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

Percentage Accurate: 100.0% → 100.0%

Time: 3.5s

Alternatives: 8

Speedup: 1.0×

• 20.6% 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-def 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. Final simplification 100.0%

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

Alternative 2: 59.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{+112} \lor \neg \left(z \leq 2 \cdot 10^{+207}\right) \land z \leq 1.1 \cdot 10^{+247}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.26e-117)
   (* y z)
   (if (<= z 2.3e-75)
     x
     (if (or (<= z 1.72e+112) (and (not (<= z 2e+207)) (<= z 1.1e+247)))
       (* y z)
       (* x (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.26e-117) {
		tmp = y * z;
	} else if (z <= 2.3e-75) {
		tmp = x;
	} else if ((z <= 1.72e+112) || (!(z <= 2e+207) && (z <= 1.1e+247))) {
		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 <= (-1.26d-117)) then
        tmp = y * z
    else if (z <= 2.3d-75) then
        tmp = x
    else if ((z <= 1.72d+112) .or. (.not. (z <= 2d+207)) .and. (z <= 1.1d+247)) 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 <= -1.26e-117) {
		tmp = y * z;
	} else if (z <= 2.3e-75) {
		tmp = x;
	} else if ((z <= 1.72e+112) || (!(z <= 2e+207) && (z <= 1.1e+247))) {
		tmp = y * z;
	} else {
		tmp = x * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.26e-117:
		tmp = y * z
	elif z <= 2.3e-75:
		tmp = x
	elif (z <= 1.72e+112) or (not (z <= 2e+207) and (z <= 1.1e+247)):
		tmp = y * z
	else:
		tmp = x * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.26e-117)
		tmp = Float64(y * z);
	elseif (z <= 2.3e-75)
		tmp = x;
	elseif ((z <= 1.72e+112) || (!(z <= 2e+207) && (z <= 1.1e+247)))
		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 <= -1.26e-117)
		tmp = y * z;
	elseif (z <= 2.3e-75)
		tmp = x;
	elseif ((z <= 1.72e+112) || (~((z <= 2e+207)) && (z <= 1.1e+247)))
		tmp = y * z;
	else
		tmp = x * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.26e-117], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.3e-75], x, If[Or[LessEqual[z, 1.72e+112], And[N[Not[LessEqual[z, 2e+207]], $MachinePrecision], LessEqual[z, 1.1e+247]]], N[(y * z), $MachinePrecision], N[(x * (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2599999999999999e-117 or 2.3e-75 < z < 1.71999999999999997e112 or 2.0000000000000001e207 < z < 1.10000000000000006e247

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 89.3%

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

   3. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   if -1.2599999999999999e-117 < z < 2.3e-75

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 75.1%

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

   if 1.71999999999999997e112 < z < 2.0000000000000001e207 or 1.10000000000000006e247 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

   3. Taylor expanded in y around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-rgt-neg-out 83.5%

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

   5. Simplified 83.5%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{+112} \lor \neg \left(z \leq 2 \cdot 10^{+207}\right) \land z \leq 1.1 \cdot 10^{+247}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-110} \lor \neg \left(x \leq 6.8 \cdot 10^{-88}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e-110) (not (<= x 6.8e-88))) (* x (- 1.0 z)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-110) || !(x <= 6.8e-88)) {
		tmp = x * (1.0 - z);
	} 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 ((x <= (-7d-110)) .or. (.not. (x <= 6.8d-88))) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-110) || !(x <= 6.8e-88)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e-110) or not (x <= 6.8e-88):
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e-110) || !(x <= 6.8e-88))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e-110) || ~((x <= 6.8e-88)))
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e-110], N[Not[LessEqual[x, 6.8e-88]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.99999999999999947e-110 or 6.79999999999999949e-88 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 77.2%

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

      1. distribute-rgt1-in 77.1%

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

      2. mul-1-neg 77.1%

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

      3. cancel-sign-sub-inv 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in x around 0 77.2%

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

   if -6.99999999999999947e-110 < x < 6.79999999999999949e-88

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 83.7%

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

   3. Taylor expanded in y around inf 80.8%

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

      1. *-commutative 80.8%

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

   5. Simplified 80.8%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-110} \lor \neg \left(x \leq 6.8 \cdot 10^{-88}\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-118} \lor \neg \left(z \leq 1.25 \cdot 10^{-71}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.6e-118) (not (<= z 1.25e-71)))
   (* (- y x) z)
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.6e-118) || !(z <= 1.25e-71)) {
		tmp = (y - x) * 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 ((z <= (-8.6d-118)) .or. (.not. (z <= 1.25d-71))) then
        tmp = (y - x) * 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 ((z <= -8.6e-118) || !(z <= 1.25e-71)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.6e-118) or not (z <= 1.25e-71):
		tmp = (y - x) * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.6e-118) || !(z <= 1.25e-71))
		tmp = Float64(Float64(y - x) * 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 ((z <= -8.6e-118) || ~((z <= 1.25e-71)))
		tmp = (y - x) * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.6e-118], N[Not[LessEqual[z, 1.25e-71]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.60000000000000036e-118 or 1.24999999999999999e-71 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 90.9%

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

   if -8.60000000000000036e-118 < z < 1.24999999999999999e-71

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.1%

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

      1. distribute-rgt1-in 75.1%

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

      2. mul-1-neg 75.1%

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

      3. cancel-sign-sub-inv 75.1%

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

   4. Simplified 75.1%

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

   5. Taylor expanded in x around 0 75.1%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-118} \lor \neg \left(z \leq 1.25 \cdot 10^{-71}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 5: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \lor \neg \left(z \leq 1.76 \cdot 10^{-19}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.1) (not (<= z 1.76e-19))) (* (- y x) z) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.1) || !(z <= 1.76e-19)) {
		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 <= (-2.1d0)) .or. (.not. (z <= 1.76d-19))) 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 <= -2.1) || !(z <= 1.76e-19)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.1) or not (z <= 1.76e-19):
		tmp = (y - x) * z
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.1) || !(z <= 1.76e-19))
		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 <= -2.1) || ~((z <= 1.76e-19)))
		tmp = (y - x) * z;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.1], N[Not[LessEqual[z, 1.76e-19]], $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 < -2.10000000000000009 or 1.75999999999999993e-19 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.3%

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

   if -2.10000000000000009 < z < 1.75999999999999993e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.5%

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

      1. *-commutative 37.0%

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

   4. Simplified 99.5%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \lor \neg \left(z \leq 1.76 \cdot 10^{-19}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.3e-117) (* y z) (if (<= z 1.6e-73) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.3e-117) {
		tmp = y * z;
	} else if (z <= 1.6e-73) {
		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 (z <= (-1.3d-117)) then
        tmp = y * z
    else if (z <= 1.6d-73) 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 (z <= -1.3e-117) {
		tmp = y * z;
	} else if (z <= 1.6e-73) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.3e-117:
		tmp = y * z
	elif z <= 1.6e-73:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.3e-117)
		tmp = Float64(y * z);
	elseif (z <= 1.6e-73)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.3e-117)
		tmp = y * z;
	elseif (z <= 1.6e-73)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.3e-117], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.6e-73], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.29999999999999992e-117 or 1.59999999999999993e-73 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 90.9%

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

   3. Taylor expanded in y around inf 57.6%

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

      1. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   if -1.29999999999999992e-117 < z < 1.59999999999999993e-73

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 75.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

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. Final simplification 100.0%

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

Alternative 8: 36.5% 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. Taylor expanded in z around 0 30.8%

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

3. Final simplification 30.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))