Details

sample141.0ms

Algorithm

intervals

Results

67.0ms	1052×	body	80	nan
19.0ms	300×	body	80	valid

simplify10.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	2855
6	1644
5	941
4	490
3	203
2	76
1	27
0	13

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize122.0ms

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

rewrite178.0ms

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` `insert-posit16` `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 → 89

Calls

4 calls:

99.0ms	(* (- a (/ 1.0 3.0)) 9.0)
1.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
39.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
34.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

series687.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (- a (/ 1.0 3.0)) 9.0)
207.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
293.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
121.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

simplify3.8s

Counts

101 → 101

Iterations

Iter	Nodes
done	5006
2	1732
1	549
0	231

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize172.0ms

Local error

Found 4 expressions with local error:

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

rewrite342.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
334×	`add-sqr-sqrt`
258×	`sqrt-prod`
255×	`*-un-lft-identity`
203×	`add-cube-cbrt`
52×	`difference-of-squares`
36×	`associate-/l*`
26×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`flip3--` `div-inv` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `associate-/l/`

Counts

4 → 343

Calls

4 calls:

65.0ms	(sqrt (- a (/ 1.0 3.0)))
3.0ms	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
80.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
128.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

series807.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (- a (/ 1.0 3.0)))
265.0ms	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
127.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
347.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify6.0s

Counts

355 → 355

Iterations

Iter	Nodes
done	5011
2	2908
1	1214
0	514

prune3.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize117.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* rand (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(* rand (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))
0.3b	(/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
0.3b	(/ 1 (sqrt (- a (/ 1.0 3.0))))

rewrite735.0ms

Algorithm

rewrite-expression-head

Rules

835×	`times-frac`
617×	`add-sqr-sqrt`
468×	`sqrt-prod`
456×	`*-un-lft-identity`
366×	`add-cube-cbrt`
202×	`associate-r`
86×	`difference-of-squares`
43×	`distribute-lft-out--`
36×	`associate-/l*`
32×	`add-exp-log`
28×	`sqrt-div` `associate-/r/`
20×	`add-cbrt-cube`
16×	`div-inv`
15×	`associate-/r*`
14×	`flip3--` `div-exp` `flip--`
11×	`unswap-sqr`
8×	`pow1`
7×	`cbrt-undiv`
5×	`prod-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-l` `cbrt-unprod` `pow-flip`
2×	`clear-num` `frac-2neg`
1×	`sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `inv-pow` `associate-/l/`

Counts

4 → 567

Calls

4 calls:

3.0ms	(fma (* rand (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
375.0ms	(* rand (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))
129.0ms	(/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
84.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

249.0ms	(fma (* rand (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
356.0ms	(* rand (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)))
290.0ms	(/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))
107.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))

simplify8.4s

Counts

579 → 579

Iterations

Iter	Nodes
done	5004
2	4418
1	1839
0	673

prune4.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- a (/ 1.0 3.0)) -1/2)
0.1b	(fma (* rand (/ (pow (- a (/ 1.0 3.0)) -1/2) (sqrt 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(* rand (/ (pow (- a (/ 1.0 3.0)) -1/2) (sqrt 9.0)))
0.3b	(/ (pow (- a (/ 1.0 3.0)) -1/2) (sqrt 9.0))

rewrite528.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
140×	`times-frac`
104×	`*-un-lft-identity`
86×	`unpow-prod-down`
76×	`add-cube-cbrt`
66×	`sqrt-prod`
64×	`associate-r`
28×	`difference-of-squares`
20×	`add-exp-log`
16×	`sqr-pow`
14×	`distribute-lft-out--`
11×	`add-cbrt-cube`
10×	`associate-/l*`
7×	`pow1` `unswap-sqr`
6×	`associate-/r*` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-l` `pow-exp`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative` `fma-udef`

Counts

4 → 220

Calls

4 calls:

68.0ms	(pow (- a (/ 1.0 3.0)) -1/2)
3.0ms	(fma (* rand (/ (pow (- a (/ 1.0 3.0)) -1/2) (sqrt 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
276.0ms	(* rand (/ (pow (- a (/ 1.0 3.0)) -1/2) (sqrt 9.0)))
157.0ms	(/ (pow (- a (/ 1.0 3.0)) -1/2) (sqrt 9.0))

series926.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(pow (- a (/ 1.0 3.0)) -1/2)
221.0ms	(fma (* rand (/ (pow (- a (/ 1.0 3.0)) -1/2) (sqrt 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
330.0ms	(* rand (/ (pow (- a (/ 1.0 3.0)) -1/2) (sqrt 9.0)))
204.0ms	(/ (pow (- a (/ 1.0 3.0)) -1/2) (sqrt 9.0))

simplify5.0s

Counts

232 → 232

Iterations

Iter	Nodes
done	5001
2	2700
1	913
0	370

prune2.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes454.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	16
1	16
0	14

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.6s	27169×	body	80	nan
1.1s	9178×	body	80	valid