Details

sample79.0ms

Algorithm

intervals

Results

34.0ms	847×	body	80	nan
13.0ms	289×	body	80	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2429
5	1149
4	547
3	208
2	76
1	27
0	13

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
0.6b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

rewrite97.0ms

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:

62.0ms	(* (- a (/ 1.0 3.0)) 9.0)
1.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
21.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
11.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

series583.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (- a (/ 1.0 3.0)) 9.0)
142.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
276.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
96.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

simplify1.8s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	2189
1	559
0	230

prune723.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
0.3b	(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

139×	`add-sqr-sqrt`
102×	`times-frac`
74×	`*-un-lft-identity`
68×	`sqrt-prod`
52×	`add-cube-cbrt`
33×	`associate-l`
30×	`add-exp-log`
22×	`associate-r`
18×	`add-cbrt-cube`
16×	`difference-of-squares`
15×	`unswap-sqr`
10×	`div-exp`
9×	`pow1` `associate-/r*`
8×	`prod-exp` `distribute-lft-out--`
6×	`sqrt-div`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `flip3--` `1-exp` `div-inv` `pow-flip` `flip--` `associate-/l*`
2×	`sqrt-pow1` `pow1/2`
1×	`frac-times` `rem-sqrt-square` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 187

Calls

4 calls:

32.0ms	(sqrt (- a (/ 1.0 3.0)))
1.0ms	(fma (* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
36.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
76.0ms	(* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0)))

series664.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- a (/ 1.0 3.0)))
210.0ms	(fma (* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
91.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
291.0ms	(* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt 9.0)))

simplify2.7s

Counts

199 → 199

Iterations

Iter	Nodes
done	5000
2	4651
1	932
0	330

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

402×	`times-frac`
301×	`add-sqr-sqrt`
234×	`sqrt-prod`
228×	`*-un-lft-identity`
180×	`add-cube-cbrt`
48×	`difference-of-squares`
24×	`distribute-lft-out--`
22×	`associate-/l*`
11×	`div-inv`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `sqrt-div`
3×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `associate-/l/`

Counts

3 → 278

Calls

3 calls:

19.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
44.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series545.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(sqrt (- a (/ 1.0 3.0)))
216.0ms	(fma (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
277.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify2.0s

Counts

287 → 287

Iterations

Iter	Nodes
done	5001
2	3969
1	1070
0	452

prune1.6s

Pruning

5 alts after pruning (5 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)))
0.0b	(+ (* (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0))))
0.3b	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
8.7b	(* (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0))))

rewrite578.0ms

Algorithm

rewrite-expression-head

Rules

1054×	`times-frac`
914×	`add-sqr-sqrt`
775×	`*-un-lft-identity`
683×	`add-cube-cbrt`
447×	`sqrt-prod`
390×	`prod-diff`
369×	`distribute-rgt-in` `distribute-lft-in`
204×	`associate-l`
164×	`associate-+l+`
92×	`difference-of-squares`
82×	`associate-+r+`
51×	`div-inv`
46×	`distribute-lft-out--`
30×	`add-cbrt-cube` `add-exp-log`
28×	`associate-*r/`
22×	`associate-/l*`
14×	`flip3--` `flip--`
10×	`pow1` `sub-neg` `frac-add`
9×	`cbrt-undiv` `associate-/r*` `div-exp` `prod-exp` `cbrt-unprod`
6×	`frac-times` `sqrt-div` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`pow-prod-down` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `fma-def` `frac-2neg` `distribute-lft1-in` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `*-commutative` `flip-+` `associate-/l/`

Counts

4 → 937

Calls

4 calls:

36.0ms	(sqrt (- a (/ 1.0 3.0)))
123.0ms	(+ (* (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0))))
46.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
222.0ms	(* (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0))))

series762.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (- a (/ 1.0 3.0)))
221.0ms	(+ (* (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0))))
208.0ms	(/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
291.0ms	(* (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) (* 1.0 (- a (/ 1.0 3.0))))

simplify4.4s

Counts

949 → 949

Iterations

Iter	Nodes
done	5001
1	3932
0	1224

prune7.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes268.0ms

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	14

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.3s	26844×	body	80	nan
1.2s	9096×	body	80	valid