Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify22.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

16.0ms	(+ (* x x) (* y y))
126.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
54.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series372.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (* x x) (* y y))
93.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
244.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.0s

Counts: 74 → 74

prune385.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
32.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite580.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 75

Calls

3 calls:

14.0ms	(+ (* x x) (* y y))
506.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
57.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series458.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* x x) (* y y))
261.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
162.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.9s

Counts: 84 → 84

prune296.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(/ (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (sqrt 3.0))
32.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

8.0ms	(+ (* x x) (* y y))
69.0ms	(/ (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (sqrt 3.0))
49.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series585.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* x x) (* y y))
371.0ms	(/ (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (sqrt 3.0))
177.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.6s

Counts: 65 → 65

prune202.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 16.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
0.4b	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
1.0b	(/ 1 (sqrt 3.0))
32.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

170×	`sqrt-prod`
148×	`add-sqr-sqrt`
120×	`times-frac`
83×	`*-un-lft-identity`
75×	`add-cube-cbrt`
25×	`associate-r` `associate-l`
24×	`unswap-sqr`
12×	`add-exp-log` `associate-/r*`
11×	`pow1`
10×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`sqrt-div` `div-inv`
4×	`sqrt-pow1` `pow1/2` `add-log-exp`
3×	`rem-sqrt-square` `pow-flip` `div-exp` `pow-prod-down`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `rec-exp` `flip3-+` `sqrt-unprod` `1-exp` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `inv-pow`

Counts

4 → 212

Calls

4 calls:

120.0ms	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
108.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
12.0ms	(/ 1 (sqrt 3.0))
51.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

series815.0ms

Counts

4 → 10

Calls

4 calls:

245.0ms	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
147.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
0.0ms	(/ 1 (sqrt 3.0))
423.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

simplify872.0ms

Counts: 222 → 222

prune775.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 16.6b

regimes613.0ms

Accuracy

61.6% (7.4b remaining)

Error of 25.7b against oracle of 18.3b and baseline of 37.5b

bsearch107.0ms

Steps

Iters	Range		Point
8	8.450123646982779e+130	1.3503261361162568e+135	9.739776979507706e+134
5	-2.294626366488831e+97	-1.033466382081211e+97	-1.472200864118953e+97

simplify71.0ms

end0.0ms

sample928.0ms

Algorithm

intervals

Results

594.0ms

8000×

body

valid