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

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

Alternatives: 6

Speedup: 1.2×

• 21.1% 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 99.9%

   \[x + \left(y - x\right) \cdot z \]
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: 61.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+57}:\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-16}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.2e+57)
   (* (- z) x)
   (if (<= z -1.8e-16) (* z y) (if (<= z 6.8e-13) (* 1.0 x) (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.2e+57) {
		tmp = -z * x;
	} else if (z <= -1.8e-16) {
		tmp = z * y;
	} else if (z <= 6.8e-13) {
		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 <= (-9.2d+57)) then
        tmp = -z * x
    else if (z <= (-1.8d-16)) then
        tmp = z * y
    else if (z <= 6.8d-13) 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 <= -9.2e+57) {
		tmp = -z * x;
	} else if (z <= -1.8e-16) {
		tmp = z * y;
	} else if (z <= 6.8e-13) {
		tmp = 1.0 * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.2e+57:
		tmp = -z * x
	elif z <= -1.8e-16:
		tmp = z * y
	elif z <= 6.8e-13:
		tmp = 1.0 * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.2e+57)
		tmp = Float64(Float64(-z) * x);
	elseif (z <= -1.8e-16)
		tmp = Float64(z * y);
	elseif (z <= 6.8e-13)
		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 <= -9.2e+57)
		tmp = -z * x;
	elseif (z <= -1.8e-16)
		tmp = z * y;
	elseif (z <= 6.8e-13)
		tmp = 1.0 * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.2e+57], N[((-z) * x), $MachinePrecision], If[LessEqual[z, -1.8e-16], N[(z * y), $MachinePrecision], If[LessEqual[z, 6.8e-13], N[(1.0 * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.1999999999999995e57

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 61.0

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

   5. Applied rewrites 61.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 61.0%

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

   if -9.1999999999999995e57 < z < -1.79999999999999991e-16 or 6.80000000000000031e-13 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 58.0

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

   5. Applied rewrites 58.0%

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

   if -1.79999999999999991e-16 < z < 6.80000000000000031e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 77.9

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

   5. Applied rewrites 77.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 77.9%

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

Alternative 3: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y - x\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-7}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y x))))
   (if (<= z -6e-17) t_0 (if (<= z 3.5e-7) (* (- 1.0 z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y - x);
	double tmp;
	if (z <= -6e-17) {
		tmp = t_0;
	} else if (z <= 3.5e-7) {
		tmp = (1.0 - z) * 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 <= (-6d-17)) then
        tmp = t_0
    else if (z <= 3.5d-7) then
        tmp = (1.0d0 - z) * 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 <= -6e-17) {
		tmp = t_0;
	} else if (z <= 3.5e-7) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y - x)
	tmp = 0
	if z <= -6e-17:
		tmp = t_0
	elif z <= 3.5e-7:
		tmp = (1.0 - z) * 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 <= -6e-17)
		tmp = t_0;
	elseif (z <= 3.5e-7)
		tmp = Float64(Float64(1.0 - z) * 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 <= -6e-17)
		tmp = t_0;
	elseif (z <= 3.5e-7)
		tmp = (1.0 - z) * 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, -6e-17], t$95$0, If[LessEqual[z, 3.5e-7], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000012e-17 or 3.49999999999999984e-7 < z

   1. Initial program 99.9%

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

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(y - x\right)} \]
   6. 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 98.8

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

   7. Applied rewrites 98.8%

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

   if -6.00000000000000012e-17 < z < 3.49999999999999984e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 77.4

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

   5. Applied rewrites 77.4%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \left(y - x\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-7}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+85}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 9:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+85) (* z y) (if (<= y 9.0) (* (- 1.0 z) x) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+85) {
		tmp = z * y;
	} else if (y <= 9.0) {
		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 <= (-1.4d+85)) then
        tmp = z * y
    else if (y <= 9.0d0) 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 <= -1.4e+85) {
		tmp = z * y;
	} else if (y <= 9.0) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e+85:
		tmp = z * y
	elif y <= 9.0:
		tmp = (1.0 - z) * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+85)
		tmp = Float64(z * y);
	elseif (y <= 9.0)
		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 <= -1.4e+85)
		tmp = z * y;
	elseif (y <= 9.0)
		tmp = (1.0 - z) * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+85], N[(z * y), $MachinePrecision], If[LessEqual[y, 9.0], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e85 or 9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 72.3

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

   5. Applied rewrites 72.3%

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

   if -1.4e85 < y < 9

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 81.4

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

   5. Applied rewrites 81.4%

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

Alternative 5: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-16}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e-16) (* z y) (if (<= z 6.8e-13) (* 1.0 x) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e-16) {
		tmp = z * y;
	} else if (z <= 6.8e-13) {
		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 <= (-1.8d-16)) then
        tmp = z * y
    else if (z <= 6.8d-13) 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 <= -1.8e-16) {
		tmp = z * y;
	} else if (z <= 6.8e-13) {
		tmp = 1.0 * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.8e-16:
		tmp = z * y
	elif z <= 6.8e-13:
		tmp = 1.0 * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e-16)
		tmp = Float64(z * y);
	elseif (z <= 6.8e-13)
		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 <= -1.8e-16)
		tmp = z * y;
	elseif (z <= 6.8e-13)
		tmp = 1.0 * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e-16], N[(z * y), $MachinePrecision], If[LessEqual[z, 6.8e-13], N[(1.0 * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999991e-16 or 6.80000000000000031e-13 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.8

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

   5. Applied rewrites 53.8%

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

   if -1.79999999999999991e-16 < z < 6.80000000000000031e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 77.9

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

   5. Applied rewrites 77.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 77.9%

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

Alternative 6: 41.8% 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 99.9%

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

3. Taylor expanded in x around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 41.1

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

5. Applied rewrites 41.1%

   \[\leadsto \color{blue}{z \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024308 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))