Details

sample173.0ms

Algorithm

intervals

Results

88.0ms	979×	body	80	nan
21.0ms	293×	body	80	valid

simplify4.2s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

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:

75.0ms	(* (- a (/ 1.0 3.0)) 9.0)
22.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
29.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (- a (/ 1.0 3.0)) 9.0)
76.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
119.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
230.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

simplify1.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	2180
1	559
0	230

prune724.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) 9.0)
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
6.5b	(* (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (* 1.0 (- a (/ 1.0 3.0))))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-sqr-sqrt`
164×	`distribute-rgt-in` `distribute-lft-in`
161×	`*-un-lft-identity`
159×	`add-cube-cbrt`
156×	`prod-diff`
133×	`times-frac`
24×	`associate-l`
20×	`add-cbrt-cube` `add-exp-log`
14×	`pow1` `div-inv`
9×	`associate-*l/`
8×	`sqrt-prod`
7×	`prod-exp` `cbrt-unprod`
6×	`flip3--` `sqrt-div` `associate-*r/` `flip--`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `associate-/r` `sub-neg` `associate-r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `*-commutative` `difference-of-squares`
1×	`clear-num` `frac-2neg` `pow1/2` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 283

Calls

4 calls:

65.0ms	(* (- a (/ 1.0 3.0)) 9.0)
25.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
28.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
199.0ms	(* (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (* 1.0 (- a (/ 1.0 3.0))))

series670.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (- a (/ 1.0 3.0)) 9.0)
104.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
251.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
246.0ms	(* (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (* 1.0 (- a (/ 1.0 3.0))))

simplify1.7s

Counts

295 → 295

Iterations

Iter	Nodes
done	5000
1	2260
0	719

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ rand (sqrt (* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) 9.0))))
0.3b	(* (sqrt (- a (/ 1.0 3.0))) 9.0)
0.4b	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) 9.0))
6.5b	(* (/ rand (sqrt (* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) 9.0)))) (* 1.0 (- a (/ 1.0 3.0))))

rewrite570.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-sqr-sqrt`
166×	`*-un-lft-identity`
164×	`distribute-rgt-in` `distribute-lft-in`
162×	`add-cube-cbrt`
156×	`prod-diff`
134×	`times-frac`
54×	`sqrt-div`
42×	`associate-l`
27×	`associate-*l/`
25×	`add-cbrt-cube` `add-exp-log`
21×	`flip3--` `flip--`
20×	`sqrt-prod`
16×	`pow1` `associate-/r/`
14×	`frac-times` `div-inv`
12×	`associate-*r/`
10×	`prod-exp` `cbrt-unprod`
7×	`pow-prod-down`
5×	`associate-r`
4×	`expm1-log1p-u` `associate-/r*` `sub-neg` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `div-exp` `-commutative` `associate-/l`
2×	`distribute-lft-out--` `unswap-sqr`
1×	`clear-num` `frac-2neg`

Counts

4 → 318

Calls

4 calls:

49.0ms	(/ rand (sqrt (* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) 9.0))))
34.0ms	(* (sqrt (- a (/ 1.0 3.0))) 9.0)
87.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) 9.0))
367.0ms	(* (/ rand (sqrt (* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) 9.0)))) (* 1.0 (- a (/ 1.0 3.0))))

series719.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(/ rand (sqrt (* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) 9.0))))
91.0ms	(* (sqrt (- a (/ 1.0 3.0))) 9.0)
52.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) 9.0))
337.0ms	(* (/ rand (sqrt (* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) 9.0)))) (* 1.0 (- a (/ 1.0 3.0))))

simplify2.1s

Counts

330 → 330

Iterations

Iter	Nodes
done	5001
1	2343
0	762

prune2.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

42.0ms	(* (- a (/ 1.0 3.0)) 9.0)
12.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
45.0ms	(/ (* 1.0 (- a (/ 1.0 3.0))) (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
73.0ms	(* rand (/ (* 1.0 (- a (/ 1.0 3.0))) (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

series542.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (- a (/ 1.0 3.0)) 9.0)
85.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
171.0ms	(/ (* 1.0 (- a (/ 1.0 3.0))) (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
216.0ms	(* rand (/ (* 1.0 (- a (/ 1.0 3.0))) (sqrt (* (- a (/ 1.0 3.0)) 9.0))))

simplify1.8s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	3475
1	699
0	248

prune700.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes168.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.6s	27152×	body	80	nan
970.0ms	9133×	body	80	valid