Details

sample173.0ms

Algorithm

intervals

Results

108.0ms	882×	body	80	nan
34.0ms	297×	body	80	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
5	2003
4	806
3	225
2	76
1	30
0	14

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
7.6b	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
24×	`associate-r` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
9×	`associate-l` `associate-*r/`
8×	`sqrt-prod`
6×	`flip3--` `sqrt-div` `flip--`
4×	`associate-/r*` `associate-/r/` `insert-posit16` `add-log-exp` `difference-of-squares`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `sub-neg` `distribute-lft-in` `sqrt-pow1` `div-exp` `associate-l/` `-commutative` `div-inv` `distribute-lft-out--`
1×	`clear-num` `frac-2neg` `pow1/2`

Counts

4 → 121

Calls

4 calls:

23.0ms	(* 9 (- a (/ 1.0 3.0)))
10.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
18.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
73.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))

series433.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 9 (- a (/ 1.0 3.0)))
68.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
139.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
179.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))

simplify900.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	2000
2	2000
1	624
0	249

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- a (/ 1.0 3.0)) (* (- a (/ 1.0 3.0)) (/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))))
0.2b	(/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))
0.2b	(* 3 (sqrt (- a (/ 1.0 3.0))))
7.6b	(* (- a (/ 1.0 3.0)) (/ rand (* 3 (sqrt (- a (/ 1.0 3.0))))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`add-cbrt-cube` `add-exp-log`
18×	`associate-r`
16×	`*-un-lft-identity`
14×	`flip3--` `flip--`
12×	`add-cube-cbrt`
10×	`frac-add`
9×	`associate-l` `associate-*r/` `add-log-exp`
8×	`pow1` `times-frac`
7×	`sqrt-prod`
6×	`frac-times` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r/` `insert-posit16` `difference-of-squares`
3×	`associate-/l*` `unswap-sqr`
2×	`associate-+l+` `sum-log` `pow-prod-down` `*-commutative` `div-inv` `distribute-lft-out--`
1×	`+-commutative` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `associate-+l-` `flip-+`

Counts

4 → 115

Calls

4 calls:

37.0ms	(+ (- a (/ 1.0 3.0)) (* (- a (/ 1.0 3.0)) (/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))))
11.0ms	(/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))
20.0ms	(* 3 (sqrt (- a (/ 1.0 3.0))))
80.0ms	(* (- a (/ 1.0 3.0)) (/ rand (* 3 (sqrt (- a (/ 1.0 3.0))))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ (- a (/ 1.0 3.0)) (* (- a (/ 1.0 3.0)) (/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))))
142.0ms	(/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))
82.0ms	(* 3 (sqrt (- a (/ 1.0 3.0))))
129.0ms	(* (- a (/ 1.0 3.0)) (/ rand (* 3 (sqrt (- a (/ 1.0 3.0))))))

simplify1.0s

Counts

127 → 127

Iterations

Iter	Nodes
done	2000
2	2000
1	804
0	289

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.0b	(+ (- a (/ 1.0 3.0)) (* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))
7.6b	(* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0)))))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
356×	`add-sqr-sqrt`
252×	`*-un-lft-identity`
194×	`add-cube-cbrt`
170×	`sqrt-prod`
123×	`associate-r`
58×	`difference-of-squares`
29×	`distribute-lft-out--`
21×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
14×	`flip3--` `flip--`
13×	`associate-/l*`
10×	`frac-add`
9×	`associate-/r*` `add-log-exp`
7×	`pow1`
6×	`frac-times` `cbrt-undiv` `sqrt-div` `div-exp` `associate-l` `associate-*l/`
5×	`unswap-sqr`
4×	`associate-/r/` `insert-posit16`
3×	`prod-exp` `associate-*r/` `cbrt-unprod`
2×	`associate-+l+` `sum-log`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `*-commutative` `associate-+l-` `flip-+` `associate-/l/`

Counts

4 → 357

Calls

4 calls:

15.0ms	(sqrt (- a (/ 1.0 3.0)))
64.0ms	(+ (- a (/ 1.0 3.0)) (* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))))
31.0ms	(/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))
66.0ms	(* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0)))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- a (/ 1.0 3.0)))
115.0ms	(+ (- a (/ 1.0 3.0)) (* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))))
176.0ms	(/ (/ rand 3) (sqrt (- a (/ 1.0 3.0))))
171.0ms	(* (- a (/ 1.0 3.0)) (/ (/ rand 3) (sqrt (- a (/ 1.0 3.0)))))

simplify1.4s

Counts

369 → 369

Iterations

Iter	Nodes
done	2001
2	2001
1	1522
0	558

prune3.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a (/ 1.0 3.0)) 3)
0.0b	(+ (- a (/ 1.0 3.0)) (* (/ (- a (/ 1.0 3.0)) 3) (/ rand (sqrt (- a (/ 1.0 3.0))))))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
7.6b	(* (/ (- a (/ 1.0 3.0)) 3) (/ rand (sqrt (- a (/ 1.0 3.0)))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
111×	`times-frac`
87×	`*-un-lft-identity`
59×	`add-cube-cbrt`
44×	`sqrt-prod`
33×	`associate-r`
28×	`difference-of-squares`
22×	`associate-l`
20×	`add-cbrt-cube` `add-exp-log`
14×	`distribute-lft-out--`
12×	`associate-/r*`
9×	`associate-/l*` `add-log-exp`
6×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `frac-add` `flip--` `unswap-sqr`
4×	`sqrt-div` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `div-inv`
3×	`frac-times` `associate-l/` `associate-r/`
2×	`associate-+l+` `clear-num` `sum-log` `frac-2neg` `associate-/l/`
1×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `div-sub` `pow-prod-down` `*-commutative` `associate-+l-` `flip-+`

Counts

4 → 201

Calls

4 calls:

19.0ms	(/ (- a (/ 1.0 3.0)) 3)
43.0ms	(+ (- a (/ 1.0 3.0)) (* (/ (- a (/ 1.0 3.0)) 3) (/ rand (sqrt (- a (/ 1.0 3.0))))))
12.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
61.0ms	(* (/ (- a (/ 1.0 3.0)) 3) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- a (/ 1.0 3.0)) 3)
150.0ms	(+ (- a (/ 1.0 3.0)) (* (/ (- a (/ 1.0 3.0)) 3) (/ rand (sqrt (- a (/ 1.0 3.0))))))
116.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
184.0ms	(* (/ (- a (/ 1.0 3.0)) 3) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify1.3s

Counts

213 → 213

Iterations

Iter	Nodes
done	2001
2	2001
1	995
0	359

prune2.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes152.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.9s	27172×	body	80	nan
1.6s	9137×	body	80	valid