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

Percentage Accurate: 100.0% → 100.0%

Time: 11.2s

Alternatives: 8

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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, z, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - x\right) \cdot z \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z, x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-39}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+193}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.25e-39)
   (* y z)
   (if (<= z 5.9e-15) x (if (<= z 6.6e+193) (* y z) (* x (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.25e-39) {
		tmp = y * z;
	} else if (z <= 5.9e-15) {
		tmp = x;
	} else if (z <= 6.6e+193) {
		tmp = 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 (z <= (-1.25d-39)) then
        tmp = y * z
    else if (z <= 5.9d-15) then
        tmp = x
    else if (z <= 6.6d+193) then
        tmp = 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 (z <= -1.25e-39) {
		tmp = y * z;
	} else if (z <= 5.9e-15) {
		tmp = x;
	} else if (z <= 6.6e+193) {
		tmp = y * z;
	} else {
		tmp = x * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.25e-39:
		tmp = y * z
	elif z <= 5.9e-15:
		tmp = x
	elif z <= 6.6e+193:
		tmp = y * z
	else:
		tmp = x * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.25e-39)
		tmp = Float64(y * z);
	elseif (z <= 5.9e-15)
		tmp = x;
	elseif (z <= 6.6e+193)
		tmp = 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 (z <= -1.25e-39)
		tmp = y * z;
	elseif (z <= 5.9e-15)
		tmp = x;
	elseif (z <= 6.6e+193)
		tmp = y * z;
	else
		tmp = x * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.25e-39], N[(y * z), $MachinePrecision], If[LessEqual[z, 5.9e-15], x, If[LessEqual[z, 6.6e+193], N[(y * z), $MachinePrecision], N[(x * (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e-39 or 5.89999999999999963e-15 < z < 6.6e193

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in y around inf 57.3%

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

      1. *-commutative 57.3%

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

   6. Simplified 57.3%

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

   if -1.25e-39 < z < 5.89999999999999963e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 78.3%

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

   if 6.6e193 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.5%

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

      1. mul-1-neg 66.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-z\right)}\right) \]

      2. unsub-neg 66.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - z\right)} \]

   5. Simplified 66.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]

   6. Taylor expanded in z around inf 66.5%

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

      1. neg-mul-1 66.5%

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

      2. distribute-rgt-neg-in 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-39}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+193}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -52 \lor \neg \left(z \leq 2.45 \cdot 10^{-13}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -52.0) (not (<= z 2.45e-13))) (* (- y x) z) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -52.0) || !(z <= 2.45e-13)) {
		tmp = (y - 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 ((z <= (-52.0d0)) .or. (.not. (z <= 2.45d-13))) then
        tmp = (y - 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 ((z <= -52.0) || !(z <= 2.45e-13)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -52.0) or not (z <= 2.45e-13):
		tmp = (y - x) * z
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -52.0) || !(z <= 2.45e-13))
		tmp = Float64(Float64(y - 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 ((z <= -52.0) || ~((z <= 2.45e-13)))
		tmp = (y - x) * z;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -52.0], N[Not[LessEqual[z, 2.45e-13]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -52 or 2.45000000000000016e-13 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in y around inf 98.2%

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

   if -52 < z < 2.45000000000000016e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.5%

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

      1. *-commutative 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -52 \lor \neg \left(z \leq 2.45 \cdot 10^{-13}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-49} \lor \neg \left(z \leq 2.75 \cdot 10^{-19}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.32e-49) (not (<= z 2.75e-19))) (* (- y x) z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.32e-49) || !(z <= 2.75e-19)) {
		tmp = (y - x) * 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 ((z <= (-1.32d-49)) .or. (.not. (z <= 2.75d-19))) then
        tmp = (y - x) * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.32e-49) || !(z <= 2.75e-19)) {
		tmp = (y - x) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.32e-49) or not (z <= 2.75e-19):
		tmp = (y - x) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.32e-49) || !(z <= 2.75e-19))
		tmp = Float64(Float64(y - x) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.32e-49) || ~((z <= 2.75e-19)))
		tmp = (y - x) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.32e-49], N[Not[LessEqual[z, 2.75e-19]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3199999999999999e-49 or 2.7499999999999998e-19 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in y around inf 97.0%

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

   if -1.3199999999999999e-49 < z < 2.7499999999999998e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 78.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-49} \lor \neg \left(z \leq 2.75 \cdot 10^{-19}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+165} \lor \neg \left(y \leq 2.8 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.8e+165) (not (<= y 2.8e+15))) (* y z) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+165) || !(y <= 2.8e+15)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - 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 <= (-3.8d+165)) .or. (.not. (y <= 2.8d+15))) then
        tmp = y * z
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+165) || !(y <= 2.8e+15)) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.8e+165) or not (y <= 2.8e+15):
		tmp = y * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.8e+165) || !(y <= 2.8e+15))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.8e+165) || ~((y <= 2.8e+15)))
		tmp = y * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.8e+165], N[Not[LessEqual[y, 2.8e+15]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999999e165 or 2.8e15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 88.0%

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

   4. Taylor expanded in y around inf 77.5%

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

      1. *-commutative 77.5%

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

   6. Simplified 77.5%

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

   if -3.7999999999999999e165 < y < 2.8e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.3%

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

      1. mul-1-neg 83.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-z\right)}\right) \]

      2. unsub-neg 83.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - z\right)} \]

   5. Simplified 83.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+165} \lor \neg \left(y \leq 2.8 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-43} \lor \neg \left(z \leq 10^{-18}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.4e-43) (not (<= z 1e-18))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e-43) || !(z <= 1e-18)) {
		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 ((z <= (-3.4d-43)) .or. (.not. (z <= 1d-18))) 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 ((z <= -3.4e-43) || !(z <= 1e-18)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.4e-43) or not (z <= 1e-18):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.4e-43) || !(z <= 1e-18))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.4e-43) || ~((z <= 1e-18)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.4e-43], N[Not[LessEqual[z, 1e-18]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000001e-43 or 1.0000000000000001e-18 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in y around inf 54.6%

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

      1. *-commutative 54.6%

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

   6. Simplified 54.6%

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

   if -3.4000000000000001e-43 < z < 1.0000000000000001e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 78.3%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-43} \lor \neg \left(z \leq 10^{-18}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. Add Preprocessing

Alternative 8: 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 z around 0 38.5%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024143 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))