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

Percentage Accurate: 98.1% → 100.0%

Time: 4.5s

Alternatives: 5

Speedup: 1.3×

• 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: 98.1% 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, 1.3× 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 97.6%

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

   1. remove-double-neg 97.6%

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

   2. distribute-rgt-neg-out 97.6%

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

   3. neg-sub0 97.6%

      \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

   4. neg-sub0 97.6%

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

   5. *-commutative 97.6%

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

   6. distribute-lft-neg-in 97.6%

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

   7. remove-double-neg 97.6%

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

   8. distribute-rgt-out-- 97.6%

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

   9. *-lft-identity 97.6%

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

   10. associate-+l- 97.6%

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

   11. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+54} \lor \neg \left(y \leq 2.25 \cdot 10^{+141}\right):\\ \;\;\;\;y - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e+54) (not (<= y 2.25e+141))) (- y (* y x)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+54) || !(y <= 2.25e+141)) {
		tmp = y - (y * x);
	} else {
		tmp = y + (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 ((y <= (-7.2d+54)) .or. (.not. (y <= 2.25d+141))) then
        tmp = y - (y * x)
    else
        tmp = y + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+54) || !(y <= 2.25e+141)) {
		tmp = y - (y * x);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.2e+54) or not (y <= 2.25e+141):
		tmp = y - (y * x)
	else:
		tmp = y + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.2e+54) || !(y <= 2.25e+141))
		tmp = Float64(y - Float64(y * x));
	else
		tmp = Float64(y + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.2e+54) || ~((y <= 2.25e+141)))
		tmp = y - (y * x);
	else
		tmp = y + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.2e+54], N[Not[LessEqual[y, 2.25e+141]], $MachinePrecision]], N[(y - N[(y * x), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2000000000000003e54 or 2.2500000000000001e141 < y

   1. Initial program 94.7%

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

      1. remove-double-neg 94.7%

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

      2. distribute-rgt-neg-out 94.7%

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

      3. neg-sub0 94.7%

         \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

      4. neg-sub0 94.7%

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

      5. *-commutative 94.7%

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

      6. distribute-lft-neg-in 94.7%

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

      7. remove-double-neg 94.7%

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

      8. distribute-rgt-out-- 94.7%

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

      9. *-lft-identity 94.7%

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

      10. associate-+l- 94.7%

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

      11. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 94.8%

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

   if -7.2000000000000003e54 < y < 2.2500000000000001e141

   1. Initial program 99.4%

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

      1. remove-double-neg 99.4%

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

      2. distribute-rgt-neg-out 99.4%

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

      3. neg-sub0 99.4%

         \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

      4. neg-sub0 99.4%

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

      5. *-commutative 99.4%

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

      6. distribute-lft-neg-in 99.4%

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

      7. remove-double-neg 99.4%

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

      8. distribute-rgt-out-- 99.4%

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

      9. *-lft-identity 99.4%

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

      10. associate-+l- 99.4%

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

      11. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. distribute-rgt-neg-out 86.0%

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

   7. Simplified 86.0%

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

      1. *-commutative 86.0%

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

      2. cancel-sign-sub 86.0%

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

      3. *-commutative 86.0%

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

      4. +-commutative 86.0%

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

   9. Applied egg-rr 86.0%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+54} \lor \neg \left(y \leq 2.25 \cdot 10^{+141}\right):\\ \;\;\;\;y - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-32} \lor \neg \left(x \leq 1.3 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.8e-32) (not (<= x 1.3e-12))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e-32) || !(x <= 1.3e-12)) {
		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 <= (-4.8d-32)) .or. (.not. (x <= 1.3d-12))) 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 <= -4.8e-32) || !(x <= 1.3e-12)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.8e-32) or not (x <= 1.3e-12):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.8e-32) || !(x <= 1.3e-12))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.8e-32) || ~((x <= 1.3e-12)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.8e-32], N[Not[LessEqual[x, 1.3e-12]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -4.8000000000000003e-32 or 1.29999999999999991e-12 < x

