Details

sample68.0ms

Algorithm

intervals

Results

25.0ms	836×	body	80	nan
12.0ms	288×	body	80	valid

simplify6.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	72	20
3	188	20
4	417	20
5	772	20
6	1496	20
7	2490	20
8	3402	20
9	4724	20
done	5000	20

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

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))))

rewrite145.0ms

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:

48.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
62.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
16.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
15.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
192.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
147.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify1.3s

Counts

126 → 126

Iterations

Useful iterations: 2 (488.0ms)

Iter	Nodes	Cost
0	303	2615
1	823	2480
2	2958	2274
done	5002	2274

prune391.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize11.0ms

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

rewrite120.0ms

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:

38.0ms	(* 9.0 (- a (/ 1.0 3.0)))
48.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
16.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
15.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 9.0 (- a (/ 1.0 3.0)))
119.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
161.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify1.1s

Counts

116 → 116

Iterations

Useful iterations: 2 (337.0ms)

Iter	Nodes	Cost
0	271	2223
1	723	2134
2	2613	1938
done	5000	1938

prune320.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize13.0ms

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

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
103×	`times-frac`
78×	`*-un-lft-identity`
68×	`sqrt-prod`
54×	`add-cube-cbrt`
36×	`associate-r`
30×	`add-exp-log`
28×	`associate-l`
20×	`add-cbrt-cube`
18×	`difference-of-squares`
16×	`unswap-sqr`
9×	`pow1` `div-exp` `prod-exp` `associate-/r*` `distribute-lft-out--`
6×	`flip3--` `sqrt-div` `flip--`
5×	`cbrt-undiv` `frac-times` `cbrt-unprod`
4×	`associate-/r/` `add-log-exp`
3×	`flip3-+` `associate-r/` `associate-l/` `flip-+` `div-inv` `associate-/l*`
2×	`rec-exp` `1-exp` `pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 196

Calls

4 calls:

16.0ms	(sqrt (- a (/ 1.0 3.0)))
47.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0))))))))
21.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
78.0ms	(* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (- a (/ 1.0 3.0)))
160.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0))))))))
89.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
199.0ms	(* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify1.7s

Counts

208 → 208

Iterations

Useful iterations: 2 (495.0ms)

Iter	Nodes	Cost
0	379	4281
1	1030	3815
2	3647	3461
done	5001	3461

prune558.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

208×	`add-sqr-sqrt`
163×	`times-frac`
123×	`*-un-lft-identity`
110×	`sqrt-prod`
87×	`add-cube-cbrt`
33×	`associate-r`
32×	`add-exp-log`
30×	`difference-of-squares`
27×	`associate-/r*`
22×	`associate-l` `add-cbrt-cube`
15×	`distribute-lft-out--` `unswap-sqr`
11×	`div-exp`
9×	`associate-/l*`
8×	`sqrt-div` `prod-exp` `associate-/r/`
7×	`cbrt-undiv`
6×	`pow1`
5×	`div-inv`
4×	`flip3--` `flip--` `cbrt-unprod` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `1-exp`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 253

Calls

4 calls:

22.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
20.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
20.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
76.0ms	(* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
82.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
81.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
185.0ms	(* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify1.2s

Counts

265 → 265

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	283	4655
1	711	4205
2	2082	3931
done	5000	3877

prune1.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes79.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	17	20
done	17	20

end0.0ms

sample1.9s

Algorithm

intervals

Results

808.0ms	26908×	body	80	nan
303.0ms	9060×	body	80	valid