Details

sample116.0ms

Algorithm

intervals

Results

54.0ms	847×	body	80	nan
19.0ms	289×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3827
6	1760
5	891
4	462
3	190
2	72
1	27
0	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

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))))

rewrite183.0ms

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:

58.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
15.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
85.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
22.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series638.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
154.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
243.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
112.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	5002
2	4499
1	857
0	303

prune761.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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))))
8.7b	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

rewrite386.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

22.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
80.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
267.0ms	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

series788.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
245.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
100.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
258.0ms	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

simplify2.2s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	4297
1	814
0	298

prune976.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.3b	(* rand (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
8.7b	(* (* rand (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))

rewrite343.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

26.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
82.0ms	(* rand (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
9.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
219.0ms	(* (* rand (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))

series877.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
313.0ms	(* rand (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
112.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
248.0ms	(* (* rand (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))

simplify2.3s

Counts

127 → 127

Iterations

Iter	Nodes
done	5002
2	4199
1	836
0	297

prune834.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (- a (/ 1.0 3.0))) (* (* (/ rand (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))))
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ rand (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
8.7b	(* (* (/ rand (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-sqr-sqrt`
92×	`times-frac`
68×	`*-un-lft-identity`
57×	`sqrt-prod`
52×	`add-cube-cbrt`
39×	`associate-r`
38×	`associate-*r/`
36×	`add-cbrt-cube` `add-exp-log`
28×	`frac-times`
25×	`flip3--` `flip--`
23×	`associate-l`
22×	`frac-add`
19×	`associate-*l/`
16×	`difference-of-squares`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `associate-/r*` `div-exp` `unswap-sqr`
8×	`distribute-lft-out--`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-log-exp`
4×	`associate-+l+` `associate-+r+` `sqrt-div` `pow-prod-down` `associate-/r/`
3×	`div-inv` `associate-/l*`
2×	`*-commutative`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `distribute-rgt-out` `flip-+`

Counts

4 → 221

Calls

4 calls:

24.0ms	(+ (* 1.0 (- a (/ 1.0 3.0))) (* (* (/ rand (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))))
23.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
77.0ms	(* (/ rand (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
151.0ms	(* (* (/ rand (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

251.0ms	(+ (* 1.0 (- a (/ 1.0 3.0))) (* (* (/ rand (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))))
106.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
323.0ms	(* (/ rand (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
330.0ms	(* (* (/ rand (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

simplify1.5s

Counts

233 → 233

Iterations

Iter	Nodes
done	5000
1	1496
0	477

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes159.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.2s	26844×	body	80	nan
751.0ms	9096×	body	80	valid