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

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 6

Speedup: 1.0×

• 21.5% 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. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + \left(y - x\right) \cdot z \]
4. Add Preprocessing

Alternative 2: 85.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+121} \lor \neg \left(x \leq -8.5 \cdot 10^{+23} \lor \neg \left(x \leq -3 \cdot 10^{-14}\right) \land x \leq 2.6 \cdot 10^{+23}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8e+121)
         (not (or (<= x -8.5e+23) (and (not (<= x -3e-14)) (<= x 2.6e+23)))))
   (- x (* x z))
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e+121) || !((x <= -8.5e+23) || (!(x <= -3e-14) && (x <= 2.6e+23)))) {
		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 <= (-8d+121)) .or. (.not. (x <= (-8.5d+23)) .or. (.not. (x <= (-3d-14))) .and. (x <= 2.6d+23))) 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 <= -8e+121) || !((x <= -8.5e+23) || (!(x <= -3e-14) && (x <= 2.6e+23)))) {
		tmp = x - (x * z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8e+121) or not ((x <= -8.5e+23) or (not (x <= -3e-14) and (x <= 2.6e+23))):
		tmp = x - (x * z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8e+121) || !((x <= -8.5e+23) || (!(x <= -3e-14) && (x <= 2.6e+23))))
		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 <= -8e+121) || ~(((x <= -8.5e+23) || (~((x <= -3e-14)) && (x <= 2.6e+23)))))
		tmp = x - (x * z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8e+121], N[Not[Or[LessEqual[x, -8.5e+23], And[N[Not[LessEqual[x, -3e-14]], $MachinePrecision], LessEqual[x, 2.6e+23]]]], $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 < -8.0000000000000003e121 or -8.5000000000000001e23 < x < -2.9999999999999998e-14 or 2.59999999999999992e23 < x

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 89.9%

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

      1. mul-1-neg 89.9%

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

      2. distribute-lft-neg-out 89.9%

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

      3. *-commutative 89.9%

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

   5. Simplified 89.9%

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

      1. distribute-rgt-neg-out 89.9%

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

      2. unsub-neg 89.9%

         \[\leadsto \color{blue}{x - z \cdot x} \]

      3. *-commutative 89.9%

         \[\leadsto x - \color{blue}{x \cdot z} \]

   7. Applied egg-rr 89.9%

      \[\leadsto \color{blue}{x - x \cdot z} \]

   if -8.0000000000000003e121 < x < -8.5000000000000001e23 or -2.9999999999999998e-14 < x < 2.59999999999999992e23

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 97.1%

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

      1. *-commutative 97.1%

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

   5. Simplified 97.1%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+121} \lor \neg \left(x \leq -8.5 \cdot 10^{+23} \lor \neg \left(x \leq -3 \cdot 10^{-14}\right) \land x \leq 2.6 \cdot 10^{+23}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-112}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4e-112)
   (* y z)
   (if (<= y 5.2e-227)
     x
     (if (<= y 2.4e-131) (* x (- z)) (if (<= y 2.4e-76) x (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e-112) {
		tmp = y * z;
	} else if (y <= 5.2e-227) {
		tmp = x;
	} else if (y <= 2.4e-131) {
		tmp = x * -z;
	} else if (y <= 2.4e-76) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-2.4d-112)) then
        tmp = y * z
    else if (y <= 5.2d-227) then
        tmp = x
    else if (y <= 2.4d-131) then
        tmp = x * -z
    else if (y <= 2.4d-76) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e-112) {
		tmp = y * z;
	} else if (y <= 5.2e-227) {
		tmp = x;
	} else if (y <= 2.4e-131) {
		tmp = x * -z;
	} else if (y <= 2.4e-76) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4e-112:
		tmp = y * z
	elif y <= 5.2e-227:
		tmp = x
	elif y <= 2.4e-131:
		tmp = x * -z
	elif y <= 2.4e-76:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4e-112)
		tmp = Float64(y * z);
	elseif (y <= 5.2e-227)
		tmp = x;
	elseif (y <= 2.4e-131)
		tmp = Float64(x * Float64(-z));
	elseif (y <= 2.4e-76)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.4e-112)
		tmp = y * z;
	elseif (y <= 5.2e-227)
		tmp = x;
	elseif (y <= 2.4e-131)
		tmp = x * -z;
	elseif (y <= 2.4e-76)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4e-112], N[(y * z), $MachinePrecision], If[LessEqual[y, 5.2e-227], x, If[LessEqual[y, 2.4e-131], N[(x * (-z)), $MachinePrecision], If[LessEqual[y, 2.4e-76], x, N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000001e-112 or 2.40000000000000013e-76 < y

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 85.5%

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

      1. *-commutative 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in x around 0 64.9%

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

   if -2.4000000000000001e-112 < y < 5.20000000000000023e-227 or 2.4e-131 < y < 2.40000000000000013e-76

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.2%

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

      1. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in x around inf 66.5%

      \[\leadsto \color{blue}{x} \]

   if 5.20000000000000023e-227 < y < 2.4e-131

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 62.9%

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

      1. mul-1-neg 62.9%

         \[\leadsto \color{blue}{-x \cdot z} \]

      2. *-commutative 62.9%

         \[\leadsto -\color{blue}{z \cdot x} \]

      3. distribute-rgt-neg-in 62.9%

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

   8. Simplified 62.9%

      \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-112}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-113} \lor \neg \left(y \leq 1.55 \cdot 10^{-74}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.5e-113) (not (<= y 1.55e-74))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e-113) || !(y <= 1.55e-74)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	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 ((y <= (-2.5d-113)) .or. (.not. (y <= 1.55d-74))) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e-113) || !(y <= 1.55e-74)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.5e-113) or not (y <= 1.55e-74):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.5e-113) || !(y <= 1.55e-74))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.5e-113) || ~((y <= 1.55e-74)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.5e-113], N[Not[LessEqual[y, 1.55e-74]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.4999999999999999e-113 or 1.5500000000000001e-74 < y

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 85.5%

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

      1. *-commutative 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in x around 0 64.9%

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

   if -2.4999999999999999e-113 < y < 1.5500000000000001e-74

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in x around inf 61.0%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-113} \lor \neg \left(y \leq 1.55 \cdot 10^{-74}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{+186}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 7e+186) (+ x (* y z)) (* x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 7e+186) {
		tmp = x + (y * z);
	} else {
		tmp = x * -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 <= 7d+186) then
        tmp = x + (y * z)
    else
        tmp = x * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 7e+186) {
		tmp = x + (y * z);
	} else {
		tmp = x * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 7e+186:
		tmp = x + (y * z)
	else:
		tmp = x * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 7e+186)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 7e+186)
		tmp = x + (y * z);
	else
		tmp = x * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 7e+186], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.99999999999999974e186

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 82.2%

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

      1. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   if 6.99999999999999974e186 < x

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.1%

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

      1. mul-1-neg 99.1%

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

      2. distribute-lft-neg-out 99.1%

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

      3. *-commutative 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in z around inf 69.3%

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

      1. mul-1-neg 69.3%

         \[\leadsto \color{blue}{-x \cdot z} \]

      2. *-commutative 69.3%

         \[\leadsto -\color{blue}{z \cdot x} \]

      3. distribute-rgt-neg-in 69.3%

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

   8. Simplified 69.3%

      \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{+186}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[x + \left(y - x\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in y around inf 77.6%

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

   1. *-commutative 77.6%

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

5. Simplified 77.6%

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

6. Taylor expanded in x around inf 35.5%

   \[\leadsto \color{blue}{x} \]

7. Final simplification 35.5%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))