Details

sample235.0ms

Algorithm

intervals

Results

145.0ms	895×	body	80	nan
42.0ms	291×	body	80	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
6	3095
5	1346
4	543
3	191
2	75
1	28
0	14

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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

rewrite65.0ms

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:

27.0ms	(* 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)))
14.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
21.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* 9 (- a (/ 1.0 3.0)))
135.0ms	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
85.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
186.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify1.1s

Counts

183 → 183

Iterations

Iter	Nodes
2	2152
1	879
0	432

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

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

rewrite93.0ms

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)))
19.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
52.0ms	(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
19.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(fma (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
60.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
140.0ms	(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
108.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify3.6s

Counts

126 → 126

Iterations

Iter	Nodes
3	4875
2	1599
1	567
0	237

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(fma (* rand (pow (* 9 (- a (/ 1.0 3.0))) -1/2)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.1b	(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
0.2b	(* rand (pow (* 9 (- a (/ 1.0 3.0))) -1/2))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
78×	`prod-diff`
77×	`add-cube-cbrt`
55×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
17×	`add-exp-log`
11×	`associate-r`
9×	`pow1`
8×	`add-cbrt-cube`
7×	`prod-exp`
6×	`associate-l` `div-inv`
4×	`expm1-log1p-u` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `unpow-prod-down` `pow-pow` `pow-prod-down` `associate-r/` `-commutative` `cbrt-unprod` `difference-of-squares`
1×	`flip3--` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 165

Calls

4 calls:

25.0ms	(* 9 (- a (/ 1.0 3.0)))
0.0ms	(fma (* rand (pow (* 9 (- a (/ 1.0 3.0))) -1/2)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
14.0ms	(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
27.0ms	(* rand (pow (* 9 (- a (/ 1.0 3.0))) -1/2))

series473.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* 9 (- a (/ 1.0 3.0)))
105.0ms	(fma (* rand (pow (* 9 (- a (/ 1.0 3.0))) -1/2)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
152.0ms	(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
148.0ms	(* rand (pow (* 9 (- a (/ 1.0 3.0))) -1/2))

simplify953.0ms

Counts

177 → 177

Iterations

Iter	Nodes
2	2282
1	908
0	431

prune2.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- a (/ 1.0 3.0)) -1/2)
0.1b	(fma (* (* rand (pow 9 -1/2)) (pow (- a (/ 1.0 3.0)) -1/2)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.3b	(* (* rand (pow 9 -1/2)) (pow (- a (/ 1.0 3.0)) -1/2))
0.4b	(* rand (pow 9 -1/2))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
26×	`add-sqr-sqrt`
24×	`prod-exp`
17×	`associate-r`
16×	`unpow-prod-down`
15×	`*-un-lft-identity`
11×	`add-cbrt-cube` `add-cube-cbrt`
9×	`pow-to-exp` `pow-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-l` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares` `sqr-pow`
3×	`pow-unpow` `unswap-sqr`
2×	`times-frac` `*-commutative` `distribute-lft-out--`
1×	`pow-pow` `fma-udef`

Counts

4 → 98

Calls

4 calls:

9.0ms	(pow (- a (/ 1.0 3.0)) -1/2)
0.0ms	(fma (* (* rand (pow 9 -1/2)) (pow (- a (/ 1.0 3.0)) -1/2)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
66.0ms	(* (* rand (pow 9 -1/2)) (pow (- a (/ 1.0 3.0)) -1/2))
15.0ms	(* rand (pow 9 -1/2))

series410.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(pow (- a (/ 1.0 3.0)) -1/2)
89.0ms	(fma (* (* rand (pow 9 -1/2)) (pow (- a (/ 1.0 3.0)) -1/2)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
125.0ms	(* (* rand (pow 9 -1/2)) (pow (- a (/ 1.0 3.0)) -1/2))
67.0ms	(* rand (pow 9 -1/2))

simplify3.0s

Counts

110 → 110

Iterations

Iter	Nodes
3	5907
2	1545
1	529
0	227

prune1.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes146.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	14
1	14
0	12

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.4s	27625×	body	80	nan
1.3s	9120×	body	80	valid