Details

sample49.0ms

Algorithm

intervals

Results

10.0ms	236×	body	160	nan
10.0ms	499×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
27.3b	(sqrt (- (* x x) 1.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

19.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
17.0ms	(+ x (sqrt (- (* x x) 1.0)))
10.0ms	(sqrt (- (* x x) 1.0))

series301.0ms

Counts

3 → 9

Calls

3 calls:

189.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
64.0ms	(+ x (sqrt (- (* x x) 1.0)))
48.0ms	(sqrt (- (* x x) 1.0))

simplify137.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	316	408
1	1042	379
2	4663	366
3	5002	365

prune128.0ms

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

5.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
10.0ms	(sqrt (+ x (sqrt 1.0)))
3.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
50.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
65.0ms	(sqrt (+ x (sqrt 1.0)))
284.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
194.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify50.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	491	1081
1	1717	994
2	5001	974

prune267.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (sqrt (- x (sqrt 1.0)))) (cbrt (sqrt (- x (sqrt 1.0)))))
0.6b	(cbrt (sqrt (- x (sqrt 1.0))))
0.6b	(cbrt (sqrt (- x (sqrt 1.0))))
0.6b	(cbrt (sqrt (- x (sqrt 1.0))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

87×	`cbrt-prod`
80×	`add-sqr-sqrt`
67×	`sqrt-prod`
42×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`cbrt-div` `sqrt-div` `swap-sqr` `difference-of-squares`
12×	`associate-r` `associate-l`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `unswap-sqr`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

57.0ms	(* (cbrt (sqrt (- x (sqrt 1.0)))) (cbrt (sqrt (- x (sqrt 1.0)))))
6.0ms	(cbrt (sqrt (- x (sqrt 1.0))))
6.0ms	(cbrt (sqrt (- x (sqrt 1.0))))
6.0ms	(cbrt (sqrt (- x (sqrt 1.0))))

series946.0ms

Counts

4 → 12

Calls

4 calls:

331.0ms	(* (cbrt (sqrt (- x (sqrt 1.0)))) (cbrt (sqrt (- x (sqrt 1.0)))))
202.0ms	(cbrt (sqrt (- x (sqrt 1.0))))
209.0ms	(cbrt (sqrt (- x (sqrt 1.0))))
205.0ms	(cbrt (sqrt (- x (sqrt 1.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	480	1882
1	1732	1759
2	5001	1626

prune437.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.4s

Algorithm

intervals

Results

346.0ms	7752×	body	160	nan
332.0ms	16280×	body	80	nan
227.0ms	8000×	body	80	valid