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

Percentage Accurate: 97.8% → 100.0%

Time: 6.8s

Alternatives: 7

Speedup: 1.3×

• 21.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot y + x \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (- 1.0 x) y) (* x z)))

C

double code(double x, double y, double z) {
	return ((1.0 - x) * y) + (x * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((1.0d0 - x) * y) + (x * z)
end function

Java

public static double code(double x, double y, double z) {
	return ((1.0 - x) * y) + (x * z);
}

Python

def code(x, y, z):
	return ((1.0 - x) * y) + (x * z)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(1.0 - x) * y) + Float64(x * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((1.0 - x) * y) + (x * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.8% 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 98.8%

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

   1. *-commutative 98.8%

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

   2. distribute-lft-out-- 98.8%

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

   3. *-rgt-identity 98.8%

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

   4. cancel-sign-sub-inv 98.8%

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

   5. associate-+l+ 98.8%

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

   6. +-commutative 98.8%

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

   7. *-commutative 98.8%

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

   8. distribute-rgt-out 100.0%

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

   9. fma-define 100.0%

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

   10. +-commutative 100.0%

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

   11. 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 61.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -3.35 \cdot 10^{+121}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -0.0005:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-31}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+124} \lor \neg \left(x \leq 1.06 \cdot 10^{+269}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -3.35e+121)
     t_0
     (if (<= x -1.55e+91)
       (* x z)
       (if (<= x -0.0005)
         t_0
         (if (<= x 2.5e-31)
           y
           (if (or (<= x 3.5e+124) (not (<= x 1.06e+269))) (* x z) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -3.35e+121) {
		tmp = t_0;
	} else if (x <= -1.55e+91) {
		tmp = x * z;
	} else if (x <= -0.0005) {
		tmp = t_0;
	} else if (x <= 2.5e-31) {
		tmp = y;
	} else if ((x <= 3.5e+124) || !(x <= 1.06e+269)) {
		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 (x <= (-3.35d+121)) then
        tmp = t_0
    else if (x <= (-1.55d+91)) then
        tmp = x * z
    else if (x <= (-0.0005d0)) then
        tmp = t_0
    else if (x <= 2.5d-31) then
        tmp = y
    else if ((x <= 3.5d+124) .or. (.not. (x <= 1.06d+269))) 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 (x <= -3.35e+121) {
		tmp = t_0;
	} else if (x <= -1.55e+91) {
		tmp = x * z;
	} else if (x <= -0.0005) {
		tmp = t_0;
	} else if (x <= 2.5e-31) {
		tmp = y;
	} else if ((x <= 3.5e+124) || !(x <= 1.06e+269)) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if x <= -3.35e+121:
		tmp = t_0
	elif x <= -1.55e+91:
		tmp = x * z
	elif x <= -0.0005:
		tmp = t_0
	elif x <= 2.5e-31:
		tmp = y
	elif (x <= 3.5e+124) or not (x <= 1.06e+269):
		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 (x <= -3.35e+121)
		tmp = t_0;
	elseif (x <= -1.55e+91)
		tmp = Float64(x * z);
	elseif (x <= -0.0005)
		tmp = t_0;
	elseif (x <= 2.5e-31)
		tmp = y;
	elseif ((x <= 3.5e+124) || !(x <= 1.06e+269))
		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 (x <= -3.35e+121)
		tmp = t_0;
	elseif (x <= -1.55e+91)
		tmp = x * z;
	elseif (x <= -0.0005)
		tmp = t_0;
	elseif (x <= 2.5e-31)
		tmp = y;
	elseif ((x <= 3.5e+124) || ~((x <= 1.06e+269)))
		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[x, -3.35e+121], t$95$0, If[LessEqual[x, -1.55e+91], N[(x * z), $MachinePrecision], If[LessEqual[x, -0.0005], t$95$0, If[LessEqual[x, 2.5e-31], y, If[Or[LessEqual[x, 3.5e+124], N[Not[LessEqual[x, 1.06e+269]], $MachinePrecision]], N[(x * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3499999999999999e121 or -1.54999999999999999e91 < x < -5.0000000000000001e-4 or 3.5000000000000001e124 < x < 1.06000000000000001e269

   1. Initial program 97.5%

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

   3. Taylor expanded in y around inf 67.9%

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

   4. Taylor expanded in x around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. *-commutative 64.6%

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

      3. distribute-rgt-neg-in 64.6%

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

   6. Simplified 64.6%

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

   if -3.3499999999999999e121 < x < -1.54999999999999999e91 or 2.5e-31 < x < 3.5000000000000001e124 or 1.06000000000000001e269 < x

