Details

sample109.0ms

Algorithm

intervals

Results

57.0ms	894×	body	80	nan
16.0ms	290×	body	80	valid

simplify7.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	2855
6	1644
5	941
4	490
3	203
2	76
1	27
0	13

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-l` `associate-*l/`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-r` `flip--` `associate-/l*`
2×	`sqrt-pow1` `pow-prod-down` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

38.0ms	(* (- a (/ 1.0 3.0)) 9.0)
0.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
22.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
23.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (- a (/ 1.0 3.0)) 9.0)
156.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
110.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
219.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

simplify1.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1711
1	545
0	227

prune663.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
334×	`add-sqr-sqrt`
258×	`sqrt-prod`
255×	`*-un-lft-identity`
203×	`add-cube-cbrt`
52×	`difference-of-squares`
36×	`associate-/l*`
26×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`flip3--` `div-inv` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `associate-/l/`

Counts

4 → 339

Calls

4 calls:

24.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
56.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
22.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))

series638.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (- a (/ 1.0 3.0)))
175.0ms	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
282.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
119.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))

simplify2.6s

Counts

351 → 351

Iterations

Iter	Nodes
done	5001
2	2951
1	1205
0	510

prune2.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite475.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1`
22×	`add-sqr-sqrt`
20×	`add-exp-log`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`pow-prod-down`
14×	`associate-*l/`
13×	`times-frac` `add-cbrt-cube`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-l`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-pow1` `flip3--` `sqrt-div` `log1p-expm1-u` `flip--` `add-log-exp`
3×	`cbrt-prod` `associate-/l*`
2×	`associate-/r/` `*-commutative` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `div-exp` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

116.0ms	(sqrt (* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0)))
154.0ms	(/ rand (sqrt (* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0))))
86.0ms	(* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0)))
116.0ms	(* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0))

series702.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0)))
239.0ms	(/ rand (sqrt (* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0))))
180.0ms	(* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0)))
164.0ms	(* (* (- a (/ 1.0 3.0)) (* (cbrt 9.0) (cbrt 9.0))) (cbrt 9.0))

simplify1.8s

Counts

118 → 118

Iterations

Iter	Nodes
done	5002
2	1738
1	554
0	227

prune781.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0))))
0.3b	(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0)))) (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0))))
0.4b	(/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0)))

rewrite488.0ms

Algorithm

rewrite-expression-head

Rules

1271×	`times-frac`
943×	`add-sqr-sqrt`
666×	`*-un-lft-identity`
589×	`sqrt-prod`
532×	`add-cube-cbrt`
422×	`cbrt-prod`
301×	`associate-r`
122×	`difference-of-squares`
82×	`add-exp-log`
61×	`distribute-lft-out--`
40×	`sqrt-div` `associate-/r/`
39×	`associate-/l*`
38×	`div-exp`
36×	`add-cbrt-cube`
32×	`unswap-sqr`
24×	`div-inv`
21×	`cbrt-undiv` `prod-exp`
20×	`flip3--` `flip--`
19×	`associate-/r*`
13×	`cbrt-unprod`
8×	`pow1`
7×	`associate-l`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-flip`
1×	`frac-times` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `inv-pow` `associate-/l/`

Counts

4 → 820

Calls

4 calls:

8.0ms	(/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0))))
28.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
292.0ms	(* (/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0)))) (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0))))
45.0ms	(/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

541.0ms	(/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0))))
84.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
300.0ms	(* (/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0)))) (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0))))
288.0ms	(/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0)))

simplify2.9s

Counts

832 → 832

Iterations

Iter	Nodes
done	5000
1	2913
0	898

prune4.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes186.0ms

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	14
1	14
0	13

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.1s	26876×	body	80	nan
670.0ms	9113×	body	80	valid