Details

sample127.0ms

Algorithm

intervals

Results

65.0ms	838×	body	80	nan
20.0ms	295×	body	80	valid

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	325
1	27	325
2	72	325
3	185	325
4	405	325
5	730	325
6	1131	325
7	2025	325
done	5000	325

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

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)))
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.3b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite224.0ms

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/` `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 → 114

Calls

4 calls:

60.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
30.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
105.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
25.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series760.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
234.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
249.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
98.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify3.2s

Counts

126 → 126

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	303	51903
1	857	45865
2	3363	44901
done	5011	44901

prune902.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize40.0ms

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	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

35.0ms	(* 9.0 (- a (/ 1.0 3.0)))
100.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
38.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
18.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series574.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* 9.0 (- a (/ 1.0 3.0)))
182.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
255.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
89.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.9s

Counts

109 → 109

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	263	40002
1	777	34757
2	3144	34276
done	5057	33996

prune680.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
7.4b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

61.0ms	(* 9.0 (- a (/ 1.0 3.0)))
34.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
20.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
110.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series753.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* 9.0 (- a (/ 1.0 3.0)))
308.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
117.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
264.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify2.4s

Counts

114 → 114

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	260	38862
1	719	33536
2	2660	33055
done	5025	33055

prune759.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.0b	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
0.3b	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
7.4b	(* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

319×	`times-frac`
230×	`add-sqr-sqrt`
190×	`sqrt-prod`
152×	`*-un-lft-identity`
106×	`add-cube-cbrt`
96×	`associate-r`
46×	`difference-of-squares`
27×	`add-cbrt-cube` `add-exp-log`
23×	`distribute-lft-out--`
21×	`div-inv`
16×	`associate-*l/`
14×	`flip3--` `flip--`
10×	`cbrt-undiv` `div-exp` `frac-add` `associate-/l*`
9×	`associate-/r*`
7×	`pow1`
6×	`frac-times` `sqrt-div` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`associate-/r/`
3×	`associate-*r/` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `*-commutative` `flip-+` `distribute-lft-out` `associate-/l/`

Counts

4 → 295

Calls

4 calls:

27.0ms	(sqrt (- a (/ 1.0 3.0)))
35.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
30.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
133.0ms	(* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))

series992.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (- a (/ 1.0 3.0)))
239.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
396.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
289.0ms	(* (- a (/ 1.0 3.0)) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))

simplify2.6s

Counts

307 → 307

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	491	157834
1	1453	140552
done	5000	139304

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes208.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	365
1	19	365
done	19	365

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.4s	27027×	body	80	nan
1.2s	9115×	body	80	valid