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×

• 21.3% 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, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) \cdot z\\ \mathbf{if}\;z \leq -33000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-27}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-101}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+279}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x) z)))
   (if (<= z -33000000000000.0)
     t_0
     (if (<= z -6.5e-27)
       (* z y)
       (if (<= z 2.55e-101) (* 1.0 x) (if (<= z 1.4e+279) (* z y) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -x * z;
	double tmp;
	if (z <= -33000000000000.0) {
		tmp = t_0;
	} else if (z <= -6.5e-27) {
		tmp = z * y;
	} else if (z <= 2.55e-101) {
		tmp = 1.0 * x;
	} else if (z <= 1.4e+279) {
		tmp = z * y;
	} 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 = -x * z
    if (z <= (-33000000000000.0d0)) then
        tmp = t_0
    else if (z <= (-6.5d-27)) then
        tmp = z * y
    else if (z <= 2.55d-101) then
        tmp = 1.0d0 * x
    else if (z <= 1.4d+279) then
        tmp = z * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -x * z;
	double tmp;
	if (z <= -33000000000000.0) {
		tmp = t_0;
	} else if (z <= -6.5e-27) {
		tmp = z * y;
	} else if (z <= 2.55e-101) {
		tmp = 1.0 * x;
	} else if (z <= 1.4e+279) {
		tmp = z * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x * z
	tmp = 0
	if z <= -33000000000000.0:
		tmp = t_0
	elif z <= -6.5e-27:
		tmp = z * y
	elif z <= 2.55e-101:
		tmp = 1.0 * x
	elif z <= 1.4e+279:
		tmp = z * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) * z)
	tmp = 0.0
	if (z <= -33000000000000.0)
		tmp = t_0;
	elseif (z <= -6.5e-27)
		tmp = Float64(z * y);
	elseif (z <= 2.55e-101)
		tmp = Float64(1.0 * x);
	elseif (z <= 1.4e+279)
		tmp = Float64(z * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x * z;
	tmp = 0.0;
	if (z <= -33000000000000.0)
		tmp = t_0;
	elseif (z <= -6.5e-27)
		tmp = z * y;
	elseif (z <= 2.55e-101)
		tmp = 1.0 * x;
	elseif (z <= 1.4e+279)
		tmp = z * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) * z), $MachinePrecision]}, If[LessEqual[z, -33000000000000.0], t$95$0, If[LessEqual[z, -6.5e-27], N[(z * y), $MachinePrecision], If[LessEqual[z, 2.55e-101], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 1.4e+279], N[(z * y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e13 or 1.4000000000000001e279 < z

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 67.9%

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

   if -3.3e13 < z < -6.50000000000000025e-27 or 2.5500000000000001e-101 < z < 1.4000000000000001e279

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 61.6

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

   5. Applied rewrites 61.6%

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

   if -6.50000000000000025e-27 < z < 2.5500000000000001e-101

   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 77.6

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 77.6%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -33000000000000:\\ \;\;\;\;\left(-x\right) \cdot z\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-27}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-101}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+279}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16500000000 \lor \neg \left(z \leq 1.4 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -16500000000.0) (not (<= z 1.4e-11)))
   (* z (- y x))
   (+ (* z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -16500000000.0) || !(z <= 1.4e-11)) {
		tmp = z * (y - x);
	} else {
		tmp = (z * y) + 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 <= (-16500000000.0d0)) .or. (.not. (z <= 1.4d-11))) then
        tmp = z * (y - x)
    else
        tmp = (z * y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -16500000000.0) || !(z <= 1.4e-11)) {
		tmp = z * (y - x);
	} else {
		tmp = (z * y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -16500000000.0) or not (z <= 1.4e-11):
		tmp = z * (y - x)
	else:
		tmp = (z * y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -16500000000.0) || !(z <= 1.4e-11))
		tmp = Float64(z * Float64(y - x));
	else
		tmp = Float64(Float64(z * y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -16500000000.0) || ~((z <= 1.4e-11)))
		tmp = z * (y - x);
	else
		tmp = (z * y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -16500000000.0], N[Not[LessEqual[z, 1.4e-11]], $MachinePrecision]], N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e10 or 1.4e-11 < 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 99.3

