Details

sample109.0ms

Algorithm

intervals

Results

49.0ms	812×	body	80	nan
20.0ms	293×	body	80	valid

simplify3.5s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

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)))))

rewrite153.0ms

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:

62.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
11.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
55.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
18.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
107.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
236.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
224.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify2.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	3356
1	858
0	303

prune788.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) 9.0)
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))))))
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

45.0ms	(* (- a (/ 1.0 3.0)) 9.0)
50.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))))))
11.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
19.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (- a (/ 1.0 3.0)) 9.0)
164.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))))))
100.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
184.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

simplify2.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	2690
1	729
0	263

prune668.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

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

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
343×	`add-sqr-sqrt`
259×	`*-un-lft-identity`
258×	`sqrt-prod`
205×	`add-cube-cbrt`
54×	`difference-of-squares`
36×	`associate-/l*`
27×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
13×	`add-cbrt-cube` `add-exp-log`
12×	`flip3--` `flip--`
9×	`div-inv`
7×	`pow1`
6×	`associate-l`
4×	`frac-times` `cbrt-undiv` `div-exp` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+`
2×	`clear-num` `frac-2neg` `associate-l/` `associate-r/`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`

Counts

4 → 354

Calls

4 calls:

13.0ms	(sqrt (- a (/ 1.0 3.0)))
56.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))))
26.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
50.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

series706.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (- a (/ 1.0 3.0)))
237.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))))
143.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
274.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify2.7s

Counts

366 → 366

Iterations

Iter	Nodes
done	5031
2	3988
1	1387
0	549

prune2.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (* rand (/ 1 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0)))))
0.2b	(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* rand (/ 1 (sqrt (- a (/ 1.0 3.0)))))
0.3b	(/ (* rand (/ 1 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
72×	`times-frac`
63×	`*-un-lft-identity`
50×	`sqrt-prod`
45×	`add-cube-cbrt`
36×	`associate-r`
34×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`difference-of-squares`
15×	`associate-/r*`
11×	`div-exp`
10×	`pow1`
9×	`associate-l` `prod-exp`
8×	`distribute-lft-out--`
6×	`cbrt-undiv` `unswap-sqr`
5×	`flip3--` `cbrt-unprod` `flip--`
4×	`frac-times` `sqrt-div` `associate-r/` `associate-/r/` `associate-/l` `add-log-exp`
3×	`rec-exp` `flip3-+` `1-exp` `flip-+` `div-inv` `pow-flip`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `un-div-inv` `-commutative` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 181

Calls

4 calls:

42.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (* rand (/ 1 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0)))))
23.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
49.0ms	(* rand (/ 1 (sqrt (- a (/ 1.0 3.0)))))
22.0ms	(/ (* rand (/ 1 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0))

series754.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ (* rand (/ 1 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0)))))
100.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
122.0ms	(* rand (/ 1 (sqrt (- a (/ 1.0 3.0)))))
308.0ms	(/ (* rand (/ 1 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0))

simplify2.0s

Counts

193 → 193

Iterations

Iter	Nodes
done	5001
2	3638
1	1011
0	371

prune960.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes192.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.0s	26714×	body	80	nan
1.4s	9159×	body	80	valid