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

Average Error: 0.02% → 0.02%

Time: 3.4s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

Python

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

↓

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

MATLAB

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

↓

function tmp = code(x, y, z)
	tmp = x + ((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[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.02

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

2. Final simplification 0.02

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

Alternatives

Alternative 1
Error	37.07%
Cost	1181

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-22}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3050000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+111} \lor \neg \left(z \leq 1.02 \cdot 10^{+224}\right) \land z \leq 6.6 \cdot 10^{+261}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 2
Error	19%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{-22} \lor \neg \left(z \leq 2.75 \cdot 10^{-14}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	1.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -125 \lor \neg \left(z \leq 7.2 \cdot 10^{-6}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4
Error	37.41%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Error	55.79%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))