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

Percentage Accurate: 97.9% → 100.0%

Time: 3.9s

Alternatives: 6

Speedup: 1.7×

• 21.2% 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 98.0%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
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: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+136}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-58}:\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2e+136)
   (* x z)
   (if (<= x -1.0) (* (- y) x) (if (<= x 9.6e-58) (* 1.0 y) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e+136) {
		tmp = x * z;
	} else if (x <= -1.0) {
		tmp = -y * x;
	} else if (x <= 9.6e-58) {
		tmp = 1.0 * y;
	} else {
		tmp = x * z;
	}
	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 <= (-2d+136)) then
        tmp = x * z
    else if (x <= (-1.0d0)) then
        tmp = -y * x
    else if (x <= 9.6d-58) then
        tmp = 1.0d0 * y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e+136) {
		tmp = x * z;
	} else if (x <= -1.0) {
		tmp = -y * x;
	} else if (x <= 9.6e-58) {
		tmp = 1.0 * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2e+136:
		tmp = x * z
	elif x <= -1.0:
		tmp = -y * x
	elif x <= 9.6e-58:
		tmp = 1.0 * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2e+136)
		tmp = Float64(x * z);
	elseif (x <= -1.0)
		tmp = Float64(Float64(-y) * x);
	elseif (x <= 9.6e-58)
		tmp = Float64(1.0 * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2e+136)
		tmp = x * z;
	elseif (x <= -1.0)
		tmp = -y * x;
	elseif (x <= 9.6e-58)
		tmp = 1.0 * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2e+136], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.0], N[((-y) * x), $MachinePrecision], If[LessEqual[x, 9.6e-58], N[(1.0 * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.00000000000000012e136 or 9.6000000000000002e-58 < x

   1. Initial program 95.8%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 61.3

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

   5. Applied rewrites 61.3%

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

   if -2.00000000000000012e136 < x < -1

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 97.2

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 70.1%

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

   if -1 < x < 9.6000000000000002e-58

   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 75.5

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

   5. Applied rewrites 75.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 75.4%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+136}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;\left(-y\right) \cdot x\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-58}:\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{-25}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-55}:\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -9e-25) t_0 (if (<= x 3e-55) (* 1.0 y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -9e-25) {
		tmp = t_0;
	} else if (x <= 3e-55) {
		tmp = 1.0 * 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 - y)
    if (x <= (-9d-25)) then
        tmp = t_0
    else if (x <= 3d-55) then
        tmp = 1.0d0 * 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 - y);
	double tmp;
	if (x <= -9e-25) {
		tmp = t_0;
	} else if (x <= 3e-55) {
		tmp = 1.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -9e-25:
		tmp = t_0
	elif x <= 3e-55:
		tmp = 1.0 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -9e-25)
		tmp = t_0;
	elseif (x <= 3e-55)
		tmp = Float64(1.0 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z - y);
	tmp = 0.0;
	if (x <= -9e-25)
		tmp = t_0;
	elseif (x <= 3e-55)
		tmp = 1.0 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e-25], t$95$0, If[LessEqual[x, 3e-55], N[(1.0 * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.0000000000000002e-25 or 3.00000000000000016e-55 < x

   1. Initial program 96.6%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 94.3

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

   5. Applied rewrites 94.3%

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

   if -9.0000000000000002e-25 < x < 3.00000000000000016e-55

   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 77.3

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 77.3%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-55}:\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+185}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+98}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.2e+185) (* x z) (if (<= z 2.2e+98) (* (- 1.0 x) y) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.2e+185) {
		tmp = x * z;
	} else if (z <= 2.2e+98) {
		tmp = (1.0 - x) * y;
	} else {
		tmp = x * z;
	}
	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 <= (-2.2d+185)) then
        tmp = x * z
    else if (z <= 2.2d+98) then
        tmp = (1.0d0 - x) * y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.2e+185) {
		tmp = x * z;
	} else if (z <= 2.2e+98) {
		tmp = (1.0 - x) * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.2e+185:
		tmp = x * z
	elif z <= 2.2e+98:
		tmp = (1.0 - x) * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.2e+185)
		tmp = Float64(x * z);
	elseif (z <= 2.2e+98)
		tmp = Float64(Float64(1.0 - x) * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.2e+185)
		tmp = x * z;
	elseif (z <= 2.2e+98)
		tmp = (1.0 - x) * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.2e+185], N[(x * z), $MachinePrecision], If[LessEqual[z, 2.2e+98], N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e185 or 2.20000000000000009e98 < z

   1. Initial program 95.2%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 81.6

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

   5. Applied rewrites 81.6%

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

   if -2.2000000000000001e185 < z < 2.20000000000000009e98

   1. Initial program 99.4%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 78.4

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

   5. Applied rewrites 78.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+185}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+98}:\\ \;\;\;\;\left(1 - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-24}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-58}:\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.15e-24) (* x z) (if (<= x 9.6e-58) (* 1.0 y) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.15e-24) {
		tmp = x * z;
	} else if (x <= 9.6e-58) {
		tmp = 1.0 * y;
	} else {
		tmp = x * z;
	}
	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 <= (-1.15d-24)) then
        tmp = x * z
    else if (x <= 9.6d-58) then
        tmp = 1.0d0 * y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.15e-24) {
		tmp = x * z;
	} else if (x <= 9.6e-58) {
		tmp = 1.0 * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.15e-24:
		tmp = x * z
	elif x <= 9.6e-58:
		tmp = 1.0 * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.15e-24)
		tmp = Float64(x * z);
	elseif (x <= 9.6e-58)
		tmp = Float64(1.0 * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.15e-24)
		tmp = x * z;
	elseif (x <= 9.6e-58)
		tmp = 1.0 * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.15e-24], N[(x * z), $MachinePrecision], If[LessEqual[x, 9.6e-58], N[(1.0 * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1500000000000001e-24 or 9.6000000000000002e-58 < x

   1. Initial program 96.6%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 56.2

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

   5. Applied rewrites 56.2%

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

   if -1.1500000000000001e-24 < x < 9.6000000000000002e-58

   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 77.3

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 77.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-24}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-58}:\\ \;\;\;\;1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.6% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
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 43.0

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

5. Applied rewrites 43.0%

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

6. Final simplification 43.0%

   \[\leadsto x \cdot z \]
7. 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 2024277 
(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)))