Details

sample125.0ms

Algorithm

intervals

Results

58.0ms	979×	body	80	nan
17.0ms	293×	body	80	valid

simplify2.5s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

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:

9.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
38.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
51.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
20.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series585.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
120.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
207.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
157.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify1.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	4506
1	858
0	303

prune747.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

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 (sqrt 9.0)) (/ (* rand 1.0) (sqrt (- a (/ 1.0 3.0)))))))
0.3b	(/ (* rand 1.0) (sqrt (- a (/ 1.0 3.0))))
0.4b	(* (/ 1 (sqrt 9.0)) (/ (* rand 1.0) (sqrt (- a (/ 1.0 3.0)))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
50×	`add-exp-log`
45×	`times-frac`
39×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`add-cbrt-cube`
28×	`associate-l`
27×	`add-cube-cbrt`
18×	`associate-r` `prod-exp`
16×	`div-exp`
10×	`cbrt-unprod` `difference-of-squares`
9×	`pow1` `cbrt-undiv` `associate-/r*`
6×	`flip3--` `sqrt-div` `flip--` `unswap-sqr`
5×	`frac-times` `distribute-lft-out--`
4×	`associate-/r/` `add-log-exp`
3×	`rec-exp` `flip3-+` `1-exp` `associate-l/` `associate-r/` `flip-+` `div-inv`
2×	`pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-/l*`

Counts

4 → 156

Calls

4 calls:

13.0ms	(sqrt (- a (/ 1.0 3.0)))
38.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (/ (* rand 1.0) (sqrt (- a (/ 1.0 3.0)))))))
20.0ms	(/ (* rand 1.0) (sqrt (- a (/ 1.0 3.0))))
71.0ms	(* (/ 1 (sqrt 9.0)) (/ (* rand 1.0) (sqrt (- a (/ 1.0 3.0)))))

series722.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (- a (/ 1.0 3.0)))
212.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (/ (* rand 1.0) (sqrt (- a (/ 1.0 3.0)))))))
156.0ms	(/ (* rand 1.0) (sqrt (- a (/ 1.0 3.0))))
315.0ms	(* (/ 1 (sqrt 9.0)) (/ (* rand 1.0) (sqrt (- a (/ 1.0 3.0)))))

simplify432.0ms

Counts

168 → 168

Iterations

Iter	Nodes
done	5001
1	1077
0	350

prune935.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

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

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

13.0ms	(sqrt (- a (/ 1.0 3.0)))
75.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* rand 1.0) (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))))
21.0ms	(/ (* rand 1.0) (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
35.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))

series639.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (- a (/ 1.0 3.0)))
239.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* rand 1.0) (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))))
256.0ms	(/ (* rand 1.0) (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
90.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))

simplify2.0s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	4489
1	791
0	269

prune518.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize22.0ms

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)) (sqrt (- a (/ 1.0 3.0)))) (/ (* rand 1.0) (sqrt 9.0))))
0.4b	(* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ (* rand 1.0) (sqrt 9.0)))
0.6b	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

228×	`add-sqr-sqrt`
149×	`times-frac`
120×	`*-un-lft-identity`
88×	`sqrt-prod`
66×	`difference-of-squares`
60×	`associate-l`
54×	`add-cube-cbrt`
33×	`distribute-lft-out--`
27×	`add-cbrt-cube` `add-exp-log`
10×	`pow1` `associate-r`
9×	`associate-/r` `associate-l/`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
7×	`flip3--` `flip--`
6×	`sqrt-div` `frac-add` `associate-/l*` `add-log-exp`
4×	`associate-/r/`
3×	`frac-times` `associate-*r/` `div-inv` `unswap-sqr`
2×	`sqrt-pow1` `pow1/2` `pow-div` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 220

Calls

4 calls:

13.0ms	(sqrt (- a (/ 1.0 3.0)))
17.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ (* rand 1.0) (sqrt 9.0))))
89.0ms	(* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ (* rand 1.0) (sqrt 9.0)))
42.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (- a (/ 1.0 3.0)))
231.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ (* rand 1.0) (sqrt 9.0))))
234.0ms	(* (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))) (/ (* rand 1.0) (sqrt 9.0)))
71.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))

simplify377.0ms

Counts

232 → 232

Iterations

Iter	Nodes
done	5001
1	1106
0	370

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes171.0ms

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	22
1	22
0	16

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.3s	27152×	body	80	nan
577.0ms	9133×	body	80	valid