   1. Initial program 95.0%

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

      1. remove-double-neg 95.0%

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

      2. distribute-rgt-neg-out 95.0%

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

      3. neg-sub0 95.0%

         \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

      4. neg-sub0 95.0%

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

      5. *-commutative 95.0%

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

      6. distribute-lft-neg-in 95.0%

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

      7. remove-double-neg 95.0%

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

      8. distribute-rgt-out-- 95.0%

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

      9. *-lft-identity 95.0%

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

      10. associate-+l- 95.0%

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

      11. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 46.0%

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

   if -4.8000000000000003e-32 < x < 1.29999999999999991e-12

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

      4. neg-sub0 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-lft-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. *-lft-identity 100.0%

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

      10. associate-+l- 100.0%

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

      11. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 90.0%

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

      1. sub-neg 90.0%

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

      2. +-commutative 90.0%

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

      3. neg-mul-1 90.0%

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

      4. distribute-neg-in 90.0%

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

      5. remove-double-neg 90.0%

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

      6. mul-1-neg 90.0%

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

      7. associate-+r+ 90.0%

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

      8. distribute-lft-in 90.0%

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

      9. +-commutative 90.0%

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

      10. mul-1-neg 90.0%

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

      11. sub-neg 90.0%

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

      12. div-sub 90.0%

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

      13. sub-neg 90.0%

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

      14. mul-1-neg 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x around 0 74.5%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-32} \lor \neg \left(x \leq 1.3 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. remove-double-neg 97.6%

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

   2. distribute-rgt-neg-out 97.6%

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

   3. neg-sub0 97.6%

      \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

   4. neg-sub0 97.6%

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

   5. *-commutative 97.6%

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

   6. distribute-lft-neg-in 97.6%

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

   7. remove-double-neg 97.6%

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

   8. distribute-rgt-out-- 97.6%

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

   9. *-lft-identity 97.6%

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

   10. associate-+l- 97.6%

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

   11. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 74.7%

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

   1. mul-1-neg 74.7%

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

   2. distribute-rgt-neg-out 74.7%

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

7. Simplified 74.7%

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

   1. *-commutative 74.7%

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

   2. cancel-sign-sub 74.7%

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

   3. *-commutative 74.7%

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

   4. +-commutative 74.7%

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

9. Applied egg-rr 74.7%

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

10. Final simplification 74.7%

    \[\leadsto y + x \cdot z \]
11. Add Preprocessing

Alternative 5: 36.3% 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 97.6%

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

   1. remove-double-neg 97.6%

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

   2. distribute-rgt-neg-out 97.6%

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

   3. neg-sub0 97.6%

      \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

   4. neg-sub0 97.6%

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

   5. *-commutative 97.6%

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

   6. distribute-lft-neg-in 97.6%

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

   7. remove-double-neg 97.6%

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

   8. distribute-rgt-out-- 97.6%

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

   9. *-lft-identity 97.6%

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

   10. associate-+l- 97.6%

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

   11. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in z around inf 86.1%

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

   1. sub-neg 86.1%

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

   2. +-commutative 86.1%

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

   3. neg-mul-1 86.1%

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

   4. distribute-neg-in 86.1%

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

   5. remove-double-neg 86.1%

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

   6. mul-1-neg 86.1%

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

   7. associate-+r+ 86.1%

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

   8. distribute-lft-in 84.5%

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

   9. +-commutative 84.5%

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

   10. mul-1-neg 84.5%

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

   11. sub-neg 84.5%

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

   12. div-sub 86.9%

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

   13. sub-neg 86.9%

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

   14. mul-1-neg 86.9%

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

7. Simplified 88.5%

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

8. Taylor expanded in x around 0 40.6%

   \[\leadsto \color{blue}{y} \]
9. Add Preprocessing

Developer Target 1: 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 2024130 
(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)))