Linear.V3:cross from linear-1.19.1.3

Average Error: 0.0 → 0.0

Time: 3.1s

Precision: binary64

Cost: 960

Math

\[x \cdot y - z \cdot t \]

↓

\[\begin{array}{l} t_1 := y \cdot \left(x \cdot 0.5\right)\\ t_1 + \left(t_1 - z \cdot t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* x y) (* z t)))

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x 0.5)))) (+ t_1 (- t_1 (* z t)))))

C

double code(double x, double y, double z, double t) {
	return (x * y) - (z * t);
}

↓

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * 0.5);
	return t_1 + (t_1 - (z * t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * y) - (z * t)
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    t_1 = y * (x * 0.5d0)
    code = t_1 + (t_1 - (z * t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * y) - (z * t);
}

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x * 0.5);
	return t_1 + (t_1 - (z * t));
}

Python

def code(x, y, z, t):
	return (x * y) - (z * t)

↓

def code(x, y, z, t):
	t_1 = y * (x * 0.5)
	return t_1 + (t_1 - (z * t))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * y) - Float64(z * t))
end

↓

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * 0.5))
	return Float64(t_1 + Float64(t_1 - Float64(z * t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * y) - (z * t);
end

↓

function tmp = code(x, y, z, t)
	t_1 = y * (x * 0.5);
	tmp = t_1 + (t_1 - (z * t));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]}, N[(t$95$1 + N[(t$95$1 - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 0.0

   \[x \cdot y - z \cdot t \]

2. Applied egg-rr 0.0

   \[\leadsto \color{blue}{y \cdot \left(x \cdot 0.5\right) + \left(y \cdot \left(x \cdot 0.5\right) - z \cdot t\right)} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	22.4
Cost	1048

\[\begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{-97}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-215}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-61}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

\[x \cdot y - z \cdot t \]

Alternative 3
Error	30.7
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2023064 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))