Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify18.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
27.4b	(sqrt (+ (* x x) (* y y)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

12.0ms	(+ (* x x) (* y y))
12.0ms	(sqrt (+ (* x x) (* y y)))

series98.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(+ (* x x) (* y y))
59.0ms	(sqrt (+ (* x x) (* y y)))

simplify791.0ms

Counts: 32 → 32

prune127.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
5.5b	(exp (log (sqrt (+ (* x x) (* y y)))))
27.4b	(sqrt (+ (* x x) (* y y)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

13.0ms	(+ (* x x) (* y y))
18.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
13.0ms	(sqrt (+ (* x x) (* y y)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* x x) (* y y))
50.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
61.0ms	(sqrt (+ (* x x) (* y y)))

simplify717.0ms

Counts: 57 → 57

prune179.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
6.3b	(pow (exp (/ 1 2)) (log (+ (* x x) (* y y))))
28.4b	(log (+ (* x x) (* y y)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `pow-pow` `*-un-lft-identity`
13×	`exp-prod`
9×	`times-frac`
6×	`pow1` `log-prod`
5×	`add-log-exp`
4×	`add-exp-log` `log-div` `pow-unpow`
3×	`unpow-prod-up` `unpow-prod-down` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`log-pow` `pow-sub`
1×	`+-commutative` `pow-to-exp` `exp-sqrt` `rem-log-exp` `pow-exp` `sum-log` `sqrt-pow2` `div-inv` `sqr-pow`

Counts

3 → 62

Calls

3 calls:

9.0ms	(+ (* x x) (* y y))
19.0ms	(pow (exp (/ 1 2)) (log (+ (* x x) (* y y))))
10.0ms	(log (+ (* x x) (* y y)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* x x) (* y y))
121.0ms	(pow (exp (/ 1 2)) (log (+ (* x x) (* y y))))
79.0ms	(log (+ (* x x) (* y y)))

simplify968.0ms

Counts: 71 → 71

prune246.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

localize49.0ms

Local error

Found 4 expressions with local error:

5.8b	(pow (pow (exp (/ 1 2)) (* (cbrt (log (+ (* x x) (* y y)))) (cbrt (log (+ (* x x) (* y y)))))) (cbrt (log (+ (* x x) (* y y)))))
28.4b	(log (+ (* x x) (* y y)))
28.4b	(log (+ (* x x) (* y y)))
28.4b	(log (+ (* x x) (* y y)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

22.0ms	(pow (pow (exp (/ 1 2)) (* (cbrt (log (+ (* x x) (* y y)))) (cbrt (log (+ (* x x) (* y y)))))) (cbrt (log (+ (* x x) (* y y)))))
11.0ms	(log (+ (* x x) (* y y)))
19.0ms	(log (+ (* x x) (* y y)))
12.0ms	(log (+ (* x x) (* y y)))

series716.0ms

Counts

4 → 12

Calls

4 calls:

470.0ms	(pow (pow (exp (/ 1 2)) (* (cbrt (log (+ (* x x) (* y y)))) (cbrt (log (+ (* x x) (* y y)))))) (cbrt (log (+ (* x x) (* y y)))))
87.0ms	(log (+ (* x x) (* y y)))
81.0ms	(log (+ (* x x) (* y y)))
78.0ms	(log (+ (* x x) (* y y)))

simplify831.0ms

Counts: 81 → 81

prune305.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

regimes380.0ms

Accuracy

58.6% (9.6b remaining)

Error of 17.5b against oracle of 7.9b and baseline of 31.2b

bsearch55.0ms

Steps

Iters	Range		Point
9	3.828787491213863e+135	1.1582935083099526e+141	2.931608767883357e+138
9	-2.0350997751618612e+124	-4.455739765009825e+115	-8.953163933293596e+119

simplify16.0ms

end0.0ms

sample552.0ms

Algorithm

intervals

Results

303.0ms

8000×

body

valid