Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify3.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.3b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite111.0ms

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:

79.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
31.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series235.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
177.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify91.0ms

Counts: 60 → 60

prune186.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.3b	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
24×	`sqrt-prod`
22×	`times-frac` `associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
17×	`sqrt-div`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `associate-l` `flip-+` `unswap-sqr`
4×	`frac-times` `sqrt-pow1` `associate-*l/` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `div-exp` `*-commutative` `div-inv`

Counts

4 → 98

Calls

4 calls:

138.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
30.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
47.0ms	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
113.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
109.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
180.0ms	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify46.0ms

Counts: 110 → 110

prune283.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 20.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`associate-r`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
9×	`sqrt-div`
8×	`unswap-sqr`
7×	`pow1`
6×	`associate-l`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`frac-times` `associate-*l/` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `div-inv`

Counts

2 → 64

Calls

2 calls:

81.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series285.0ms

Counts

2 → 6

Calls

2 calls:

180.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
105.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify59.0ms

Counts: 70 → 70

prune177.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 20.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.9b	(exp (log (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`sqrt-prod`
17×	`*-un-lft-identity`
16×	`sqrt-div` `associate-r`
15×	`add-cube-cbrt`
13×	`pow1` `times-frac`
8×	`unswap-sqr`
7×	`exp-prod`
6×	`associate-l` `pow-prod-down`
5×	`add-exp-log` `log-div` `sqrt-pow1` `flip3-+` `pow1/2` `exp-diff` `add-cbrt-cube` `flip-+`
4×	`frac-times` `associate-*l/` `log-pow`
3×	`add-log-exp`
2×	`associate-*r/`
1×	`rem-sqrt-square` `log-prod` `sqrt-unprod` `exp-sum` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `rem-exp-log`

Counts

3 → 85

Calls

3 calls:

82.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
105.0ms	(exp (log (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))))
37.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series459.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
177.0ms	(exp (log (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))))
107.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify64.0ms

Counts: 94 → 94

prune253.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 20.4b

regimes524.0ms

Accuracy

64.2% (7.1b remaining)

Error of 25.7b against oracle of 18.6b and baseline of 38.5b

bsearch83.0ms

Steps

Iters	Range		Point
7	1.3902720376798892e+132	1.3995183731881648e+134	2.2733836340085665e+132
10	-7.258963654046787e+141	-6.600088119136522e+124	-2.8004366194075308e+135

simplify2.0ms

end0.0ms

sample721.0ms

Algorithm

intervals

Results

465.0ms

8000×

body

valid