Details

sample121.0ms

Algorithm

intervals

Results

89.0ms

256×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1857
3	505
2	152
1	62
0	29

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.1b	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
2.6b	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
22.4b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

0.0ms	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
22.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
31.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

series664.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
53.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
129.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
430.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify2.4s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	1532
1	462
0	200

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

6.1b	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
15.0b	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
15.2b	(* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
18.3b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
82×	`times-frac`
56×	`associate-r`
55×	`add-cube-cbrt`
50×	`add-exp-log`
47×	`sqrt-prod`
32×	`add-cbrt-cube`
22×	`prod-exp`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`pow1` `div-exp` `cbrt-unprod`
7×	`cbrt-undiv`
6×	`associate-/r*`
5×	`associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `un-div-inv` `div-inv`
2×	`frac-times` `associate-l/` `-commutative` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `flip--`

Counts

4 → 194

Calls

4 calls:

2.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
25.0ms	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
76.0ms	(* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
38.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

series1.5s

Counts

4 → 12

Calls

4 calls:

166.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
227.0ms	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
453.0ms	(* (* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))
657.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ 1 (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))))

simplify2.9s

Counts

206 → 206

Iterations

Iter	Nodes
done	5000
2	2833
1	888
0	320

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

6.1b	(sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))
15.0b	(/ (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)) (- x 2.0))
15.2b	(/ (/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))) (/ (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)) (- x 2.0)))
19.2b	(/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

2196×	`times-frac`
1202×	`add-sqr-sqrt`
1201×	`*-un-lft-identity`
911×	`add-cube-cbrt`
711×	`sqrt-prod`
145×	`distribute-lft-out--` `difference-of-squares`
63×	`div-inv`
49×	`associate-/r/`
47×	`associate-/r*`
31×	`associate-/l*`
24×	`flip3--` `flip--`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 989

Calls

4 calls:

1.0ms	(sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))
9.0ms	(/ (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)) (- x 2.0))
34.0ms	(/ (/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))) (/ (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)) (- x 2.0)))
7.0ms	(/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)))

series1.5s

Counts

4 → 12

Calls

4 calls:

168.0ms	(sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))
271.0ms	(/ (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)) (- x 2.0))
426.0ms	(/ (/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))) (/ (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)) (- x 2.0)))
617.0ms	(/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (sqrt (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606)))

simplify5.1s

Counts

1001 → 1001

Iterations

Iter	Nodes
done	5000
1	3936
0	1107

prune7.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y)
0.1b	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.1b	(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
22.2b	(/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

0.0ms	(fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y)
0.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0ms	(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
9.0ms	(/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))

series634.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y)
56.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
60.0ms	(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
432.0ms	(/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (fma x (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) 47.066876606))

simplify2.6s

Counts

75 → 75

Iterations

Iter	Nodes
done	5008
3	2058
2	620
1	252
0	135

prune705.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes429.0ms

Accuracy

96.4% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 23.3b

bsearch350.0ms

Steps

Iters	Range		Point
8	1.6695195003064574e+19	1.3481347608348084e+23	1.3289883024938852e+23
5	-1.0272784703264377e+25	-4.3544505000805266e+24	-1.0082194143627248e+25

simplify7.0ms

Iterations

Iter	Nodes
done	42
1	42
0	35

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.5s

8008×

body

valid