Details

sample87.0ms

Algorithm

intervals

Results

44.0ms	959×	body	80	nan
13.0ms	295×	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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

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

rewrite142.0ms

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:

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

series957.0ms

Counts

4 → 12

Calls

4 calls:

500.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
203.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
169.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
85.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify1.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	4501
1	857
0	303

prune811.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(* (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.3b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube` `add-exp-log`
12×	`associate-r`
11×	`pow1`
10×	`add-cube-cbrt`
8×	`associate-*r/`
7×	`associate-l`
6×	`times-frac` `flip3--` `flip--`
4×	`distribute-rgt-in` `frac-times` `associate-/r*` `sub-neg` `distribute-lft-in` `sqrt-div` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `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 → 99

Calls

4 calls:

41.0ms	(* 9.0 (- a (/ 1.0 3.0)))
137.0ms	(* (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
23.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
10.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* 9.0 (- a (/ 1.0 3.0)))
152.0ms	(* (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
261.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
110.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify1.4s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	3860
1	747
0	260

prune624.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

154.0ms	(* (+ 1.0 (/ (* 1.0 rand) (sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))))) (- a (/ 1.0 3.0)))
43.0ms	(/ (* 1.0 rand) (sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))))
44.0ms	(* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))
46.0ms	(sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0)))))

series909.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (+ 1.0 (/ (* 1.0 rand) (sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))))) (- a (/ 1.0 3.0)))
392.0ms	(/ (* 1.0 rand) (sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))))
159.0ms	(* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0))))
171.0ms	(sqrt (* (sqrt 9.0) (* (sqrt 9.0) (- a (/ 1.0 3.0)))))

simplify1.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	4703
1	885
0	313

prune613.0ms

Pruning

8 alts after pruning (6 fresh and 2 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	(* (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt`
93×	`times-frac`
72×	`*-un-lft-identity`
63×	`sqrt-prod`
54×	`add-cube-cbrt`
39×	`associate-r`
25×	`associate-l`
20×	`add-cbrt-cube` `add-exp-log`
18×	`difference-of-squares`
10×	`unswap-sqr`
9×	`pow1` `associate-/r*` `distribute-lft-out--`
6×	`flip3--` `sqrt-div` `flip--`
5×	`frac-times` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/r/` `add-log-exp`
3×	`flip3-+` `associate-l/` `associate-r/` `flip-+` `div-inv` `associate-/l*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `*-commutative`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 188

Calls

4 calls:

21.0ms	(sqrt (- a (/ 1.0 3.0)))
46.0ms	(* (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
18.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
78.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series663.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (- a (/ 1.0 3.0)))
170.0ms	(* (+ 1.0 (* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
138.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
304.0ms	(* (/ 1.0 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify478.0ms

Counts

200 → 200

Iterations

Iter	Nodes
done	5001
1	1071
0	370

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes287.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	26
2	26
1	25
0	17

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.4s	26968×	body	80	nan
1.2s	9189×	body	80	valid