Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Average Error: 0.0 → 0.0

Time: 7.2s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y, double z) {
	return x + ((z * y) - (x * 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 + ((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 + ((z * y) - (x * z))
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	1.0
Cost	712

\[\begin{array}{l} t_0 := z \cdot y - x \cdot z\\ \mathbf{if}\;z \leq -74365371.24979533:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.262321529900886 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	17.1
Cost	584

\[\begin{array}{l} t_0 := x - x \cdot z\\ \mathbf{if}\;x \leq -5.594168104867363 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.289504036318504 \cdot 10^{+23}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	9.4
Cost	584

\[\begin{array}{l} t_0 := x - x \cdot z\\ \mathbf{if}\;x \leq -1.1068163066662685 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+110}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.0
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(y - x\right)\\ \mathbf{if}\;z \leq -74365371.24979533:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.262321529900886 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	24.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -3.581408467595153 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.289504036318504 \cdot 10^{+23}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	0.0
Cost	448

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

Alternative 7
Error	35.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022294 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))