Details

sample30.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify23.0ms

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

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)
33.7b	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

rewrite15.0ms

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` `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 → 76

Calls

4 calls:

0.0ms	(fma x x (* z z))
0.0ms	(fma y y (fma x x (* z z)))
5.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
7.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

series482.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma x x (* z z))
73.0ms	(fma y y (fma x x (* z z)))
85.0ms	(/ (fma y y (fma x x (* z z))) 3.0)
262.0ms	(sqrt (/ (fma y y (fma x x (* z z))) 3.0))

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	2870
2	597
1	186
0	117

prune588.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma y y (fma x x (* z z)))
0.1b	(/ 1 (/ 3.0 (fma y y (fma x x (* z z)))))
1.0b	(/ 3.0 (fma y y (fma x x (* z z))))
33.7b	(sqrt (/ 1 (/ 3.0 (fma y y (fma x x (* z z))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
98×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
89×	`add-cube-cbrt`
44×	`sqrt-prod`
17×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
10×	`div-inv`
8×	`div-exp`
7×	`pow1`
6×	`associate-/l*`
5×	`rem-sqrt-square`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/r/` `pow-flip` `inv-pow`
1×	`pow1/2` `sqrt-div` `fma-udef`

Counts

4 → 180

Calls

4 calls:

0.0ms	(fma y y (fma x x (* z z)))
11.0ms	(/ 1 (/ 3.0 (fma y y (fma x x (* z z)))))
7.0ms	(/ 3.0 (fma y y (fma x x (* z z))))
20.0ms	(sqrt (/ 1 (/ 3.0 (fma y y (fma x x (* z z))))))

series859.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma y y (fma x x (* z z)))
111.0ms	(/ 1 (/ 3.0 (fma y y (fma x x (* z z)))))
412.0ms	(/ 3.0 (fma y y (fma x x (* z z))))
269.0ms	(sqrt (/ 1 (/ 3.0 (fma y y (fma x x (* z z))))))

simplify1.9s

Counts

192 → 192

Iterations

Iter	Nodes
done	5002
2	2304
1	504
0	260

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
0.3b	(* (sqrt (sqrt (fma y y (fma x x (* z z))))) (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))
33.7b	(sqrt (fma y y (fma x x (* z z))))
33.7b	(sqrt (fma y y (fma x x (* z z))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

102×	`sqrt-prod`
73×	`add-sqr-sqrt`
44×	`times-frac`
36×	`*-un-lft-identity` `add-cube-cbrt`
25×	`associate-r`
12×	`unswap-sqr`
11×	`pow1`
9×	`associate-l`
6×	`add-cbrt-cube` `add-exp-log`
5×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`sqrt-div` `div-inv`
1×	`sqrt-unprod` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod`

Counts

4 → 130

Calls

4 calls:

10.0ms	(sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
45.0ms	(* (sqrt (sqrt (fma y y (fma x x (* z z))))) (sqrt (/ (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))))

series863.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0))
277.0ms	(* (sqrt (sqrt (fma y y (fma x x (* z z))))) (sqrt (/ (sqrt (fma y y (fma x x (* z z)))) 3.0)))
179.0ms	(sqrt (fma y y (fma x x (* z z))))
172.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify1.3s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	1161
1	290
0	165

prune738.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.4b

localize68.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (sqrt (fma y y (fma x x (* z z))))) (sqrt 3.0))
33.7b	(sqrt (fma y y (fma x x (* z z))))
33.7b	(sqrt (fma y y (fma x x (* z z))))
33.7b	(sqrt (fma y y (fma x x (* z z))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

102×	`sqrt-prod`
54×	`times-frac`
51×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-/l*`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `sqrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 129

Calls

4 calls:

14.0ms	(/ (sqrt (sqrt (fma y y (fma x x (* z z))))) (sqrt 3.0))
2.0ms	(sqrt (fma y y (fma x x (* z z))))
2.0ms	(sqrt (fma y y (fma x x (* z z))))
2.0ms	(sqrt (fma y y (fma x x (* z z))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(/ (sqrt (sqrt (fma y y (fma x x (* z z))))) (sqrt 3.0))
125.0ms	(sqrt (fma y y (fma x x (* z z))))
134.0ms	(sqrt (fma y y (fma x x (* z z))))
171.0ms	(sqrt (fma y y (fma x x (* z z))))

simplify2.3s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
3	4350
2	779
1	240
0	145

prune924.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 17.4b

regimes423.0ms

Accuracy

62.9% (7.3b remaining)

Error of 25.5b against oracle of 18.2b and baseline of 37.9b

bsearch61.0ms

Steps

Iters	Range		Point
9	5.361487689279259e+122	5.111664819953359e+128	1.196300017523969e+127
4	-7.940145703991965e+117	-5.397638469289235e+117	-6.58943873555614e+117

simplify7.0ms

Iterations

Iter	Nodes
done	30
2	30
1	27
0	22

end0.0ms

sample904.0ms

Algorithm

intervals

Results

643.0ms

8000×

body

valid