Details

sample49.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
0.0b	(fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
2.3b	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
24.2b	(* (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 (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
32.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
20.0ms	(* (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)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
86.0ms	(fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606)
112.0ms	(/ (- x 2.0) (fma (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894) x 47.066876606))
411.0ms	(* (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)))

simplify2.3s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	1543
1	465
0	197

prune988.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894) x 47.066876606)
0.0b	(* (fma (+ 43.3400022514 x) x 263.505074721) x)
2.3b	(/ (- x 2.0) (fma (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894) x 47.066876606))
24.2b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894) x 47.066876606)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

0.0ms	(fma (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894) x 47.066876606)
11.0ms	(* (fma (+ 43.3400022514 x) x 263.505074721) x)
23.0ms	(/ (- x 2.0) (fma (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894) x 47.066876606))
29.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894) x 47.066876606)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894) x 47.066876606)
48.0ms	(* (fma (+ 43.3400022514 x) x 263.505074721) x)
116.0ms	(/ (- x 2.0) (fma (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894) x 47.066876606))
468.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894) x 47.066876606)))

simplify2.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1695
1	497
0	212

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ 263.505074721 (* x x)))
2.3b	(/ (- x 2.0) (fma (+ (fma (* x x) 43.3400022514 (* x (+ 263.505074721 (* x x)))) 313.399215894) x 47.066876606))
7.3b	(fma (* x x) 43.3400022514 (* x (+ 263.505074721 (* x x))))
24.2b	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (+ (fma (* x x) 43.3400022514 (* x (+ 263.505074721 (* x x)))) 313.399215894) x 47.066876606)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

14.0ms	(* x (+ 263.505074721 (* x x)))
13.0ms	(/ (- x 2.0) (fma (+ (fma (* x x) 43.3400022514 (* x (+ 263.505074721 (* x x)))) 313.399215894) x 47.066876606))
0.0ms	(fma (* x x) 43.3400022514 (* x (+ 263.505074721 (* x x))))
17.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (+ (fma (* x x) 43.3400022514 (* x (+ 263.505074721 (* x x)))) 313.399215894) x 47.066876606)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* x (+ 263.505074721 (* x x)))
115.0ms	(/ (- x 2.0) (fma (+ (fma (* x x) 43.3400022514 (* x (+ 263.505074721 (* x x)))) 313.399215894) x 47.066876606))
39.0ms	(fma (* x x) 43.3400022514 (* x (+ 263.505074721 (* x x))))
386.0ms	(* (fma x (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y) z) (/ (- x 2.0) (fma (+ (fma (* x x) 43.3400022514 (* x (+ 263.505074721 (* x x)))) 313.399215894) x 47.066876606)))

simplify2.2s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	2048
1	568
0	222

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x (fma x x 263.505074721) 313.399215894)
2.1b	(/ (fma x (fma (* x x) 43.3400022514 (fma x (fma x x 263.505074721) 313.399215894)) 47.066876606) (- x 2.0))
7.3b	(fma (* x x) 43.3400022514 (fma x (fma x x 263.505074721) 313.399215894))
24.0b	(/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (/ (fma x (fma (* x x) 43.3400022514 (fma x (fma x x 263.505074721) 313.399215894)) 47.066876606) (- x 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
104×	`add-sqr-sqrt` `*-un-lft-identity`
72×	`add-cube-cbrt`
26×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
6×	`div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef`

Counts

4 → 167

Calls

4 calls:

0.0ms	(fma x (fma x x 263.505074721) 313.399215894)
8.0ms	(/ (fma x (fma (* x x) 43.3400022514 (fma x (fma x x 263.505074721) 313.399215894)) 47.066876606) (- x 2.0))
0.0ms	(fma (* x x) 43.3400022514 (fma x (fma x x 263.505074721) 313.399215894))
19.0ms	(/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (/ (fma x (fma (* x x) 43.3400022514 (fma x (fma x x 263.505074721) 313.399215894)) 47.066876606) (- x 2.0)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma x (fma x x 263.505074721) 313.399215894)
151.0ms	(/ (fma x (fma (* x x) 43.3400022514 (fma x (fma x x 263.505074721) 313.399215894)) 47.066876606) (- x 2.0))
43.0ms	(fma (* x x) 43.3400022514 (fma x (fma x x 263.505074721) 313.399215894))
362.0ms	(/ (fma x (fma x (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) y) z) (/ (fma x (fma (* x x) 43.3400022514 (fma x (fma x x 263.505074721) 313.399215894)) 47.066876606) (- x 2.0)))

simplify2.5s

Counts

179 → 179

Iterations

Iter	Nodes
done	5004
2	2242
1	696
0	298

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes346.0ms

Accuracy

96.9% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 24.3b

bsearch296.0ms

Steps

Iters	Range		Point
8	6.68994686148466e+41	4.921254434932496e+45	1.692613215272597e+44
8	-5.5526078831285184e+17	-22511205481733.605	-5.140336158145698e+17

simplify27.0ms

Iterations

Iter	Nodes
done	41
1	41
0	35

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.8s

8007×

body

valid