Details

sample24.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize10.0ms

Local error

Found 1 expressions with local error:

29.3b

(sqrt (+ (* x x) (* y y)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

13.0ms

(sqrt (+ (* x x) (* y y)))

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(sqrt (+ (* x x) (* y y)))

simplify143.0ms

Counts: 18 → 18

prune72.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.2b

localize17.0ms

Local error

Found 2 expressions with local error:

5.8b	(exp (log (sqrt (+ (* x x) (* y y)))))
29.3b	(sqrt (+ (* x x) (* y y)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `log-prod` `exp-prod` `*-un-lft-identity` `exp-sum` `sqrt-prod`
5×	`pow1`
4×	`sqrt-div`
3×	`log-pow`
2×	`add-exp-log` `log-div` `sqrt-pow1` `flip3-+` `pow1/2` `exp-diff` `add-cbrt-cube` `flip-+` `add-log-exp`
1×	`rem-sqrt-square` `rem-exp-log`

Counts

2 → 37

Calls

2 calls:

17.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
14.0ms	(sqrt (+ (* x x) (* y y)))

series113.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
60.0ms	(sqrt (+ (* x x) (* y y)))

simplify140.0ms

Counts: 43 → 43

prune125.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

localize35.0ms

Local error

Found 4 expressions with local error:

5.8b	(pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))
29.3b	(sqrt (+ (* x x) (* y y)))
29.3b	(sqrt (+ (* x x) (* y y)))
29.3b	(sqrt (+ (* x x) (* y y)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow-unpow` `sqrt-prod`
6×	`cbrt-prod` `sqrt-div`
5×	`add-log-exp`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube`
3×	`unpow-prod-down` `rem-sqrt-square` `pow-pow` `flip3-+` `log-pow` `flip-+`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

10.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))
10.0ms	(sqrt (+ (* x x) (* y y)))
9.0ms	(sqrt (+ (* x x) (* y y)))
9.0ms	(sqrt (+ (* x x) (* y y)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

378.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))
41.0ms	(sqrt (+ (* x x) (* y y)))
41.0ms	(sqrt (+ (* x x) (* y y)))
50.0ms	(sqrt (+ (* x x) (* y y)))

simplify84.0ms

Counts: 82 → 82

prune381.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

localize48.0ms

Local error

Found 4 expressions with local error:

5.9b	(pow (pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt 1/2)) (cbrt (log (+ (* x x) (* y y)))))
29.3b	(sqrt (+ (* x x) (* y y)))
29.3b	(sqrt (+ (* x x) (* y y)))
30.5b	(log (+ (* x x) (* y y)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`unpow-prod-down`
8×	`pow1`
7×	`pow-unpow`
6×	`add-exp-log` `sqrt-prod`
4×	`cbrt-prod` `sqrt-div` `pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`log-prod` `flip3-+` `flip-+`
2×	`pow-to-exp` `rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `log-pow` `sqr-pow`
1×	`pow-pow` `rem-log-exp`

Counts

4 → 71

Calls

4 calls:

12.0ms	(pow (pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt 1/2)) (cbrt (log (+ (* x x) (* y y)))))
15.0ms	(sqrt (+ (* x x) (* y y)))
13.0ms	(sqrt (+ (* x x) (* y y)))
10.0ms	(log (+ (* x x) (* y y)))

series826.0ms

Counts

4 → 12

Calls

4 calls:

664.0ms	(pow (pow (exp (* (cbrt (log (sqrt (+ (* x x) (* y y))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))) (cbrt 1/2)) (cbrt (log (+ (* x x) (* y y)))))
50.0ms	(sqrt (+ (* x x) (* y y)))
43.0ms	(sqrt (+ (* x x) (* y y)))
69.0ms	(log (+ (* x x) (* y y)))

simplify65.0ms

Counts: 83 → 83

prune497.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

regimes335.0ms

Accuracy

59.9% (9.6b remaining)

Error of 17.4b against oracle of 7.8b and baseline of 31.8b

bsearch122.0ms

Steps

Iters	Range		Point
6	5.821487682704008e+89	6.005187599711439e+90	5.899170308214914e+90
8	2.7254438761517156e-266	2.170652764408631e-263	1.1651218342937014e-265
9	-4.1201153154948957e-246	-2.4644447198226205e-252	-1.0549430860212959e-251
8	-1.8374033615322846e+99	-2.2216582865176536e+95	-1.698394078287103e+99

simplify47.0ms

end0.0ms

sample620.0ms

Algorithm

intervals

Results

375.0ms

8000×

body

valid