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

   5. Applied rewrites 99.3%

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

   if -1.65e10 < z < 1.4e-11

   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 99.8

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

   5. Applied rewrites 99.8%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16500000000 \lor \neg \left(z \leq 1.4 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-27} \lor \neg \left(z \leq 2.55 \cdot 10^{-101}\right):\\ \;\;\;\;z \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.5e-27) (not (<= z 2.55e-101))) (* z (- y x)) (* 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e-27) || !(z <= 2.55e-101)) {
		tmp = z * (y - x);
	} else {
		tmp = 1.0 * 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 <= (-6.5d-27)) .or. (.not. (z <= 2.55d-101))) then
        tmp = z * (y - x)
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e-27) || !(z <= 2.55e-101)) {
		tmp = z * (y - x);
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.5e-27) or not (z <= 2.55e-101):
		tmp = z * (y - x)
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.5e-27) || !(z <= 2.55e-101))
		tmp = Float64(z * Float64(y - x));
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.5e-27) || ~((z <= 2.55e-101)))
		tmp = z * (y - x);
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.5e-27], N[Not[LessEqual[z, 2.55e-101]], $MachinePrecision]], N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000025e-27 or 2.5500000000000001e-101 < z

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   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 93.0

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

   5. Applied rewrites 93.0%

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

   if -6.50000000000000025e-27 < z < 2.5500000000000001e-101

   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 77.6

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 77.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-27} \lor \neg \left(z \leq 2.55 \cdot 10^{-101}\right):\\ \;\;\;\;z \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+39} \lor \neg \left(y \leq 7.8 \cdot 10^{+142}\right):\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e+39) (not (<= y 7.8e+142))) (* z y) (* (- 1.0 z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+39) || !(y <= 7.8e+142)) {
		tmp = z * y;
	} else {
		tmp = (1.0 - z) * 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 <= (-4.2d+39)) .or. (.not. (y <= 7.8d+142))) then
        tmp = z * y
    else
        tmp = (1.0d0 - z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+39) || !(y <= 7.8e+142)) {
		tmp = z * y;
	} else {
		tmp = (1.0 - z) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e+39) or not (y <= 7.8e+142):
		tmp = z * y
	else:
		tmp = (1.0 - z) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e+39) || !(y <= 7.8e+142))
		tmp = Float64(z * y);
	else
		tmp = Float64(Float64(1.0 - z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.2e+39) || ~((y <= 7.8e+142)))
		tmp = z * y;
	else
		tmp = (1.0 - z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e+39], N[Not[LessEqual[y, 7.8e+142]], $MachinePrecision]], N[(z * y), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999997e39 or 7.8000000000000001e142 < 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 78.9

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

   5. Applied rewrites 78.9%

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

   if -4.1999999999999997e39 < y < 7.8000000000000001e142

   1. Initial program 99.9%

      \[x + \left(y - x\right) \cdot z \]
   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 80.6

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

   5. Applied rewrites 80.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+39} \lor \neg \left(y \leq 7.8 \cdot 10^{+142}\right):\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-27} \lor \neg \left(z \leq 2.55 \cdot 10^{-101}\right):\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.5e-27) (not (<= z 2.55e-101))) (* z y) (* 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e-27) || !(z <= 2.55e-101)) {
		tmp = z * y;
	} else {
		tmp = 1.0 * 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 <= (-6.5d-27)) .or. (.not. (z <= 2.55d-101))) then
        tmp = z * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e-27) || !(z <= 2.55e-101)) {
		tmp = z * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.5e-27) or not (z <= 2.55e-101):
		tmp = z * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.5e-27) || !(z <= 2.55e-101))
		tmp = Float64(z * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.5e-27) || ~((z <= 2.55e-101)))
		tmp = z * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.5e-27], N[Not[LessEqual[z, 2.55e-101]], $MachinePrecision]], N[(z * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000025e-27 or 2.5500000000000001e-101 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 53.6

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

   5. Applied rewrites 53.6%

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

   if -6.50000000000000025e-27 < z < 2.5500000000000001e-101

   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 77.6

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 77.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-27} \lor \neg \left(z \leq 2.55 \cdot 10^{-101}\right):\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.9% 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 42.3

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

5. Applied rewrites 42.3%

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

6. Final simplification 42.3%

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

Reproduce

herbie shell --seed 2024271 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))