Details

sample27.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify3.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.9b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`times-frac`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`rem-sqrt-square` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `clear-num` `flip-+`

Counts

2 → 54

Calls

2 calls:

96.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
47.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series314.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
227.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify74.0ms

Counts: 60 → 60

prune253.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (/ 6004799503160661.0 18014398509481984.0) (+ (pow x 2) (+ (pow y 2) (pow z 2))))
34.9b	(sqrt (* (/ 6004799503160661.0 18014398509481984.0) (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
13×	`associate-l`
10×	`add-cube-cbrt` `times-frac`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r`
5×	`sqrt-div` `distribute-lft-out`
4×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
3×	`unpow-prod-down`
2×	`sqrt-pow1` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `pow1/2` `div-exp` `sqrt-prod` `*-commutative` `div-inv`

Counts

2 → 57

Calls

2 calls:

213.0ms	(* (/ 6004799503160661.0 18014398509481984.0) (+ (pow x 2) (+ (pow y 2) (pow z 2))))
65.0ms	(sqrt (* (/ 6004799503160661.0 18014398509481984.0) (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series265.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(* (/ 6004799503160661.0 18014398509481984.0) (+ (pow x 2) (+ (pow y 2) (pow z 2))))
209.0ms	(sqrt (* (/ 6004799503160661.0 18014398509481984.0) (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify43.0ms

Counts: 63 → 63

prune220.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
0.2b	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
34.9b	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

526×	`times-frac`
405×	`sqrt-prod`
295×	`add-sqr-sqrt`
278×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-/l*`
16×	`div-inv`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
7×	`rem-sqrt-square`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

3 → 369

Calls

3 calls:

109.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
96.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
59.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

series733.0ms

Counts

3 → 9

Calls

3 calls:

259.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
188.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
286.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

simplify105.0ms

Counts: 378 → 378

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 18.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
34.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.9b	(sqrt (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

rewrite751.0ms

Algorithm

rewrite-expression-head

Rules

5195×	`times-frac`
3492×	`sqrt-prod`
2356×	`add-sqr-sqrt`
2291×	`*-un-lft-identity`
2285×	`add-cube-cbrt`
167×	`sqrt-div`
164×	`associate-/r/`
132×	`div-inv`
83×	`flip3-+` `flip-+`
40×	`associate-/l*`
24×	`rem-sqrt-square` `associate-/r*`
16×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-undiv` `div-exp`
7×	`pow1`
4×	`add-log-exp`
3×	`sqrt-pow1` `pow1/2`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 2071

Calls

4 calls:

137.0ms	(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
35.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
275.0ms	(sqrt (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

series573.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
125.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
134.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
245.0ms	(sqrt (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

simplify737.0ms

Counts: 2083 → 2083

prune9.0s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 18.3b

regimes605.0ms

Accuracy

59.3% (8.2b remaining)

Error of 26.4b against oracle of 18.2b and baseline of 38.2b

bsearch105.0ms

Steps

Iters	Range		Point
9	1.6558114091021875e+84	4.612323731361669e+91	4.376373199179286e+91
7	-1.8875295458160305e+40	-3.852270064556066e+38	-1.8637040731758233e+40

simplify67.0ms

end0.0ms

sample820.0ms

Algorithm

intervals

Results

516.0ms

8000×

body

valid