Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

Average Error: 0.0 → 0.0

Time: 23.5s

Precision: binary64

Cost: 576

Math

\[\left(\frac{x}{2} + y \cdot x\right) + z \]

↓

\[\frac{x}{2} + \left(x \cdot y + z\right) \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))

↓

(FPCore (x y z) :precision binary64 (+ (/ x 2.0) (+ (* x y) z)))

C

double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

↓

double code(double x, double y, double z) {
	return (x / 2.0) + ((x * y) + z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x / 2.0d0) + (y * x)) + z
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x / 2.0d0) + ((x * y) + z)
end function

Java

public static double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

↓

public static double code(double x, double y, double z) {
	return (x / 2.0) + ((x * y) + z);
}

Python

def code(x, y, z):
	return ((x / 2.0) + (y * x)) + z

↓

def code(x, y, z):
	return (x / 2.0) + ((x * y) + z)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x / 2.0) + Float64(y * x)) + z)
end

↓

function code(x, y, z)
	return Float64(Float64(x / 2.0) + Float64(Float64(x * y) + z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x / 2.0) + (y * x)) + z;
end

↓

function tmp = code(x, y, z)
	tmp = (x / 2.0) + ((x * y) + z);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x / 2.0), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(x / 2.0), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\left(\frac{x}{2} + y \cdot x\right) + z \]

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{x}{2} + \left(x \cdot y + z\right)} \]
   Proof

   [Start] 0.0	\[ \left(\frac{x}{2} + y \cdot x\right) + z \]
   rational.json-simplify-1 [=>] 0.0	\[ \color{blue}{z + \left(\frac{x}{2} + y \cdot x\right)} \]
   rational.json-simplify-41 [=>] 0.0	\[ \color{blue}{\frac{x}{2} + \left(y \cdot x + z\right)} \]
   rational.json-simplify-2 [=>] 0.0	\[ \frac{x}{2} + \left(\color{blue}{x \cdot y} + z\right) \]

3. Final simplification 0.0

   \[\leadsto \frac{x}{2} + \left(x \cdot y + z\right) \]

Alternatives

Alternative 1
Error	27.2
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-27}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-154}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-196}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-149}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{-103}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-54}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 2
Error	16.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-13}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-39}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 3
Error	10.8
Cost	584

\[\begin{array}{l} t_0 := z + y \cdot x\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{-116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-63}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.8
Cost	584

\[\begin{array}{l} t_0 := z + y \cdot x\\ \mathbf{if}\;y \leq -450:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{2} + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	0.0
Cost	576

\[\left(\frac{x}{2} + y \cdot x\right) + z \]

Alternative 6
Error	27.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-30}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-54}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7
Error	0.0
Cost	448

\[z + \left(0.5 + y\right) \cdot x \]

Alternative 8
Error	34.3
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023064 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2.0) (* y x)) z))