Details

sample47.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify21.0ms

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: 38.9b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (fma y y (fma x x (* z z))) 3.0)
36.1b	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 56

Calls

2 calls:

8.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
5.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

series662.0ms

Counts

2 → 6

Calls

2 calls:

385.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
276.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify1.4s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	1755
2	455
1	167
0	101

prune528.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
36.1b	(sqrt (fma y y (fma x x (* z z))))
36.1b	(sqrt (fma y y (fma x x (* z z))))
36.1b	(sqrt (* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
58×	`times-frac`
38×	`*-un-lft-identity`
36×	`sqrt-prod`
32×	`add-cube-cbrt`
22×	`associate-r` `associate-l`
21×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
7×	`div-exp`
6×	`prod-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `sqrt-pow1` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `sqrt-div`
2×	`frac-times` `rem-sqrt-square` `1-exp` `pow-prod-down` `associate-l/` `associate-r/` `div-inv`
1×	`*-commutative`

Counts

4 → 129

Calls

4 calls:

45.0ms	(* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
2.0ms	(sqrt (fma y y (fma x x (* z z))))
2.0ms	(sqrt (fma y y (fma x x (* z z))))
13.0ms	(sqrt (* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))

series747.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
156.0ms	(sqrt (fma y y (fma x x (* z z))))
204.0ms	(sqrt (fma y y (fma x x (* z z))))
266.0ms	(sqrt (* (/ (sqrt (fma y y (fma x x (* z z)))) 1) (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))

simplify4.8s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	4271
1	499
0	168

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.3b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b

(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0)))

0.1b

(/ (fma y y (fma x x (* z z))) (cbrt 3.0))

36.1b

(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
51×	`times-frac`
50×	`add-exp-log`
36×	`*-un-lft-identity`
33×	`add-cube-cbrt`
24×	`cbrt-prod`
22×	`associate-r`
20×	`prod-exp`
18×	`add-cbrt-cube`
16×	`div-exp`
9×	`unswap-sqr`
8×	`pow1` `cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
4×	`rec-exp` `1-exp`
3×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`frac-times` `sqrt-pow1` `pow-prod-down` `associate-l/` `associate-r/`
1×	`clear-num` `frac-2neg` `pow1/2` `*-commutative` `sqrt-prod`

Counts

3 → 129

Calls

3 calls:

63.0ms

(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0)))

9.0ms

(/ (fma y y (fma x x (* z z))) (cbrt 3.0))

61.0ms

(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0))))

series871.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms

(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (cbrt 3.0)))

189.0ms

(/ (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))))

simplify2.0s

Counts

138 → 138

Iterations

Iter	Nodes
done	5001
2	3166
1	559
0	203

prune810.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (/ 1 (cbrt 3.0)) (cbrt 3.0)) (sqrt (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (sqrt (cbrt 3.0))))
1.0b	(/ (/ (/ 1 (cbrt 3.0)) (cbrt 3.0)) (sqrt (cbrt 3.0)))
1.0b	(/ 1 (cbrt 3.0))
36.1b	(sqrt (* (/ (/ (/ 1 (cbrt 3.0)) (cbrt 3.0)) (sqrt (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (sqrt (cbrt 3.0)))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

7524×	`times-frac`
3902×	`add-sqr-sqrt`
3313×	`cbrt-prod`
3243×	`*-un-lft-identity`
3195×	`add-cube-cbrt`
1827×	`sqrt-prod`
1228×	`associate-l`
149×	`div-inv`
148×	`unswap-sqr`
139×	`associate-/l*`
73×	`add-exp-log`
41×	`div-exp`
37×	`add-cbrt-cube`
31×	`associate-r`
23×	`cbrt-undiv`
18×	`pow1`
15×	`associate-/r*`
12×	`prod-exp`
10×	`pow-div`
8×	`cbrt-unprod`
5×	`sqrt-pow1` `pow-flip`
4×	`expm1-log1p-u` `rec-exp` `pow1/3` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `sqrt-div` `inv-pow`
2×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/`
1×	`*-commutative` `associate-/l/`

Counts

4 → 2898

Calls

4 calls:

1.0s	(* (/ (/ (/ 1 (cbrt 3.0)) (cbrt 3.0)) (sqrt (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (sqrt (cbrt 3.0))))
85.0ms	(/ (/ (/ 1 (cbrt 3.0)) (cbrt 3.0)) (sqrt (cbrt 3.0)))
8.0ms	(/ 1 (cbrt 3.0))
92.0ms	(sqrt (* (/ (/ (/ 1 (cbrt 3.0)) (cbrt 3.0)) (sqrt (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (sqrt (cbrt 3.0)))))

series607.0ms

Counts

4 → 8

Calls

4 calls:

170.0ms	(* (/ (/ (/ 1 (cbrt 3.0)) (cbrt 3.0)) (sqrt (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (sqrt (cbrt 3.0))))
0.0ms	(/ (/ (/ 1 (cbrt 3.0)) (cbrt 3.0)) (sqrt (cbrt 3.0)))
0.0ms	(/ 1 (cbrt 3.0))
437.0ms	(sqrt (* (/ (/ (/ 1 (cbrt 3.0)) (cbrt 3.0)) (sqrt (cbrt 3.0))) (/ (fma y y (fma x x (* z z))) (sqrt (cbrt 3.0)))))

simplify2.7s

Counts

2906 → 2906

Iterations

Iter	Nodes
done	5001
0	2149

prune24.7s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 19.3b

regimes423.0ms

Accuracy

61.4% (7.5b remaining)

Error of 25.3b against oracle of 17.8b and baseline of 37.2b

bsearch114.0ms

Steps

Iters	Range		Point
8	4.894347796388268e+59	1.6925211481097654e+62	1.6755932361979678e+62
8	-4.929461773712573e+105	-2.6664585819665247e+101	-2.2246552119313502e+105

simplify11.0ms

Iterations

Iter	Nodes
done	34
2	34
1	31
0	25

end0.0ms

sample1.0s

Algorithm

intervals

Results

643.0ms

8000×

body

valid