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

Percentage Accurate: 97.9% → 100.0%

Time: 4.9s

Alternatives: 7

Speedup: 1.7×

• 20.6% 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: 97.9% 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 96.8%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
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. *-commutative N/A

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

   3. sub-neg N/A

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

   4. mul-1-neg N/A

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

   5. +-commutative N/A

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

   6. distribute-lft1-in N/A

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

   7. associate-*r* N/A

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

   8. +-commutative N/A

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

   9. mul-1-neg N/A

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

   10. unsub-neg N/A

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

   11. associate-+l- N/A

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

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

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

   13. unsub-neg N/A

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

   14. mul-1-neg N/A

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

   15. sub-neg N/A

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

   16. mul-1-neg N/A

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

   17. +-commutative N/A

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

   18. mul-1-neg N/A

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

   19. *-commutative N/A

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

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

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

   21. 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: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.028:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-38}:\\ \;\;\;\;1 \cdot y\\ \mathbf{elif}\;x \leq 29000000000000:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.028)
   (* z x)
   (if (<= x 3.5e-38)
     (* 1.0 y)
     (if (<= x 29000000000000.0) (* z x) (* (- y) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.028) {
		tmp = z * x;
	} else if (x <= 3.5e-38) {
		tmp = 1.0 * y;
	} else if (x <= 29000000000000.0) {
		tmp = z * x;
	} else {
		tmp = -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 (x <= (-0.028d0)) then
        tmp = z * x
    else if (x <= 3.5d-38) then
        tmp = 1.0d0 * y
    else if (x <= 29000000000000.0d0) then
        tmp = z * x
    else
        tmp = -y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.028) {
		tmp = z * x;
	} else if (x <= 3.5e-38) {
		tmp = 1.0 * y;
	} else if (x <= 29000000000000.0) {
		tmp = z * x;
	} else {
		tmp = -y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.028:
		tmp = z * x
	elif x <= 3.5e-38:
		tmp = 1.0 * y
	elif x <= 29000000000000.0:
		tmp = z * x
	else:
		tmp = -y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.028)
		tmp = Float64(z * x);
	elseif (x <= 3.5e-38)
		tmp = Float64(1.0 * y);
	elseif (x <= 29000000000000.0)
		tmp = Float64(z * x);
	else
		tmp = Float64(Float64(-y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.028)
		tmp = z * x;
	elseif (x <= 3.5e-38)
		tmp = 1.0 * y;
	elseif (x <= 29000000000000.0)
		tmp = z * x;
	else
		tmp = -y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.028], N[(z * x), $MachinePrecision], If[LessEqual[x, 3.5e-38], N[(1.0 * y), $MachinePrecision], If[LessEqual[x, 29000000000000.0], N[(z * x), $MachinePrecision], N[((-y) * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0280000000000000006 or 3.5000000000000001e-38 < x < 2.9e13

   1. Initial program 95.9%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 60.5

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

   5. Applied rewrites 60.5%

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

   if -0.0280000000000000006 < x < 3.5000000000000001e-38

   1. Initial program 99.9%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 76.1

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

   5. Applied rewrites 76.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.4%

      \[\leadsto 1 \cdot y \]

   if 2.9e13 < x

   1. Initial program 92.5%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      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 60.5%

      \[\leadsto \left(-y\right) \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - y\right) \cdot x\\ \mathbf{if}\;x \leq -0.41:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z y) x)))
   (if (<= x -0.41) t_0 (if (<= x 3.5e-38) (fma (- y) x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z - y) * x;
	double tmp;
	if (x <= -0.41) {
		tmp = t_0;
	} else if (x <= 3.5e-38) {
		tmp = fma(-y, 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 <= -0.41)
		tmp = t_0;
	elseif (x <= 3.5e-38)
		tmp = fma(Float64(-y), x, y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -0.41], t$95$0, If[LessEqual[x, 3.5e-38], N[((-y) * x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.409999999999999976 or 3.5000000000000001e-38 < x

   1. Initial program 94.7%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      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 96.7

