Details

sample42.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify30.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.3b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

37.0ms	(+ (+ (* x x) (* y y)) (* z z))
12.0ms	(+ (* x x) (* y y))
105.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
51.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series426.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (+ (* x x) (* y y)) (* z z))
39.0ms	(+ (* x x) (* y y))
71.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
259.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify709.0ms

Counts: 90 → 90

prune392.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
36.3b	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 380

Calls

4 calls:

17.0ms	(+ (* x x) (* y y))
133.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
130.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
77.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

series817.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* x x) (* y y))
254.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
191.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
341.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

simplify1.3s

Counts: 392 → 392

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 16.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.3b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
36.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

31.0ms	(+ (+ (* x x) (* y y)) (* z z))
9.0ms	(+ (* x x) (* y y))
116.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (+ (* x x) (* y y)) (* z z))
36.0ms	(+ (* x x) (* y y))
218.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
174.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify736.0ms

Counts: 100 → 100

prune386.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 16.8b

localize14.0ms

Local error

Found 1 expressions with local error:

0.4b	(* (* -1 x) (sqrt (/ 1 3.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-r`
13×	`sqrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`distribute-lft-neg-out` `mul-1-neg` `sqrt-div` `associate-r/` `associate-l` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

53.0ms

(* (* -1 x) (sqrt (/ 1 3.0)))

series94.0ms

Counts

1 → 3

Calls

1 calls:

93.0ms

(* (* -1 x) (sqrt (/ 1 3.0)))

simplify1.5s

Counts: 36 → 36

prune73.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 16.8b

regimes890.0ms

Accuracy

63.8% (7.2b remaining)

Error of 25.7b against oracle of 18.5b and baseline of 38.5b

bsearch111.0ms

Steps

Iters	Range		Point
6	9.511611764451066e+128	1.0540223684506411e+130	1.0387356868587109e+130
10	-7.065909207097609e+129	-8.427565781023528e+111	-2.344189575344255e+116

simplify39.0ms

end0.0ms

sample959.0ms

Algorithm

intervals

Results

611.0ms

8000×

body

valid