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

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

Alternatives: 8

Speedup: 1.0×

• 20.7% 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: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+160}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+100} \lor \neg \left(y \leq -1.7 \cdot 10^{+14}\right) \land y \leq 1.4 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e+160)
   (* y z)
   (if (or (<= y -1.4e+100) (and (not (<= y -1.7e+14)) (<= y 1.4e+178)))
     (* x (- 1.0 z))
     (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+160) {
		tmp = y * z;
	} else if ((y <= -1.4e+100) || (!(y <= -1.7e+14) && (y <= 1.4e+178))) {
		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 (y <= (-4d+160)) then
        tmp = y * z
    else if ((y <= (-1.4d+100)) .or. (.not. (y <= (-1.7d+14))) .and. (y <= 1.4d+178)) 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 (y <= -4e+160) {
		tmp = y * z;
	} else if ((y <= -1.4e+100) || (!(y <= -1.7e+14) && (y <= 1.4e+178))) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4e+160:
		tmp = y * z
	elif (y <= -1.4e+100) or (not (y <= -1.7e+14) and (y <= 1.4e+178)):
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e+160)
		tmp = Float64(y * z);
	elseif ((y <= -1.4e+100) || (!(y <= -1.7e+14) && (y <= 1.4e+178)))
		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 (y <= -4e+160)
		tmp = y * z;
	elseif ((y <= -1.4e+100) || (~((y <= -1.7e+14)) && (y <= 1.4e+178)))
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e+160], N[(y * z), $MachinePrecision], If[Or[LessEqual[y, -1.4e+100], And[N[Not[LessEqual[y, -1.7e+14]], $MachinePrecision], LessEqual[y, 1.4e+178]]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000003e160 or -1.3999999999999999e100 < y < -1.7e14 or 1.39999999999999997e178 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 85.1%

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

   3. Taylor expanded in y around inf 80.3%

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

      1. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   if -4.00000000000000003e160 < y < -1.3999999999999999e100 or -1.7e14 < y < 1.39999999999999997e178

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.2%

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

      1. distribute-rgt1-in 80.2%

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

      2. mul-1-neg 80.2%

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

      3. cancel-sign-sub-inv 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in x around 0 80.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+160}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+100} \lor \neg \left(y \leq -1.7 \cdot 10^{+14}\right) \land y \leq 1.4 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+153}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -2e+52)
     t_0
     (if (<= z -1.2e-37)
       (* y z)
       (if (<= z 5.8e-13) x (if (<= z 3.6e+153) (* y z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -2e+52) {
		tmp = t_0;
	} else if (z <= -1.2e-37) {
		tmp = y * z;
	} else if (z <= 5.8e-13) {
		tmp = x;
	} else if (z <= 3.6e+153) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (z <= (-2d+52)) then
        tmp = t_0
    else if (z <= (-1.2d-37)) then
        tmp = y * z
    else if (z <= 5.8d-13) then
        tmp = x
    else if (z <= 3.6d+153) then
        tmp = y * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -2e+52) {
		tmp = t_0;
	} else if (z <= -1.2e-37) {
		tmp = y * z;
	} else if (z <= 5.8e-13) {
		tmp = x;
	} else if (z <= 3.6e+153) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -2e+52:
		tmp = t_0
	elif z <= -1.2e-37:
		tmp = y * z
	elif z <= 5.8e-13:
		tmp = x
	elif z <= 3.6e+153:
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -2e+52)
		tmp = t_0;
	elseif (z <= -1.2e-37)
		tmp = Float64(y * z);
	elseif (z <= 5.8e-13)
		tmp = x;
	elseif (z <= 3.6e+153)
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -2e+52)
		tmp = t_0;
	elseif (z <= -1.2e-37)
		tmp = y * z;
	elseif (z <= 5.8e-13)
		tmp = x;
	elseif (z <= 3.6e+153)
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -2e+52], t$95$0, If[LessEqual[z, -1.2e-37], N[(y * z), $MachinePrecision], If[LessEqual[z, 5.8e-13], x, If[LessEqual[z, 3.6e+153], N[(y * z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e52 or 3.6000000000000001e153 < 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 64.2%

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

      1. mul-1-neg 64.2%

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

      2. distribute-rgt-neg-out 64.2%

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

   5. Simplified 64.2%

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

   if -2e52 < z < -1.19999999999999995e-37 or 5.7999999999999995e-13 < z < 3.6000000000000001e153

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 88.0%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   if -1.19999999999999995e-37 < z < 5.7999999999999995e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 76.4%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+153}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 4: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-37} \lor \neg \left(z \leq 4800\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.12e-37) (not (<= z 4800.0))) (* (- y x) z) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.12e-37) || !(z <= 4800.0)) {
		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 <= (-1.12d-37)) .or. (.not. (z <= 4800.0d0))) 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 <= -1.12e-37) || !(z <= 4800.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.12e-37) or not (z <= 4800.0):
		tmp = (y - x) * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.12e-37) || !(z <= 4800.0))
		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 <= -1.12e-37) || ~((z <= 4800.0)))
		tmp = (y - x) * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.12e-37], N[Not[LessEqual[z, 4800.0]], $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 < -1.12e-37 or 4800 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 96.2%

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

   if -1.12e-37 < z < 4800

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.4%

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

      1. distribute-rgt1-in 76.4%

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

      2. mul-1-neg 76.4%

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

      3. cancel-sign-sub-inv 76.4%

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

   4. Simplified 76.4%

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

   5. Taylor expanded in x around 0 76.4%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-37} \lor \neg \left(z \leq 4800\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 5: 98.9% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0))) (* (- y x) z) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		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 <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) 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 <= -1.0) || !(z <= 1.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		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 <= -1.0) || ~((z <= 1.0)))
		tmp = (y - x) * z;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $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 < -1 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 98.3%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.2%

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

      1. *-commutative 29.1%

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

   4. Simplified 99.2%

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

4. Final simplification 98.8%

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

Alternative 6: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2e-37) (* y z) (if (<= z 7.4e-12) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e-37) {
		tmp = y * z;
	} else if (z <= 7.4e-12) {
		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 <= (-1.2d-37)) then
        tmp = y * z
    else if (z <= 7.4d-12) 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 <= -1.2e-37) {
		tmp = y * z;
	} else if (z <= 7.4e-12) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.2e-37:
		tmp = y * z
	elif z <= 7.4e-12:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2e-37)
		tmp = Float64(y * z);
	elseif (z <= 7.4e-12)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.2e-37)
		tmp = y * z;
	elseif (z <= 7.4e-12)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2e-37], N[(y * z), $MachinePrecision], If[LessEqual[z, 7.4e-12], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999995e-37 or 7.39999999999999997e-12 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 95.0%

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

   3. Taylor expanded in y around inf 54.2%

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

      1. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   if -1.19999999999999995e-37 < z < 7.39999999999999997e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 76.4%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

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: 36.3% 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. Taylor expanded in z around 0 40.7%

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

3. Final simplification 40.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))