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

   5. Applied rewrites 96.7%

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

   if -0.409999999999999976 < x < 3.5000000000000001e-38

   1. Initial program 99.9%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 76.1

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

   5. Applied rewrites 76.1%

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

   7. Applied rewrites 76.1%

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

Alternative 4: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - y\right) \cdot x\\ \mathbf{if}\;x \leq -0.41:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-38}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z y) x)))
   (if (<= x -0.41) t_0 (if (<= x 3.5e-38) (* (- 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 <= -0.41) {
		tmp = t_0;
	} else if (x <= 3.5e-38) {
		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 <= (-0.41d0)) then
        tmp = t_0
    else if (x <= 3.5d-38) 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 <= -0.41) {
		tmp = t_0;
	} else if (x <= 3.5e-38) {
		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 <= -0.41:
		tmp = t_0
	elif x <= 3.5e-38:
		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 <= -0.41)
		tmp = t_0;
	elseif (x <= 3.5e-38)
		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 <= -0.41)
		tmp = t_0;
	elseif (x <= 3.5e-38)
		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, -0.41], t$95$0, If[LessEqual[x, 3.5e-38], N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.409999999999999976 or 3.5000000000000001e-38 < x

   1. Initial program 94.7%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      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 96.7

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

   5. Applied rewrites 96.7%

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

   if -0.409999999999999976 < x < 3.5000000000000001e-38

   1. Initial program 99.9%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 76.1

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

   5. Applied rewrites 76.1%

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

Alternative 5: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - x\right) \cdot y\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{-132}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-51}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 x) y)))
   (if (<= y -1.35e-132) t_0 (if (<= y 3.5e-51) (* z x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - x) * y;
	double tmp;
	if (y <= -1.35e-132) {
		tmp = t_0;
	} else if (y <= 3.5e-51) {
		tmp = 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 = (1.0d0 - x) * y
    if (y <= (-1.35d-132)) then
        tmp = t_0
    else if (y <= 3.5d-51) then
        tmp = 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 = (1.0 - x) * y;
	double tmp;
	if (y <= -1.35e-132) {
		tmp = t_0;
	} else if (y <= 3.5e-51) {
		tmp = z * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - x) * y
	tmp = 0
	if y <= -1.35e-132:
		tmp = t_0
	elif y <= 3.5e-51:
		tmp = z * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - x) * y)
	tmp = 0.0
	if (y <= -1.35e-132)
		tmp = t_0;
	elseif (y <= 3.5e-51)
		tmp = Float64(z * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - x) * y;
	tmp = 0.0;
	if (y <= -1.35e-132)
		tmp = t_0;
	elseif (y <= 3.5e-51)
		tmp = z * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.35e-132], t$95$0, If[LessEqual[y, 3.5e-51], N[(z * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.34999999999999995e-132 or 3.4999999999999997e-51 < y

   1. Initial program 94.9%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 80.9

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

   5. Applied rewrites 80.9%

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

   if -1.34999999999999995e-132 < y < 3.4999999999999997e-51

   1. Initial program 99.9%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 75.9

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

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{z \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 61.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.028:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-38}:\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.028) (* z x) (if (<= x 3.5e-38) (* 1.0 y) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.028) {
		tmp = z * x;
	} else if (x <= 3.5e-38) {
		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 <= (-0.028d0)) then
        tmp = z * x
    else if (x <= 3.5d-38) 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 <= -0.028) {
		tmp = z * x;
	} else if (x <= 3.5e-38) {
		tmp = 1.0 * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.028:
		tmp = z * x
	elif x <= 3.5e-38:
		tmp = 1.0 * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.028)
		tmp = Float64(z * x);
	elseif (x <= 3.5e-38)
		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 <= -0.028)
		tmp = z * x;
	elseif (x <= 3.5e-38)
		tmp = 1.0 * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.028], N[(z * x), $MachinePrecision], If[LessEqual[x, 3.5e-38], N[(1.0 * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0280000000000000006 or 3.5000000000000001e-38 < x

   1. Initial program 94.7%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 55.7

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

   5. Applied rewrites 55.7%

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

   if -0.0280000000000000006 < x < 3.5000000000000001e-38

   1. Initial program 99.9%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 76.1

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

   5. Applied rewrites 76.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.4%

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

Alternative 7: 40.3% 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 96.8%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
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 43.5

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

5. Applied rewrites 43.5%

   \[\leadsto \color{blue}{z \cdot x} \]
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 2024249 
(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)))