Details

sample36.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify29.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
3	32
2	26
1	16
0	11

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (* z z))
0.0b	(fma y y (fma x x (* z z)))
0.1b	(/ (fma y y (fma x x (* z z))) 3.0)
32.9b	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`sqrt-prod`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `fma-udef` `div-inv`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp`

Counts

4 → 80

Calls

4 calls:

0.0ms	(fma x x (* z z))
0.0ms	(fma y y (fma x x (* z z)))
7.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
17.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

series423.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(fma x x (* z z))
62.0ms	(fma y y (fma x x (* z z)))
77.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
218.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify1.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
3	1463
2	433
1	190
0	121

prune500.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (* z z))
0.1b	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0)))
0.2b	(/ (fma y y (fma x x (* z z))) (cbrt 3.0))
32.9b	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
51×	`times-frac` `add-exp-log`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
24×	`cbrt-prod`
22×	`associate-r`
20×	`prod-exp`
19×	`add-cbrt-cube`
16×	`div-exp`
9×	`pow1` `unswap-sqr`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-div` `div-inv` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `pow-prod-down` `associate-l/` `associate-r/`
1×	`clear-num` `frac-2neg` `pow1/2` `*-commutative` `sqrt-prod` `fma-udef`

Counts

4 → 143

Calls

4 calls:

0.0ms	(fma x x (* z z))
65.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0)))
4.0ms	(/ (fma y y (fma x x (* z z))) (cbrt 3.0))
36.0ms	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

37.0ms	(fma x x (* z z))
211.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0)))
237.0ms	(/ (fma y y (fma x x (* z z))) (cbrt 3.0))
524.0ms	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0))))

simplify2.8s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
2	1955
1	536
0	218

prune890.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (* z z))
0.0b	(fma y y (fma x x (* z z)))
0.4b	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
32.8b	(sqrt (fma y y (fma x x (* z z))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`sqrt-prod`
17×	`*-un-lft-identity`
16×	`associate-r`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`pow1`
8×	`unswap-sqr`
6×	`add-cbrt-cube` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`fma-udef`
1×	`rem-sqrt-square` `sqrt-unprod` `sqrt-div` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 86

Calls

4 calls:

0.0ms	(fma x x (* z z))
0.0ms	(fma y y (fma x x (* z z)))
23.0ms	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
2.0ms	(sqrt (fma y y (fma x x (* z z))))

series545.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma x x (* z z))
69.0ms	(fma y y (fma x x (* z z)))
235.0ms	(* (sqrt (fma y y (fma x x (* z z)))) (sqrt (/ 1 3.0)))
182.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify1.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	5006
3	1417
2	482
1	213
0	125

prune516.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (* z z))
0.0b	(fma y y (fma x x (* z z)))
0.4b	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
32.8b	(sqrt (fma y y (fma x x (* z z))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma x x (* z z))
0.0ms	(fma y y (fma x x (* z z)))
10.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
1.0ms	(sqrt (fma y y (fma x x (* z z))))

series637.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma x x (* z z))
75.0ms	(fma y y (fma x x (* z z)))
347.0ms	(/ (sqrt (fma y y (fma x x (* z z)))) (sqrt 3.0))
169.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify1.6s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	1192
2	408
1	198
0	130

prune548.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 17.4b

regimes398.0ms

Accuracy

58.7% (7.1b remaining)

Error of 24.7b against oracle of 17.6b and baseline of 34.8b

bsearch165.0ms

Steps

Iters	Range		Point
10	4.061019733899818e+187	2.906428026807137e+202	4.1448401758462134e+187
10	-9.235597319251238e+162	-3.8921699737818773e+149	-6.54063272250118e+150

simplify11.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.4s

8000×

body

valid