Details

sample192.0ms

Algorithm

intervals

Results

103.0ms	1052×	body	80	nan
27.0ms	300×	body	80	valid

simplify6.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	2025
6	1131
5	730
4	405
3	185
2	72
1	27
0	13

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize117.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

180.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
158.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
38.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
22.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series831.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
277.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
213.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
127.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify6.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5011
2	3314
1	862
0	307

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize170.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
0.2b	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.4b	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

rewrite645.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-sqr-sqrt`
102×	`times-frac`
76×	`*-un-lft-identity`
62×	`add-exp-log` `sqrt-prod`
54×	`add-cube-cbrt`
39×	`associate-r`
38×	`add-cbrt-cube`
29×	`associate-l`
26×	`prod-exp`
17×	`div-exp`
16×	`difference-of-squares` `unswap-sqr`
14×	`cbrt-unprod`
13×	`pow1`
9×	`cbrt-undiv` `associate-/r*`
8×	`distribute-lft-out--`
7×	`associate-*l/`
6×	`frac-times`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`rec-exp` `sqrt-div` `1-exp` `associate-*r/` `associate-/r/` `insert-posit16` `add-log-exp`
3×	`flip3-+` `-commutative` `flip-+` `div-inv` `associate-/l`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in`

Counts

4 → 213

Calls

4 calls:

157.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
229.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
50.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
175.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

306.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
395.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
125.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
314.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

simplify8.3s

Counts

225 → 225

Iterations

Iter	Nodes
done	5015
2	4597
1	1230
0	419

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize201.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* rand (/ 1.0 (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (* rand (/ 1.0 (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0))))
0.3b	(* rand (/ 1.0 (sqrt 9.0)))

rewrite663.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`times-frac`
28×	`sqrt-prod`
26×	`associate-r`
25×	`add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
9×	`pow1` `associate-/r` `associate-l*`
8×	`difference-of-squares`
5×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `cbrt-unprod` `flip--`
4×	`frac-times` `sqrt-div` `associate-*r/` `insert-posit16` `distribute-lft-out--` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `flip-+`
2×	`pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `div-inv`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `distribute-lft-out` `associate-/l*` `associate-/l/`

Counts

4 → 134

Calls

4 calls:

59.0ms	(sqrt (- a (/ 1.0 3.0)))
441.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* rand (/ 1.0 (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0))))))
93.0ms	(/ (* rand (/ 1.0 (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0))))
50.0ms	(* rand (/ 1.0 (sqrt 9.0)))

series822.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (- a (/ 1.0 3.0)))
269.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* rand (/ 1.0 (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0))))))
375.0ms	(/ (* rand (/ 1.0 (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0))))
95.0ms	(* rand (/ 1.0 (sqrt 9.0)))

simplify6.0s

Counts

146 → 146

Iterations

Iter	Nodes
done	5131
2	3284
1	867
0	306

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize105.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
0.2b	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite402.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

117.0ms	(* 9.0 (- a (/ 1.0 3.0)))
179.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
61.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
31.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* 9.0 (- a (/ 1.0 3.0)))
169.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
252.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
109.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify5.1s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	2818
1	766
0	274

prune1.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes661.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.7s	27169×	body	80	nan
1.0s	9178×	body	80	valid