Details

sample223.0ms

Algorithm

intervals

Results

141.0ms	979×	body	80	nan
37.0ms	297×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
6	3385
5	1621
4	684
3	218
2	75
1	30
0	14

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
83×	`add-cube-cbrt`
78×	`prod-diff`
67×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
7×	`div-inv`
6×	`associate-r` `associate-*r/`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-l` `flip--` `associate-/l*`
2×	`sub-neg` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 171

Calls

4 calls:

48.0ms	(* 9 (- a (/ 1.0 3.0)))
0.0ms	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
16.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
22.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 9 (- a (/ 1.0 3.0)))
112.0ms	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
158.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
116.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify898.0ms

Counts

183 → 183

Iterations

Iter	Nodes
2	2155
1	881
0	432

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.3b	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`times-frac`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
13×	`pow1`
11×	`add-cbrt-cube`
8×	`sqrt-prod`
7×	`associate-*r/`
6×	`sqrt-div`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-pow1` `div-exp` `prod-exp` `associate-/r/` `insert-posit16` `log1p-expm1-u` `pow-flip` `add-log-exp`
3×	`flip3--` `associate-l` `pow-prod-down` `flip--` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `un-div-inv` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 114

Calls

4 calls:

0.0ms	(fma (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
70.0ms	(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
28.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
37.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(fma (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
184.0ms	(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
113.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
68.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify1.9s

Counts

126 → 126

Iterations

Iter	Nodes
3	4449
2	1516
1	562
0	237

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))
1.2b	(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
62×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
19×	`associate-/r*`
17×	`add-exp-log` `sqrt-prod`
11×	`add-cbrt-cube`
8×	`pow1` `div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`expm1-log1p-u` `cbrt-undiv` `sqrt-div` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`pow1/2` `pow-prod-down` `associate-/r/` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 154

Calls

4 calls:

0.0ms	(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
17.0ms	(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
16.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
29.0ms	(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))

series674.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
211.0ms	(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
96.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
240.0ms	(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))

simplify5.6s

Counts

166 → 166

Iterations

Iter	Nodes
3	5635
2	1994
1	775
0	314

prune1.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ 1 rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.3b	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.3b	(/ (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ 1 rand))
0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

585×	`times-frac`
258×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`add-exp-log`
47×	`sqrt-prod`
35×	`div-inv`
34×	`div-exp`
32×	`sqrt-div` `associate-*r/`
31×	`associate-/r/`
21×	`associate-/l*`
18×	`add-cbrt-cube`
17×	`associate-/r*`
16×	`flip3--` `flip--`
11×	`pow1`
9×	`cbrt-undiv` `rec-exp` `1-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `pow-flip` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow1/2` `pow-prod-down`
1×	`fma-udef` `inv-pow` `associate-/l/`

Counts

4 → 370

Calls

4 calls:

0.0ms	(fma (/ (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ 1 rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
29.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
40.0ms	(/ (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ 1 rand))
21.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(fma (/ (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ 1 rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
128.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
230.0ms	(/ (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ 1 rand))
92.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify1.8s

Counts

382 → 382

Iterations

Iter	Nodes
2	3832
1	1939
0	652

prune5.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes161.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	17
1	17
0	14

end0.0ms

sample6.4s

Algorithm

intervals

Results

4.1s	27345×	body	80	nan
1.4s	9165×	body	80	valid