Details

sample60.0ms

Algorithm

intervals

Results

26.0ms	759×	body	80	nan
10.0ms	280×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	74	19
3	192	19
4	448	19
5	888	19
6	1616	19
7	2761	19
done	5001	19

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

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

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `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` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 122

Calls

4 calls:

28.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
39.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
36.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
193.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
154.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
80.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify1.1s

Counts

134 → 134

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	311	2723
1	871	2576
2	3677	2342
done	5000	2337

prune433.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
78×	`add-cube-cbrt` `prod-diff`
60×	`times-frac`
42×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`associate-r`
9×	`associate-l`
8×	`associate-*r/`
7×	`div-inv`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`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×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out` `associate-/l*`

Counts

4 → 183

Calls

4 calls:

32.0ms	(* 9.0 (- a (/ 1.0 3.0)))
53.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
10.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
35.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 9.0 (- a (/ 1.0 3.0)))
127.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
212.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
79.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify410.0ms

Counts

195 → 195

Iterations

Useful iterations: done (395.0ms)

Iter	Nodes	Cost
0	489	5591
1	1173	5037
done	5000	3946

prune403.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
10.2b	(* (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-sqr-sqrt`
156×	`prod-diff`
151×	`*-un-lft-identity`
147×	`add-cube-cbrt`
118×	`times-frac`
82×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-exp-log` `add-cbrt-cube`
14×	`div-inv`
13×	`associate-l`
12×	`associate-r`
11×	`pow1`
10×	`associate-*r/`
6×	`flip3--` `sqrt-div` `prod-exp` `flip--` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `sub-neg` `div-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-prod-down`
2×	`frac-times` `sqrt-pow1` `*-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `associate-l/` `clear-num` `associate-/l`

Counts

4 → 270

Calls

4 calls:

32.0ms	(* 9.0 (- a (/ 1.0 3.0)))
10.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
34.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
72.0ms	(* (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

series521.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 9.0 (- a (/ 1.0 3.0)))
205.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
80.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
189.0ms	(* (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

simplify445.0ms

Counts

282 → 282

Iterations

Useful iterations: done (430.0ms)

Iter	Nodes	Cost
0	593	10703
1	1468	9756
done	5000	9570

prune695.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- a (/ 1.0 3.0))
0.0b	(sqrt (- a (/ 1.0 3.0)))
0.3b	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
10.2b	(* (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

401×	`times-frac`
338×	`add-sqr-sqrt`
257×	`*-un-lft-identity`
209×	`add-cube-cbrt`
190×	`sqrt-prod`
117×	`prod-diff`
96×	`associate-l`
48×	`difference-of-squares`
41×	`distribute-rgt-in` `distribute-lft-in`
30×	`div-inv`
27×	`add-exp-log` `add-cbrt-cube`
24×	`distribute-lft-out--`
10×	`cbrt-undiv` `div-exp` `associate-/l*`
9×	`associate-/r*`
7×	`pow1`
6×	`flip3--` `sqrt-div` `associate-r` `prod-exp` `flip--` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 420

Calls

4 calls:

8.0ms	(- a (/ 1.0 3.0))
16.0ms	(sqrt (- a (/ 1.0 3.0)))
20.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
99.0ms	(* (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- a (/ 1.0 3.0))
46.0ms	(sqrt (- a (/ 1.0 3.0)))
241.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
239.0ms	(* (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))

simplify529.0ms

Counts

432 → 432

Iterations

Useful iterations: done (506.0ms)

Iter	Nodes	Cost
0	642	13510
1	1756	12565
done	5001	12342

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes78.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	19	27
done	19	27

end0.0ms

sample1.8s

Algorithm

intervals

Results

842.0ms	26969×	body	80	nan
311.0ms	9094×	body	80	valid