Details

sample102.0ms

Algorithm

intervals

Results

71.0ms

257×

body

valid

simplify1.8s

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: 22.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
0.1b	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
3.3b	(/ (- 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)))

rewrite32.0ms

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 (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
0.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
12.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
18.0ms	(* (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)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
48.0ms	(fma x (fma x 4.16438922228 78.6994924154) 137.519416416)
133.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
367.0ms	(* (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)))

simplify2.1s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
2	1519
1	458
0	195

prune984.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

6.8b	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
13.6b	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
13.8b	(* (* (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))))
19.1b	(* (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))))

rewrite104.0ms

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:

3.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
18.0ms	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
55.0ms	(* (* (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))))
25.0ms	(* (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))))

series1.3s

Counts

4 → 12

Calls

4 calls:

139.0ms	(sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
243.0ms	(/ (- x 2.0) (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
406.0ms	(* (* (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))))
515.0ms	(* (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))))

simplify2.6s

Counts

206 → 206

Iterations

Iter	Nodes
done	5000
2	2833
1	888
0	320

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

13.6b	(sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
13.6b	(sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
13.8b	(* (* (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)))) (/ 1 (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
19.1b	(* (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))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
58×	`sqrt-prod`
57×	`add-sqr-sqrt`
53×	`associate-r`
49×	`times-frac`
43×	`*-un-lft-identity`
41×	`add-cube-cbrt`
40×	`prod-exp`
30×	`add-cbrt-cube`
20×	`div-exp`
15×	`pow1`
12×	`cbrt-unprod`
10×	`rec-exp` `1-exp`
8×	`sqrt-pow1`
6×	`cbrt-undiv`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `pow1/2` `associate-l` `pow-prod-down` `associate-*r/` `un-div-inv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `associate-l/` `-commutative` `div-inv`

Counts

4 → 171

Calls

4 calls:

2.0ms	(sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
2.0ms	(sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
53.0ms	(* (* (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)))) (/ 1 (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
21.0ms	(* (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))))

series1.9s

Counts

4 → 12

Calls

4 calls:

215.0ms	(sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
263.0ms	(sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
855.0ms	(* (* (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)))) (/ 1 (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
520.0ms	(* (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))))

simplify2.8s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
2	2193
1	736
0	279

prune2.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

13.6b	(sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
13.8b	(* (* (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)))) (/ 1 (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
17.5b	(cbrt (* (* (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
19.1b	(* (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))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
53×	`add-sqr-sqrt` `associate-r`
49×	`times-frac`
48×	`sqrt-prod`
41×	`*-un-lft-identity`
40×	`prod-exp`
39×	`add-cube-cbrt`
30×	`add-cbrt-cube`
20×	`div-exp`
13×	`pow1`
12×	`cbrt-unprod`
10×	`rec-exp` `1-exp`
6×	`cbrt-undiv`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `pow-prod-down` `associate-*r/` `un-div-inv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `pow1/2` `associate-l/` `-commutative` `div-inv`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 162

Calls

4 calls:

2.0ms	(sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
45.0ms	(* (* (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)))) (/ 1 (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
45.0ms	(cbrt (* (* (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
18.0ms	(* (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))))

series1.6s

Counts

4 → 12

Calls

4 calls:

186.0ms	(sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))
730.0ms	(* (* (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)))) (/ 1 (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
236.0ms	(cbrt (* (* (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))) (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))) (sqrt (sqrt (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)))))
456.0ms	(* (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))))

simplify2.3s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
2	2300
1	768
0	291

prune1.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes216.0ms

Accuracy

96.3% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 23.6b

bsearch442.0ms

Steps

Iters	Range		Point
8	3.178840255699709e+39	9.580806910646127e+42	9.455030365015399e+42
7	-6.588293099414571e+23	-1.602448967471145e+22	-6.460947809195672e+23

simplify21.0ms

Iterations

Iter	Nodes
done	53
1	53
0	43

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.4s

8006×

body

valid