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

Percentage Accurate: 100.0% → 100.0%

Time: 2.3s

Alternatives: 3

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

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

C

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

Java

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)

Julia

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

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

C

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

Java

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)

Julia

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

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

C

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

Java

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)

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+230} \lor \neg \left(x \leq -1.02 \cdot 10^{+167}\right) \land \left(x \leq -3 \cdot 10^{-5} \lor \neg \left(x \leq 0.082\right)\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.15e+230)
         (and (not (<= x -1.02e+167)) (or (<= x -3e-5) (not (<= x 0.082)))))
   (- x (* x z))
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e+230) || (!(x <= -1.02e+167) && ((x <= -3e-5) || !(x <= 0.082)))) {
		tmp = x - (x * z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.15d+230)) .or. (.not. (x <= (-1.02d+167))) .and. (x <= (-3d-5)) .or. (.not. (x <= 0.082d0))) then
        tmp = x - (x * z)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e+230) || (!(x <= -1.02e+167) && ((x <= -3e-5) || !(x <= 0.082)))) {
		tmp = x - (x * z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.15e+230) or (not (x <= -1.02e+167) and ((x <= -3e-5) or not (x <= 0.082))):
		tmp = x - (x * z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.15e+230) || (!(x <= -1.02e+167) && ((x <= -3e-5) || !(x <= 0.082))))
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.15e+230) || (~((x <= -1.02e+167)) && ((x <= -3e-5) || ~((x <= 0.082)))))
		tmp = x - (x * z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e+230], And[N[Not[LessEqual[x, -1.02e+167]], $MachinePrecision], Or[LessEqual[x, -3e-5], N[Not[LessEqual[x, 0.082]], $MachinePrecision]]]], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1499999999999999e230 or -1.02e167 < x < -3.00000000000000008e-5 or 0.0820000000000000034 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.9%

      \[\leadsto x + \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 84.9%

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

      2. distribute-rgt-neg-out 84.9%

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

   4. Simplified 84.9%

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

   if -1.1499999999999999e230 < x < -1.02e167 or -3.00000000000000008e-5 < x < 0.0820000000000000034

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.9%

      \[\leadsto x + \color{blue}{y \cdot z} \]
   3. Step-by-step derivation

      1. *-commutative 93.9%

         \[\leadsto x + \color{blue}{z \cdot y} \]

   4. Simplified 93.9%

      \[\leadsto x + \color{blue}{z \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+230} \lor \neg \left(x \leq -1.02 \cdot 10^{+167}\right) \land \left(x \leq -3 \cdot 10^{-5} \lor \neg \left(x \leq 0.082\right)\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 3: 76.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + y \cdot z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around inf 78.4%

   \[\leadsto x + \color{blue}{y \cdot z} \]
3. Step-by-step derivation

   1. *-commutative 78.4%

      \[\leadsto x + \color{blue}{z \cdot y} \]

4. Simplified 78.4%

   \[\leadsto x + \color{blue}{z \cdot y} \]

5. Final simplification 78.4%

   \[\leadsto x + y \cdot z \]

Reproduce

herbie shell --seed 2023215 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))