Details

sample133.0ms

Algorithm

intervals

Results

79.0ms	886×	body	80	nan
26.0ms	302×	body	80	valid

simplify3.2s

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

localize18.0ms

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))))
0.3b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

rewrite84.0ms

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:

35.0ms	(* 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)))
33.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
11.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series812.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* 9 (- a (/ 1.0 3.0)))
106.0ms	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
83.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
548.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify921.0ms

Counts

183 → 183

Iterations

Iter	Nodes
2	2152
1	881
0	432

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (/ rand (* 3 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.3b	(/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))
0.3b	(* 3 (sqrt (- a (/ 1.0 3.0))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
13×	`sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log`
10×	`add-cube-cbrt`
9×	`associate-r`
7×	`pow1`
6×	`sqrt-div`
5×	`times-frac`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`flip3--` `associate-l` `flip--` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `fma-udef` `div-inv`

Counts

4 → 88

Calls

4 calls:

22.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (/ rand (* 3 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
25.0ms	(/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))
48.0ms	(* 3 (sqrt (- a (/ 1.0 3.0))))

series417.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (- a (/ 1.0 3.0)))
89.0ms	(fma (/ rand (* 3 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
149.0ms	(/ rand (* 3 (sqrt (- a (/ 1.0 3.0)))))
111.0ms	(* 3 (sqrt (- a (/ 1.0 3.0))))

simplify1.8s

Counts

100 → 100

Iterations

Iter	Nodes
3	4329
2	1311
1	472
0	207

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ 1 (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.3b	(/ (* 3 (sqrt (- a (/ 1.0 3.0)))) rand)
0.3b	(* 3 (sqrt (- a (/ 1.0 3.0))))
0.8b	(/ 1 (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

37×	`times-frac`
34×	`add-sqr-sqrt`
32×	`add-exp-log`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
20×	`add-cbrt-cube`
14×	`div-exp`
10×	`associate-/r*`
9×	`associate-r`
7×	`pow1` `cbrt-undiv` `sqrt-prod`
6×	`div-inv`
5×	`prod-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate-r/` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `flip3--` `flip--` `difference-of-squares` `unswap-sqr` `associate-/l/`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `fma-udef` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 126

Calls

4 calls:

0.0ms	(fma (/ 1 (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
28.0ms	(/ (* 3 (sqrt (- a (/ 1.0 3.0)))) rand)
46.0ms	(* 3 (sqrt (- a (/ 1.0 3.0))))
36.0ms	(/ 1 (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) rand))

series643.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(fma (/ 1 (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
198.0ms	(/ (* 3 (sqrt (- a (/ 1.0 3.0)))) rand)
103.0ms	(* 3 (sqrt (- a (/ 1.0 3.0))))
196.0ms	(/ 1 (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify4.3s

Counts

138 → 138

Iterations

Iter	Nodes
3	6630
2	1895
1	684
0	286

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
64×	`times-frac`
56×	`*-un-lft-identity`
49×	`sqrt-prod`
40×	`add-cube-cbrt`
33×	`associate-r`
16×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`pow1`
6×	`sqrt-div`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-l` `flip--` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `fma-udef`

Counts

4 → 144

Calls

4 calls:

11.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
12.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
42.0ms	(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (- a (/ 1.0 3.0)))
125.0ms	(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
123.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
166.0ms	(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify1.6s

Counts

156 → 156

Iterations

Iter	Nodes
3	4453
2	1517
1	603
0	263

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes161.0ms

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
2	16
1	16
0	13

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.4s	27200×	body	80	nan
1.3s	9162×	body	80	valid