Diagrams.Color.HSV:lerp from diagrams-contrib-1.3.0.5

Percentage Accurate: 98.0% → 100.0%

Time: 4.6s

Alternatives: 6

Speedup: 1.7×

• 21.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot y + x \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (- 1.0 x) y) (* x z)))

C

double code(double x, double y, double z) {
	return ((1.0 - 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 = ((1.0d0 - x) * y) + (x * z)
end function

Java

public static double code(double x, double y, double z) {
	return ((1.0 - x) * y) + (x * z);
}

Python

def code(x, y, z):
	return ((1.0 - x) * y) + (x * z)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(1.0 - x) * y) + Float64(x * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((1.0 - x) * y) + (x * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot y + x \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (- 1.0 x) y) (* x z)))

C

double code(double x, double y, double z) {
	return ((1.0 - 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 = ((1.0d0 - x) * y) + (x * z)
end function

Java

public static double code(double x, double y, double z) {
	return ((1.0 - x) * y) + (x * z);
}

Python

def code(x, y, z):
	return ((1.0 - x) * y) + (x * z)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(1.0 - x) * y) + Float64(x * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((1.0 - x) * y) + (x * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z - y, x, y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- z y) x y))

C

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

Julia

function code(x, y, z)
	return fma(Float64(z - y), x, y)
end

Wolfram

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

Derivation

1. Initial program 95.3%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Add Preprocessing

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. distribute-rgt-out-- N/A

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

   3. unsub-neg N/A

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

   4. mul-1-neg N/A

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

   5. *-lft-identity N/A

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

   6. +-commutative N/A

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

   7. +-commutative N/A

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

   8. mul-1-neg N/A

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

   9. unsub-neg N/A

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

   10. associate-+l- N/A

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

   11. distribute-lft-out-- N/A

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

   12. unsub-neg N/A

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

   13. mul-1-neg N/A

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

   14. sub-neg N/A

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

   15. mul-1-neg N/A

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

   16. +-commutative N/A

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

   17. mul-1-neg N/A

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

   18. *-commutative N/A

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

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

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

   20. lower-fma.f64 N/A

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

5. Applied rewrites 100.0%

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

Alternative 2: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - y\right) \cdot x\\ \mathbf{if}\;x \leq -27:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z y) x)))
   (if (<= x -27.0) t_0 (if (<= x 6.8e-56) (* (- 1.0 x) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z - y) * x;
	double tmp;
	if (x <= -27.0) {
		tmp = t_0;
	} else if (x <= 6.8e-56) {
		tmp = (1.0 - x) * 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 = (z - y) * x
    if (x <= (-27.0d0)) then
        tmp = t_0
    else if (x <= 6.8d-56) then
        tmp = (1.0d0 - x) * 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 = (z - y) * x;
	double tmp;
	if (x <= -27.0) {
		tmp = t_0;
	} else if (x <= 6.8e-56) {
		tmp = (1.0 - x) * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z - y) * x
	tmp = 0
	if x <= -27.0:
		tmp = t_0
	elif x <= 6.8e-56:
		tmp = (1.0 - x) * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z - y) * x)
	tmp = 0.0
	if (x <= -27.0)
		tmp = t_0;
	elseif (x <= 6.8e-56)
		tmp = Float64(Float64(1.0 - x) * y);
	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 (x <= -27.0)
		tmp = t_0;
	elseif (x <= 6.8e-56)
		tmp = (1.0 - x) * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -27.0], t$95$0, If[LessEqual[x, 6.8e-56], N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -27 or 6.79999999999999964e-56 < x

