Details

sample127.0ms

Algorithm

intervals

Results

74.0ms	810×	body	80	nan
24.0ms	292×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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

rewrite113.0ms

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/` `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 → 140

Calls

4 calls:

25.0ms	(* 9 (- a (/ 1.0 3.0)))
10.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
27.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
49.0ms	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))

series341.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* 9 (- a (/ 1.0 3.0)))
84.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
77.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
113.0ms	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))

simplify2.9s

Counts

152 → 152

Iterations

Iter	Nodes
3	6141
2	1942
1	659
0	252

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

243×	`add-sqr-sqrt`
157×	`times-frac`
124×	`*-un-lft-identity`
86×	`sqrt-prod`
66×	`difference-of-squares`
60×	`associate-r`
58×	`add-cube-cbrt`
33×	`distribute-lft-out--`
18×	`add-cbrt-cube` `add-exp-log`
13×	`associate-l`
10×	`pow1`
9×	`associate-/r*` `add-log-exp`
7×	`flip3--` `flip--`
6×	`sqrt-div` `frac-add` `associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `associate-/r/` `cbrt-unprod`
3×	`frac-times` `associate-l/` `associate-r/` `div-inv`
2×	`associate-+l+` `sum-log` `sqrt-pow1` `pow1/2` `pow-div` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-prod-down` `*-commutative` `associate-+l-` `flip-+`

Counts

4 → 226

Calls

4 calls:

8.0ms	(sqrt (- a (/ 1.0 3.0)))
45.0ms	(+ (- a (/ 1.0 3.0)) (* (/ rand 3) (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))))
64.0ms	(* (/ rand 3) (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))))
37.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (- a (/ 1.0 3.0)))
148.0ms	(+ (- a (/ 1.0 3.0)) (* (/ rand 3) (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))))
153.0ms	(* (/ rand 3) (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))))
80.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

simplify2.0s

Counts

238 → 238

Iterations

Iter	Nodes
2	3756
1	1053
0	360

prune2.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (sqrt a) (/ (sqrt 1.0) (sqrt 3.0)))
0.4b	(/ (+ (sqrt a) (/ (sqrt 1.0) (sqrt 3.0))) (/ 3 rand))
1.0b	(/ (sqrt 1.0) (sqrt 3.0))
1.0b	(/ (sqrt 1.0) (sqrt 3.0))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac`
139×	`*-un-lft-identity`
137×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
97×	`sqrt-prod`
25×	`associate-/r*`
16×	`associate-/l*`
14×	`distribute-lft-out`
13×	`add-cbrt-cube` `add-exp-log`
10×	`difference-of-squares`
8×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`clear-num` `frac-2neg`
2×	`sqrt-undiv` `associate-/l/`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `associate-/r/` `flip-+` `flip--` `distribute-lft-out--`

Counts

4 → 231

Calls

4 calls:

14.0ms	(- (sqrt a) (/ (sqrt 1.0) (sqrt 3.0)))
34.0ms	(/ (+ (sqrt a) (/ (sqrt 1.0) (sqrt 3.0))) (/ 3 rand))
9.0ms	(/ (sqrt 1.0) (sqrt 3.0))
9.0ms	(/ (sqrt 1.0) (sqrt 3.0))

series287.0ms

Counts

4 → 8

Calls

4 calls:

78.0ms	(- (sqrt a) (/ (sqrt 1.0) (sqrt 3.0)))
209.0ms	(/ (+ (sqrt a) (/ (sqrt 1.0) (sqrt 3.0))) (/ 3 rand))
0.0ms	(/ (sqrt 1.0) (sqrt 3.0))
0.0ms	(/ (sqrt 1.0) (sqrt 3.0))

simplify2.8s

Counts

239 → 239

Iterations

Iter	Nodes
3	5544
2	1995
1	716
0	306

prune3.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.2b	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `times-frac`
24×	`associate-l` `add-cube-cbrt`
19×	`add-exp-log`
15×	`pow1`
13×	`add-cbrt-cube`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
5×	`prod-exp`
4×	`frac-times` `associate-/r*` `sqrt-pow1` `div-exp` `pow-prod-down` `associate-/r/` `pow-flip` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `associate-l/` `cbrt-unprod` `flip-+` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `pow1/2` `1-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `distribute-lft-out--` `inv-pow`

Counts

4 → 124

Calls

4 calls:

28.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
6.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
17.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
62.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)

series523.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
73.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
116.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
243.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)

simplify1.7s

Counts

136 → 136

Iterations

Iter	Nodes
2	2571
1	740
0	277

prune1.7s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes164.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	14
1	14
0	12

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.8s	27547×	body	80	nan
1.3s	9085×	body	80	valid