqrt 1.0))))
6.0ms	(sqrt (sqrt (- x (sqrt 1.0))))
92.0ms	(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0))))) (sqrt (sqrt (- x (sqrt 1.0)))))
40.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0)))))

series875.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(sqrt (sqrt (- x (sqrt 1.0))))
185.0ms	(sqrt (sqrt (- x (sqrt 1.0))))
198.0ms	(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0))))) (sqrt (sqrt (- x (sqrt 1.0)))))
294.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	768	2304
1	2919	2103
2	5001	2052

prune721.0ms

Filtered

163 candidates to 106 candidates (65.0%)

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	16	15
1	16	15

end0.0ms

sample1.3s

Algorithm

intervals

Results

342.0ms	7553×	body	160	nan
324.0ms	15697×	body	80	nan
229.0ms	8000×	body	80	valid