   1. Initial program 91.6%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 95.0

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

   5. Applied rewrites 95.0%

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

   if -27 < x < 6.79999999999999964e-56

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.9

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

   5. Applied rewrites 74.9%

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

Alternative 3: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+94}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e+64) (* z x) (if (<= z 2.3e+94) (* (- 1.0 x) y) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+64) {
		tmp = z * x;
	} else if (z <= 2.3e+94) {
		tmp = (1.0 - x) * y;
	} else {
		tmp = 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 (z <= (-5.8d+64)) then
        tmp = z * x
    else if (z <= 2.3d+94) then
        tmp = (1.0d0 - x) * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+64) {
		tmp = z * x;
	} else if (z <= 2.3e+94) {
		tmp = (1.0 - x) * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e+64:
		tmp = z * x
	elif z <= 2.3e+94:
		tmp = (1.0 - x) * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e+64)
		tmp = Float64(z * x);
	elseif (z <= 2.3e+94)
		tmp = Float64(Float64(1.0 - x) * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.8e+64)
		tmp = z * x;
	elseif (z <= 2.3e+94)
		tmp = (1.0 - x) * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e+64], N[(z * x), $MachinePrecision], If[LessEqual[z, 2.3e+94], N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999986e64 or 2.3e94 < z

   1. Initial program 90.9%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.2

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

   5. Applied rewrites 78.2%

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

   if -5.79999999999999986e64 < z < 2.3e94

   1. Initial program 97.6%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 80.1

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

   5. Applied rewrites 80.1%

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

Alternative 4: 61.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0) (* (- y) x) (if (<= x 6.8e-56) (* 1.0 y) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = -y * x;
	} else if (x <= 6.8e-56) {
		tmp = 1.0 * y;
	} else {
		tmp = 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 (x <= (-1.0d0)) then
        tmp = -y * x
    else if (x <= 6.8d-56) then
        tmp = 1.0d0 * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = -y * x;
	} else if (x <= 6.8e-56) {
		tmp = 1.0 * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = -y * x
	elif x <= 6.8e-56:
		tmp = 1.0 * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(-y) * x);
	elseif (x <= 6.8e-56)
		tmp = Float64(1.0 * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = -y * x;
	elseif (x <= 6.8e-56)
		tmp = 1.0 * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], N[((-y) * x), $MachinePrecision], If[LessEqual[x, 6.8e-56], N[(1.0 * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 88.1%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 61.7%

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

   if -1 < x < 6.79999999999999964e-56

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.9

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

   5. Applied rewrites 74.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 73.7%

      \[\leadsto 1 \cdot y \]

   if 6.79999999999999964e-56 < x

   1. Initial program 94.1%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 58.4

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

   5. Applied rewrites 58.4%

      \[\leadsto \color{blue}{z \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 61.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-28}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.5e-28) (* z x) (if (<= x 6.8e-56) (* 1.0 y) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e-28) {
		tmp = z * x;
	} else if (x <= 6.8e-56) {
		tmp = 1.0 * y;
	} else {
		tmp = 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 (x <= (-2.5d-28)) then
        tmp = z * x
    else if (x <= 6.8d-56) then
        tmp = 1.0d0 * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e-28) {
		tmp = z * x;
	} else if (x <= 6.8e-56) {
		tmp = 1.0 * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.5e-28:
		tmp = z * x
	elif x <= 6.8e-56:
		tmp = 1.0 * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e-28)
		tmp = Float64(z * x);
	elseif (x <= 6.8e-56)
		tmp = Float64(1.0 * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.5e-28)
		tmp = z * x;
	elseif (x <= 6.8e-56)
		tmp = 1.0 * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e-28], N[(z * x), $MachinePrecision], If[LessEqual[x, 6.8e-56], N[(1.0 * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5000000000000001e-28 or 6.79999999999999964e-56 < x

   1. Initial program 91.8%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 51.5

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

   5. Applied rewrites 51.5%

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

   if -2.5000000000000001e-28 < x < 6.79999999999999964e-56

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.1

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

   5. Applied rewrites 75.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 75.1%

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

Alternative 6: 42.2% accurate, 2.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return z * 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 = z * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Add Preprocessing

3. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 41.0

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

5. Applied rewrites 41.0%

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

Developer Target 1: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ y - x \cdot \left(y - z\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return y - (x * (y - 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 = y - (x * (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024235 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (! :herbie-platform default (- y (* x (- y z))))

  (+ (* (- 1.0 x) y) (* x z)))