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

Percentage Accurate: 97.9% → 100.0%

Time: 4.4s

Alternatives: 7

Speedup: 1.3×

• 21.4% 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, 0.1× 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 98.4%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Step-by-step derivation

   1. *-commutative 98.4%

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

   2. distribute-lft-out-- 98.4%

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

   3. *-rgt-identity 98.4%

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

   4. cancel-sign-sub-inv 98.4%

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

   5. +-commutative 98.4%

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

   6. +-commutative 98.4%

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

   7. associate-+l+ 98.4%

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

   8. +-commutative 98.4%

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

   9. *-commutative 98.4%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-33}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+145}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= x -1.02e+57)
     t_0
     (if (<= x -2e-45)
       (* x z)
       (if (<= x 2.3e-33) y (if (<= x 1.1e+145) (* x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -1.02e+57) {
		tmp = t_0;
	} else if (x <= -2e-45) {
		tmp = x * z;
	} else if (x <= 2.3e-33) {
		tmp = y;
	} else if (x <= 1.1e+145) {
		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 = y * -x
    if (x <= (-1.02d+57)) then
        tmp = t_0
    else if (x <= (-2d-45)) then
        tmp = x * z
    else if (x <= 2.3d-33) then
        tmp = y
    else if (x <= 1.1d+145) 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 = y * -x;
	double tmp;
	if (x <= -1.02e+57) {
		tmp = t_0;
	} else if (x <= -2e-45) {
		tmp = x * z;
	} else if (x <= 2.3e-33) {
		tmp = y;
	} else if (x <= 1.1e+145) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if x <= -1.02e+57:
		tmp = t_0
	elif x <= -2e-45:
		tmp = x * z
	elif x <= 2.3e-33:
		tmp = y
	elif x <= 1.1e+145:
		tmp = x * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (x <= -1.02e+57)
		tmp = t_0;
	elseif (x <= -2e-45)
		tmp = Float64(x * z);
	elseif (x <= 2.3e-33)
		tmp = y;
	elseif (x <= 1.1e+145)
		tmp = Float64(x * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (x <= -1.02e+57)
		tmp = t_0;
	elseif (x <= -2e-45)
		tmp = x * z;
	elseif (x <= 2.3e-33)
		tmp = y;
	elseif (x <= 1.1e+145)
		tmp = x * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[x, -1.02e+57], t$95$0, If[LessEqual[x, -2e-45], N[(x * z), $MachinePrecision], If[LessEqual[x, 2.3e-33], y, If[LessEqual[x, 1.1e+145], N[(x * z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02e57 or 1.10000000000000004e145 < x

   1. Initial program 95.9%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. *-commutative 65.2%

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

      3. distribute-rgt-neg-in 65.2%

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

   7. Simplified 65.2%

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

   if -1.02e57 < x < -1.99999999999999997e-45 or 2.29999999999999986e-33 < x < 1.10000000000000004e145

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 61.3%

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

   if -1.99999999999999997e-45 < x < 2.29999999999999986e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 73.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-33}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+145}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-45} \lor \neg \left(x \leq 2.1 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.6e-45) (not (<= x 2.1e-32))) (* x (- z y)) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e-45) || !(x <= 2.1e-32)) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.6d-45)) .or. (.not. (x <= 2.1d-32))) then
        tmp = x * (z - y)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e-45) || !(x <= 2.1e-32)) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.6e-45) or not (x <= 2.1e-32):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.6e-45) || !(x <= 2.1e-32))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.6e-45) || ~((x <= 2.1e-32)))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.6e-45], N[Not[LessEqual[x, 2.1e-32]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000004e-45 or 2.0999999999999999e-32 < x

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf 96.2%

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

      1. mul-1-neg 96.2%

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

      2. sub-neg 96.2%

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

   4. Simplified 96.2%

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

   if -1.60000000000000004e-45 < x < 2.0999999999999999e-32

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 73.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-45} \lor \neg \left(x \leq 2.1 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-45} \lor \neg \left(x \leq 510000000\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2e-45) (not (<= x 510000000.0)))
   (* x (- z y))
   (* y (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e-45) || !(x <= 510000000.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y * (1.0 - 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 <= (-2d-45)) .or. (.not. (x <= 510000000.0d0))) then
        tmp = x * (z - y)
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e-45) || !(x <= 510000000.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2e-45) or not (x <= 510000000.0):
		tmp = x * (z - y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2e-45) || !(x <= 510000000.0))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2e-45) || ~((x <= 510000000.0)))
		tmp = x * (z - y);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2e-45], N[Not[LessEqual[x, 510000000.0]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999997e-45 or 5.1e8 < x

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 97.5%

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

      1. mul-1-neg 97.5%

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

      2. sub-neg 97.5%

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

   4. Simplified 97.5%

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

   if -1.99999999999999997e-45 < x < 5.1e8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 72.7%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-45} \lor \neg \left(x \leq 510000000\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 61.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-45} \lor \neg \left(x \leq 1.25 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2e-45) (not (<= x 1.25e-34))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e-45) || !(x <= 1.25e-34)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2d-45)) .or. (.not. (x <= 1.25d-34))) then
        tmp = x * z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e-45) || !(x <= 1.25e-34)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2e-45) or not (x <= 1.25e-34):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2e-45) || !(x <= 1.25e-34))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2e-45) || ~((x <= 1.25e-34)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2e-45], N[Not[LessEqual[x, 1.25e-34]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999997e-45 or 1.2500000000000001e-34 < x

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 48.8%

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

   if -1.99999999999999997e-45 < x < 1.2500000000000001e-34

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 73.2%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-45} \lor \neg \left(x \leq 1.25 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Step-by-step derivation

   1. *-commutative 98.4%

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

   2. distribute-lft-out-- 98.4%

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

   3. *-rgt-identity 98.4%

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

   4. cancel-sign-sub-inv 98.4%

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

   5. +-commutative 98.4%

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

   6. +-commutative 98.4%

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

   7. associate-+l+ 98.4%

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

   8. +-commutative 98.4%

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

   9. *-commutative 98.4%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. unsub-neg 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, z - y, y\right)} \]
4. Step-by-step derivation

   1. fma-udef 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 7: 35.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 98.4%

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

2. Taylor expanded in x around 0 32.4%

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

3. Final simplification 32.4%

   \[\leadsto y \]

Developer target: 100.0% accurate, 1.3× 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 2023318 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (- y (* x (- y z)))

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