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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 7

Speedup: 1.2×

• 20.5% 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, 1.2× 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. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 60.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+217}:\\ \;\;\;\;\left(-x\right) \cdot z\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-19}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-91}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.1e+217)
   (* (- x) z)
   (if (<= z -6.6e-19) (* z y) (if (<= z 4.1e-91) (* 1.0 x) (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e+217) {
		tmp = -x * z;
	} else if (z <= -6.6e-19) {
		tmp = z * y;
	} else if (z <= 4.1e-91) {
		tmp = 1.0 * x;
	} else {
		tmp = z * y;
	}
	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 <= (-3.1d+217)) then
        tmp = -x * z
    else if (z <= (-6.6d-19)) then
        tmp = z * y
    else if (z <= 4.1d-91) then
        tmp = 1.0d0 * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e+217) {
		tmp = -x * z;
	} else if (z <= -6.6e-19) {
		tmp = z * y;
	} else if (z <= 4.1e-91) {
		tmp = 1.0 * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.1e+217:
		tmp = -x * z
	elif z <= -6.6e-19:
		tmp = z * y
	elif z <= 4.1e-91:
		tmp = 1.0 * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.1e+217)
		tmp = Float64(Float64(-x) * z);
	elseif (z <= -6.6e-19)
		tmp = Float64(z * y);
	elseif (z <= 4.1e-91)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.1e+217)
		tmp = -x * z;
	elseif (z <= -6.6e-19)
		tmp = z * y;
	elseif (z <= 4.1e-91)
		tmp = 1.0 * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.1e+217], N[((-x) * z), $MachinePrecision], If[LessEqual[z, -6.6e-19], N[(z * y), $MachinePrecision], If[LessEqual[z, 4.1e-91], N[(1.0 * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1000000000000002e217

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.0%

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

   if -3.1000000000000002e217 < z < -6.5999999999999995e-19 or 4.10000000000000024e-91 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 60.4

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

   5. Applied rewrites 60.4%

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

   if -6.5999999999999995e-19 < z < 4.10000000000000024e-91

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 76.5

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

   5. Applied rewrites 76.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 76.5%

      \[\leadsto 1 \cdot x \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+217}:\\ \;\;\;\;\left(-x\right) \cdot z\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-19}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-91}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y - x\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;z \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y x))))
   (if (<= z -1.0) t_0 (if (<= z 1.0) (+ (* z y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y - x);
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = (z * y) + x;
	} 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 * (y - x)
    if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = (z * y) + x
    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 * (y - x);
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = (z * y) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y - x)
	tmp = 0
	if z <= -1.0:
		tmp = t_0
	elif z <= 1.0:
		tmp = (z * y) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y - x))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(Float64(z * y) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y - x);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = (z * y) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 1.0], N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 98.0

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

   5. Applied rewrites 98.0%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 99.5

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

   5. Applied rewrites 99.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot \left(y - x\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;z \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y - x\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-73}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y x))))
   (if (<= z -1.08e-27) t_0 (if (<= z 3.2e-73) (* 1.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y - x);
	double tmp;
	if (z <= -1.08e-27) {
		tmp = t_0;
	} else if (z <= 3.2e-73) {
		tmp = 1.0 * x;
	} 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 * (y - x)
    if (z <= (-1.08d-27)) then
        tmp = t_0
    else if (z <= 3.2d-73) then
        tmp = 1.0d0 * x
    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 * (y - x);
	double tmp;
	if (z <= -1.08e-27) {
		tmp = t_0;
	} else if (z <= 3.2e-73) {
		tmp = 1.0 * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y - x)
	tmp = 0
	if z <= -1.08e-27:
		tmp = t_0
	elif z <= 3.2e-73:
		tmp = 1.0 * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y - x))
	tmp = 0.0
	if (z <= -1.08e-27)
		tmp = t_0;
	elseif (z <= 3.2e-73)
		tmp = Float64(1.0 * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y - x);
	tmp = 0.0;
	if (z <= -1.08e-27)
		tmp = t_0;
	elseif (z <= 3.2e-73)
		tmp = 1.0 * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e-27], t$95$0, If[LessEqual[z, 3.2e-73], N[(1.0 * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.08e-27 or 3.19999999999999986e-73 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 94.4

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

   5. Applied rewrites 94.4%

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

   if -1.08e-27 < z < 3.19999999999999986e-73

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 76.9

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

   5. Applied rewrites 76.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 76.9%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \left(y - x\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-73}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+143}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e+97) (* z y) (if (<= y 5.2e+143) (* (- 1.0 z) x) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+97) {
		tmp = z * y;
	} else if (y <= 5.2e+143) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = z * y;
	}
	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 <= (-4.5d+97)) then
        tmp = z * y
    else if (y <= 5.2d+143) then
        tmp = (1.0d0 - z) * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+97) {
		tmp = z * y;
	} else if (y <= 5.2e+143) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e+97:
		tmp = z * y
	elif y <= 5.2e+143:
		tmp = (1.0 - z) * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e+97)
		tmp = Float64(z * y);
	elseif (y <= 5.2e+143)
		tmp = Float64(Float64(1.0 - z) * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.5e+97)
		tmp = z * y;
	elseif (y <= 5.2e+143)
		tmp = (1.0 - z) * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e+97], N[(z * y), $MachinePrecision], If[LessEqual[y, 5.2e+143], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999976e97 or 5.1999999999999998e143 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 80.1

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

   5. Applied rewrites 80.1%

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

   if -4.49999999999999976e97 < y < 5.1999999999999998e143

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 76.4

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

   5. Applied rewrites 76.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+143}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-19}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-91}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.6e-19) (* z y) (if (<= z 4.1e-91) (* 1.0 x) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.6e-19) {
		tmp = z * y;
	} else if (z <= 4.1e-91) {
		tmp = 1.0 * x;
	} else {
		tmp = z * y;
	}
	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 <= (-6.6d-19)) then
        tmp = z * y
    else if (z <= 4.1d-91) then
        tmp = 1.0d0 * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.6e-19) {
		tmp = z * y;
	} else if (z <= 4.1e-91) {
		tmp = 1.0 * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.6e-19:
		tmp = z * y
	elif z <= 4.1e-91:
		tmp = 1.0 * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.6e-19)
		tmp = Float64(z * y);
	elseif (z <= 4.1e-91)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.6e-19)
		tmp = z * y;
	elseif (z <= 4.1e-91)
		tmp = 1.0 * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.6e-19], N[(z * y), $MachinePrecision], If[LessEqual[z, 4.1e-91], N[(1.0 * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5999999999999995e-19 or 4.10000000000000024e-91 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

   if -6.5999999999999995e-19 < z < 4.10000000000000024e-91

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. distribute-rgt1-in N/A

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

      6. +-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 76.5

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

   5. Applied rewrites 76.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 76.5%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-19}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-91}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.6% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf

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

   1. lower-*.f64 44.3

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

5. Applied rewrites 44.3%

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

6. Final simplification 44.3%

   \[\leadsto z \cdot y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024267 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))