Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify3.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize9.0ms

Local error

Found 1 expressions with local error:

36.2b

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

rewrite43.0ms

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:

42.0ms

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

series109.0ms

Counts

1 → 3

Calls

1 calls:

109.0ms

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

simplify91.0ms

Counts: 18 → 18

prune54.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
0.5b	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

34.0ms	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
159.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
37.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
106.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
102.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
102.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify43.0ms

Counts: 146 → 146

prune276.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) 4)
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

40.0ms	(pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) 4)
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) 4)
105.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
104.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
109.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify92.0ms

Counts: 84 → 84

prune291.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.4b

localize35.0ms

Local error

Found 4 expressions with local error:

6.6b	(pow (pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (* (cbrt 4) (cbrt 4))) (cbrt 4))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

28×	`unpow-prod-down`
18×	`sqrt-prod`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
7×	`pow1`
6×	`add-exp-log` `pow-unpow` `sqrt-div`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-to-exp` `sqr-pow`
1×	`pow-pow`

Counts

4 → 80

Calls

4 calls:

80.0ms	(pow (pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (* (cbrt 4) (cbrt 4))) (cbrt 4))
40.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series773.0ms

Counts

4 → 12

Calls

4 calls:

447.0ms	(pow (pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (* (cbrt 4) (cbrt 4))) (cbrt 4))
109.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
108.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
108.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify68.0ms

Counts: 92 → 92

prune358.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.4b

regimes403.0ms

Accuracy

64.4% (7.1b remaining)

Error of 25.6b against oracle of 18.5b and baseline of 38.4b

bsearch57.0ms

Steps

Iters	Range		Point
7	1.3902720376798892e+132	1.3995183731881648e+134	2.2733836340085665e+132
10	-7.258963654046787e+141	-6.600088119136522e+124	-1.514147348156685e+135

simplify1.0ms

end0.0ms

sample645.0ms

Algorithm

intervals

Results

406.0ms

8000×

body

valid