Details

sample72.0ms

Algorithm

intervals

Results

31.0ms	988×	body	80	nan
10.0ms	298×	body	80	valid

simplify4.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	70	20
3	172	20
4	352	20
5	667	20
6	1102	20
7	1857	20
8	3926	20
done	5000	20

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
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)))))

rewrite84.0ms

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:

29.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
35.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series551.0ms

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)))
77.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
192.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
154.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify1.1s

Counts

126 → 126

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	303	2615
1	822	2480
2	2976	2274
done	5001	2268

prune379.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
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)))))
8.3b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-l`
23×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
8×	`sqrt-prod`
7×	`associate-*r/` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-*l/`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`associate-r` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 111

Calls

4 calls:

7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
37.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
108.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series595.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
192.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
156.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
168.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify899.0ms

Counts

123 → 123

Iterations

Useful iterations: done (895.0ms)

Iter	Nodes	Cost
0	291	2353
1	754	2261
2	2567	2003
done	5000	1995

prune358.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))
8.3b	(* (- a (/ 1.0 3.0)) (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-exp-log`
101×	`add-sqr-sqrt`
82×	`times-frac`
69×	`*-un-lft-identity`
61×	`associate-l` `add-cbrt-cube`
55×	`prod-exp`
53×	`add-cube-cbrt`
52×	`sqrt-prod`
29×	`cbrt-unprod`
22×	`div-exp`
20×	`pow1`
16×	`difference-of-squares`
15×	`associate-*l/`
12×	`cbrt-undiv`
10×	`frac-times` `pow-prod-down`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`associate-*r/`
6×	`rec-exp` `flip3--` `1-exp` `flip--`
5×	`associate-r`
4×	`sqrt-div` `associate-/r/` `add-log-exp`
3×	`-commutative` `div-inv` `associate-/l` `unswap-sqr`
1×	`frac-2neg` `clear-num`

Counts

4 → 209

Calls

4 calls:

36.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
13.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
42.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))
131.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)))

series705.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
89.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
241.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))
208.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)))

simplify1.3s

Counts

221 → 221

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	414	4526
1	1094	4071
2	3740	3509
done	5001	3483

prune577.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.3b	(/ (* (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (- a (/ 1.0 3.0))) (sqrt 9.0))
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
8.2b	(* (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (- a (/ 1.0 3.0)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
70×	`times-frac`
60×	`*-un-lft-identity`
49×	`sqrt-prod`
44×	`add-cube-cbrt`
34×	`add-exp-log` `associate-l` `add-cbrt-cube`
16×	`difference-of-squares`
15×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`associate-r` `associate-*l/`
8×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
6×	`flip3--` `flip--`
5×	`associate-/l/`
4×	`frac-times` `sqrt-div` `associate-r/` `pow-prod-down` `associate-/r/` `associate-/l` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`

Counts

4 → 174

Calls

4 calls:

34.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
51.0ms	(/ (* (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (- a (/ 1.0 3.0))) (sqrt 9.0))
13.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
58.0ms	(* (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (- a (/ 1.0 3.0)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
205.0ms	(/ (* (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (- a (/ 1.0 3.0))) (sqrt 9.0))
84.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
130.0ms	(* (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand) (- a (/ 1.0 3.0)))

simplify1.6s

Counts

186 → 186

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	361	3531
1	940	3349
2	3515	2971
done	5000	2955

prune502.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes56.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	19	27
done	19	27

end0.0ms

sample1.8s

Algorithm

intervals

Results

886.0ms	27681×	body	80	nan
322.0ms	9139×	body	80	valid