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

Percentage Accurate: 97.9% → 100.0%

Time: 5.4s

Alternatives: 6

Speedup: 1.7×

• 20.9% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. distribute-lft-in N/A

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

   3. mul-1-neg N/A

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

   4. distribute-rgt-neg-in N/A

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

   5. mul-1-neg N/A

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

   6. associate-+r+ N/A

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

   7. mul-1-neg N/A

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

   8. unsub-neg N/A

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

   9. associate-+l- N/A

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

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

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

   11. unsub-neg N/A

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

   12. mul-1-neg N/A

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

   13. sub-neg N/A

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

   14. mul-1-neg N/A

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

   15. +-commutative N/A

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

   16. mul-1-neg N/A

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

   17. distribute-rgt-neg-in N/A

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

   18. lower-fma.f64 N/A

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

5. Applied rewrites 100.0%

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

Alternative 2: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= z -1.8e-11) t_0 (if (<= z 2.9e-38) (fma (- y) x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (z <= -1.8e-11) {
		tmp = t_0;
	} else if (z <= 2.9e-38) {
		tmp = fma(-y, x, y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (z <= -1.8e-11)
		tmp = t_0;
	elseif (z <= 2.9e-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[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e-11], t$95$0, If[LessEqual[z, 2.9e-38], N[((-y) * x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999992e-11 or 2.89999999999999994e-38 < z

   1. Initial program 98.5%

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

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 83.4

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

   5. Applied rewrites 83.4%

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

   if -1.79999999999999992e-11 < z < 2.89999999999999994e-38

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \color{blue}{1 \cdot y - x \cdot y} \]

      2. *-lft-identity N/A

         \[\leadsto \color{blue}{y} - x \cdot y \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{y - x \cdot y} \]

      4. *-commutative N/A

         \[\leadsto y - \color{blue}{y \cdot x} \]

      5. lower-*.f64 88.7

         \[\leadsto y - \color{blue}{y \cdot x} \]

   5. Applied rewrites 88.7%

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

   7. Applied rewrites 88.7%

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

Alternative 3: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-38}:\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= z -1.8e-11) t_0 (if (<= z 2.9e-38) (- y (* x y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (z <= -1.8e-11) {
		tmp = t_0;
	} else if (z <= 2.9e-38) {
		tmp = y - (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 = x * (z - y)
    if (z <= (-1.8d-11)) then
        tmp = t_0
    else if (z <= 2.9d-38) then
        tmp = y - (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 = x * (z - y);
	double tmp;
	if (z <= -1.8e-11) {
		tmp = t_0;
	} else if (z <= 2.9e-38) {
		tmp = y - (x * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if z <= -1.8e-11:
		tmp = t_0
	elif z <= 2.9e-38:
		tmp = y - (x * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (z <= -1.8e-11)
		tmp = t_0;
	elseif (z <= 2.9e-38)
		tmp = Float64(y - Float64(x * 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 (z <= -1.8e-11)
		tmp = t_0;
	elseif (z <= 2.9e-38)
		tmp = y - (x * 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[z, -1.8e-11], t$95$0, If[LessEqual[z, 2.9e-38], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999992e-11 or 2.89999999999999994e-38 < z

   1. Initial program 98.5%

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

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 83.4

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

   5. Applied rewrites 83.4%

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

   if -1.79999999999999992e-11 < z < 2.89999999999999994e-38

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \color{blue}{1 \cdot y - x \cdot y} \]

      2. *-lft-identity N/A

         \[\leadsto \color{blue}{y} - x \cdot y \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{y - x \cdot y} \]

      4. *-commutative N/A

         \[\leadsto y - \color{blue}{y \cdot x} \]

      5. lower-*.f64 88.7

         \[\leadsto y - \color{blue}{y \cdot x} \]

   5. Applied rewrites 88.7%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-38}:\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -7.3 \cdot 10^{+164}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{+108}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= y -7.3e+164) t_0 (if (<= y 7.3e+108) (* x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (y <= -7.3e+164) {
		tmp = t_0;
	} else if (y <= 7.3e+108) {
		tmp = x * z;
	} 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 * -y
    if (y <= (-7.3d+164)) then
        tmp = t_0
    else if (y <= 7.3d+108) then
        tmp = x * z
    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 * -y;
	double tmp;
	if (y <= -7.3e+164) {
		tmp = t_0;
	} else if (y <= 7.3e+108) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if y <= -7.3e+164:
		tmp = t_0
	elif y <= 7.3e+108:
		tmp = x * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -7.3e+164)
		tmp = t_0;
	elseif (y <= 7.3e+108)
		tmp = Float64(x * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -y;
	tmp = 0.0;
	if (y <= -7.3e+164)
		tmp = t_0;
	elseif (y <= 7.3e+108)
		tmp = x * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -7.3e+164], t$95$0, If[LessEqual[y, 7.3e+108], N[(x * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.30000000000000047e164 or 7.2999999999999998e108 < y

   1. Initial program 97.3%

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

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 57.3

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

   5. Applied rewrites 57.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 54.6%

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

   if -7.30000000000000047e164 < y < 7.2999999999999998e108

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 59.5

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

   5. Applied rewrites 59.5%

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

Alternative 5: 65.2% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

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

   2. remove-double-neg N/A

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

   3. mul-1-neg N/A

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

   4. mul-1-neg N/A

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

   5. distribute-neg-in N/A

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

   6. lower-*.f64 N/A

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

   7. +-commutative N/A

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

   8. distribute-neg-in N/A

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

   9. unsub-neg N/A

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

   10. mul-1-neg N/A

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

   11. remove-double-neg N/A

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

   12. lower--.f64 66.2

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

5. Applied rewrites 66.2%

   \[\leadsto \color{blue}{x \cdot \left(z - y\right)} \]
6. 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 99.2%

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

3. Taylor expanded in y around 0

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

   1. lower-*.f64 45.2

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

5. Applied rewrites 45.2%

   \[\leadsto \color{blue}{x \cdot z} \]
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 2024223 
(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)))