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 64.3%

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

   if -5.0000000000000001e-4 < x < 2.5e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.35 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -0.0005:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-31}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+124} \lor \neg \left(x \leq 1.06 \cdot 10^{+269}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+100} \lor \neg \left(z \leq 1.35 \cdot 10^{+25}\right) \land \left(z \leq 2 \cdot 10^{+72} \lor \neg \left(z \leq 1.6 \cdot 10^{+141}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.7e+100)
         (and (not (<= z 1.35e+25)) (or (<= z 2e+72) (not (<= z 1.6e+141)))))
   (* x z)
   (* y (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e+100) || (!(z <= 1.35e+25) && ((z <= 2e+72) || !(z <= 1.6e+141)))) {
		tmp = x * z;
	} 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 ((z <= (-2.7d+100)) .or. (.not. (z <= 1.35d+25)) .and. (z <= 2d+72) .or. (.not. (z <= 1.6d+141))) then
        tmp = x * z
    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 ((z <= -2.7e+100) || (!(z <= 1.35e+25) && ((z <= 2e+72) || !(z <= 1.6e+141)))) {
		tmp = x * z;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.7e+100) or (not (z <= 1.35e+25) and ((z <= 2e+72) or not (z <= 1.6e+141))):
		tmp = x * z
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.7e+100) || (!(z <= 1.35e+25) && ((z <= 2e+72) || !(z <= 1.6e+141))))
		tmp = Float64(x * z);
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.7e+100) || (~((z <= 1.35e+25)) && ((z <= 2e+72) || ~((z <= 1.6e+141)))))
		tmp = x * z;
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.7e+100], And[N[Not[LessEqual[z, 1.35e+25]], $MachinePrecision], Or[LessEqual[z, 2e+72], N[Not[LessEqual[z, 1.6e+141]], $MachinePrecision]]]], N[(x * z), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999998e100 or 1.35e25 < z < 1.99999999999999989e72 or 1.60000000000000009e141 < z

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 76.3%

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

   if -2.69999999999999998e100 < z < 1.35e25 or 1.99999999999999989e72 < z < 1.60000000000000009e141

   1. Initial program 98.8%

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

   3. Taylor expanded in y around inf 82.4%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+100} \lor \neg \left(z \leq 1.35 \cdot 10^{+25}\right) \land \left(z \leq 2 \cdot 10^{+72} \lor \neg \left(z \leq 1.6 \cdot 10^{+141}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -165000 \lor \neg \left(z \leq 3.4\right):\\ \;\;\;\;y + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -165000.0) (not (<= z 3.4))) (+ y (* x z)) (* y (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -165000.0) || !(z <= 3.4)) {
		tmp = y + (x * z);
	} 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 ((z <= (-165000.0d0)) .or. (.not. (z <= 3.4d0))) then
        tmp = y + (x * z)
    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 ((z <= -165000.0) || !(z <= 3.4)) {
		tmp = y + (x * z);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -165000.0) or not (z <= 3.4):
		tmp = y + (x * z)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -165000.0) || !(z <= 3.4))
		tmp = Float64(y + Float64(x * z));
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -165000.0) || ~((z <= 3.4)))
		tmp = y + (x * z);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -165000.0], N[Not[LessEqual[z, 3.4]], $MachinePrecision]], N[(y + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -165000 or 3.39999999999999991 < z

   1. Initial program 97.7%

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

      1. remove-double-neg 97.7%

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

      2. distribute-rgt-neg-out 97.7%

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

      3. neg-sub0 97.7%

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

      4. neg-sub0 97.7%

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

      5. *-commutative 97.7%

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

      6. distribute-lft-neg-in 97.7%

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

      7. remove-double-neg 97.7%

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

      8. distribute-rgt-out-- 97.7%

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

      9. *-lft-identity 97.7%

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

      10. associate-+l- 97.7%

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

      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 0 89.0%

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

      1. neg-mul-1 89.0%

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

      2. distribute-rgt-neg-in 89.0%

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

   7. Simplified 89.0%

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

      1. sub-neg 89.0%

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

      2. +-commutative 89.0%

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

      3. distribute-rgt-neg-out 89.0%

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

      4. remove-double-neg 89.0%

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

   9. Applied egg-rr 89.0%

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

   if -165000 < z < 3.39999999999999991

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -165000 \lor \neg \left(z \leq 3.4\right):\\ \;\;\;\;y + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-18} \lor \neg \left(x \leq 4 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.4e-18) (not (<= x 4e-30))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e-18) || !(x <= 4e-30)) {
		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 <= (-2.4d-18)) .or. (.not. (x <= 4d-30))) 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 <= -2.4e-18) || !(x <= 4e-30)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.4e-18) or not (x <= 4e-30):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.4e-18) || !(x <= 4e-30))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.4e-18) || ~((x <= 4e-30)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.4e-18], N[Not[LessEqual[x, 4e-30]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999994e-18 or 4e-30 < x

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 49.6%

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

   if -2.39999999999999994e-18 < x < 4e-30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-18} \lor \neg \left(x \leq 4 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

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 98.8%

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

   1. remove-double-neg 98.8%

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

   2. distribute-rgt-neg-out 98.8%

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

   3. neg-sub0 98.8%

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

   4. neg-sub0 98.8%

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

   5. *-commutative 98.8%

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

   6. distribute-lft-neg-in 98.8%

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

   7. remove-double-neg 98.8%

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

   8. distribute-rgt-out-- 98.8%

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

   9. *-lft-identity 98.8%

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

   10. associate-+l- 98.8%

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

   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 7: 36.2% 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 98.8%

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

3. Taylor expanded in x around 0 38.1%

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

4. Final simplification 38.1%

   \[\leadsto y \]
5. Add Preprocessing

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 2024050 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (- y (* x (- y z)))

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