Details

sample193.0ms

Algorithm

intervals

Results

106.0ms	926×	body	80	nan
45.0ms	285×	body	80	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
7	3296
6	1984
5	1152
4	612
3	202
2	71
1	28
0	14

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.2b	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.3b	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
59×	`times-frac`
50×	`*-un-lft-identity`
36×	`associate-r`
30×	`add-cube-cbrt`
20×	`difference-of-squares`
14×	`sqrt-prod`
13×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
10×	`distribute-lft-out--`
9×	`associate-*r/`
6×	`sqrt-div` `associate-l` `associate-/l*`
5×	`flip3--` `flip--`
4×	`associate-/r*` `associate-/r/` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `associate-/l/`
1×	`clear-num` `frac-2neg` `pow1/2` `div-sub`

Counts

4 → 144

Calls

4 calls:

37.0ms	(* 9 (- a (/ 1.0 3.0)))
80.0ms	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
30.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
6.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* 9 (- a (/ 1.0 3.0)))
126.0ms	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
106.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
91.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify3.1s

Counts

156 → 156

Iterations

Iter	Nodes
3	6256
2	1922
1	663
0	256

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (sqrt a) (sqrt (/ 1.0 3.0)))
0.1b	(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
0.2b	(* rand (* (/ (+ (sqrt (/ 1.0 3.0)) (sqrt a)) 3) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (+ (sqrt (/ 1.0 3.0)) (sqrt a)) 3)

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

263×	`add-sqr-sqrt`
179×	`sqrt-prod`
148×	`times-frac`
133×	`*-un-lft-identity`
90×	`difference-of-squares`
49×	`add-cube-cbrt`
34×	`distribute-lft-out--`
26×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
12×	`associate-/r*`
9×	`pow1` `prod-exp` `cbrt-unprod`
8×	`distribute-lft-out`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`associate-*r/` `insert-posit16` `associate-/l/`
3×	`flip3--` `associate-l` `pow-prod-down` `flip--`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-/r/` `div-inv`
1×	`frac-times` `sub-neg` `flip3-+` `diff-log` `div-sub` `associate-r` `associate-l/` `-commutative` `flip-+`

Counts

4 → 224

Calls

4 calls:

18.0ms	(- (sqrt a) (sqrt (/ 1.0 3.0)))
57.0ms	(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
140.0ms	(* rand (* (/ (+ (sqrt (/ 1.0 3.0)) (sqrt a)) 3) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))))
60.0ms	(/ (+ (sqrt (/ 1.0 3.0)) (sqrt a)) 3)

series1.3s

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (sqrt a) (sqrt (/ 1.0 3.0)))
291.0ms	(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
887.0ms	(* rand (* (/ (+ (sqrt (/ 1.0 3.0)) (sqrt a)) 3) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))))
78.0ms	(/ (+ (sqrt (/ 1.0 3.0)) (sqrt a)) 3)

simplify1.8s

Counts

236 → 236

Iterations

Iter	Nodes
2	3699
1	1121
0	435

prune3.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (sqrt a) (sqrt (/ 1.0 3.0)))
0.1b	(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
0.3b	(* rand (* (+ (sqrt (/ 1.0 3.0)) (sqrt a)) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (* rand (* (+ (sqrt (/ 1.0 3.0)) (sqrt a)) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))))) 3)

rewrite594.0ms

Algorithm

rewrite-expression-head

Rules

255×	`add-sqr-sqrt`
171×	`sqrt-prod`
136×	`times-frac`
109×	`*-un-lft-identity`
90×	`difference-of-squares`
41×	`add-cube-cbrt`
34×	`distribute-lft-out--`
29×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r` `associate-r/` `associate-/l*`
10×	`prod-exp` `cbrt-unprod`
9×	`pow1`
7×	`cbrt-undiv` `div-exp` `associate-/l/`
6×	`add-log-exp`
4×	`frac-times` `flip3-+` `associate-*l/` `flip-+` `insert-posit16`
3×	`flip3--` `associate-l` `pow-prod-down` `flip--`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-/r/` `div-inv`
1×	`sub-neg` `diff-log` `div-sub` `associate-r` `*-commutative`

Counts

4 → 215

Calls

4 calls:

15.0ms	(- (sqrt a) (sqrt (/ 1.0 3.0)))
48.0ms	(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
81.0ms	(* rand (* (+ (sqrt (/ 1.0 3.0)) (sqrt a)) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))))
440.0ms	(/ (* rand (* (+ (sqrt (/ 1.0 3.0)) (sqrt a)) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))))) 3)

series1.9s

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (sqrt a) (sqrt (/ 1.0 3.0)))
246.0ms	(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
771.0ms	(* rand (* (+ (sqrt (/ 1.0 3.0)) (sqrt a)) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))))
792.0ms	(/ (* rand (* (+ (sqrt (/ 1.0 3.0)) (sqrt a)) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))))) 3)

simplify1.5s

Counts

227 → 227

Iterations

Iter	Nodes
2	4100
1	1150
0	432

prune2.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.2b	(* rand (* 1/3 (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))))
0.4b	(* 1/3 (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))))
0.5b	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

227×	`add-sqr-sqrt`
143×	`times-frac`
119×	`*-un-lft-identity`
85×	`sqrt-prod`
66×	`difference-of-squares`
61×	`associate-r`
53×	`add-cube-cbrt`
33×	`distribute-lft-out--`
20×	`add-cbrt-cube` `add-exp-log`
15×	`pow1`
9×	`associate-/r*`
7×	`prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-l` `associate-/l*`
4×	`flip3--` `pow-prod-down` `associate-/r/` `insert-posit16` `flip--` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-*r/` `unswap-sqr`
2×	`sqrt-pow1` `pow1/2` `*-commutative` `div-inv` `pow-div` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `div-sub`

Counts

4 → 211

Calls

4 calls:

13.0ms	(sqrt (- a (/ 1.0 3.0)))
45.0ms	(* rand (* 1/3 (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))))
51.0ms	(* 1/3 (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))))
41.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (- a (/ 1.0 3.0)))
158.0ms	(* rand (* 1/3 (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))))
104.0ms	(* 1/3 (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))))
62.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

simplify820.0ms

Counts

223 → 223

Iterations

Iter	Nodes
2	2310
1	780
0	297

prune2.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes180.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	21
1	21
0	17

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.8s	27076×	body	80	nan
1.4s	9100×	body	80	valid