Details

sample144.0ms

Algorithm

intervals

Results

54.0ms	854×	body	80	nan
29.0ms	289×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	72	20
3	190	20
4	459	20
5	929	20
6	1800	20
7	3828	20
done	5000	20

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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)
0.2b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`frac-times` `associate-/r*` `associate-/r/` `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` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 114

Calls

4 calls:

60.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
89.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
30.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
17.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series679.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
241.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
177.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
88.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.2s

Counts

126 → 126

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	303	2615
1	857	2480
2	4527	2306
done	5002	2304

prune576.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`times-frac`
11×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`associate-*r/`
6×	`flip3--` `flip--`
5×	`sqrt-prod`
4×	`frac-times` `sqrt-div` `associate-/r*` `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` `frac-2neg` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 104

Calls

4 calls:

41.0ms	(* 9.0 (- a (/ 1.0 3.0)))
53.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
26.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
12.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* 9.0 (- a (/ 1.0 3.0)))
158.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
188.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
76.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify1.6s

Counts

116 → 116

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	271	2223
1	764	2134
2	3569	1974
done	5000	1970

prune627.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

403×	`times-frac`
310×	`add-sqr-sqrt`
234×	`sqrt-prod`
232×	`*-un-lft-identity`
182×	`add-cube-cbrt`
50×	`difference-of-squares`
25×	`distribute-lft-out--`
22×	`associate-/l*`
11×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
6×	`pow1` `associate-l`
5×	`flip3--` `flip--`
4×	`frac-times` `sqrt-div`
3×	`cbrt-undiv` `flip3-+` `div-exp` `associate-r` `flip-+` `add-log-exp`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`

Counts

3 → 295

Calls

3 calls:

18.0ms	(sqrt (- a (/ 1.0 3.0)))
58.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))))
57.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series542.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(sqrt (- a (/ 1.0 3.0)))
234.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))))
259.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify701.0ms

Counts

304 → 304

Iterations

Useful iterations: done (670.0ms)

Iter	Nodes	Cost
0	491	7742
1	1250	7086
done	5000	6936

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

87.0ms	(* (cbrt 9.0) (- a (/ 1.0 3.0)))
86.0ms	(/ rand (sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))))
104.0ms	(* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))
69.0ms	(sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0)))))

series655.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (cbrt 9.0) (- a (/ 1.0 3.0)))
242.0ms	(/ rand (sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))))
192.0ms	(* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))
130.0ms	(sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0)))))

simplify2.0s

Counts

124 → 124

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	226	2323
1	585	2221
2	2905	1683
done	5001	1404

prune643.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes234.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	21
1	17	21
done	17	21

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.3s	27625×	body	80	nan
1.7s	9180×	body	80	valid