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

Percentage Accurate: 98.0% → 100.0%

Time: 5.7s

Alternatives: 8

Speedup: 1.3×

• 21.7% 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: 98.0% 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. sub-neg 98.4%

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

   2. +-commutative 98.4%

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

   3. distribute-rgt1-in 98.4%

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

   4. associate-+l+ 98.4%

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

   5. +-commutative 98.4%

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

   6. *-commutative 98.4%

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

   7. neg-mul-1 98.4%

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

   8. associate-*r* 98.4%

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

   9. *-commutative 98.4%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. 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: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+137}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= x -1.0) t_0 (if (<= x 1.0) y (if (<= x 1.42e+137) t_0 (* x z))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y;
	} else if (x <= 1.42e+137) {
		tmp = t_0;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * -x
    if (x <= (-1.0d0)) then
        tmp = t_0
    else if (x <= 1.0d0) then
        tmp = y
    else if (x <= 1.42d+137) then
        tmp = t_0
    else
        tmp = x * z
    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 <= -1.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y;
	} else if (x <= 1.42e+137) {
		tmp = t_0;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if x <= -1.0:
		tmp = t_0
	elif x <= 1.0:
		tmp = y
	elif x <= 1.42e+137:
		tmp = t_0
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = y;
	elseif (x <= 1.42e+137)
		tmp = t_0;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = y;
	elseif (x <= 1.42e+137)
		tmp = t_0;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, 1.0], y, If[LessEqual[x, 1.42e+137], t$95$0, N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 1 < x < 1.42e137

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 62.7%

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

   3. Taylor expanded in x around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. distribute-rgt-neg-out 61.3%

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

   5. Simplified 61.3%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.0%

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

   if 1.42e137 < x

   1. Initial program 94.4%

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

   2. Taylor expanded in y around 0 69.9%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+137}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-78} \lor \neg \left(y \leq 1.55 \cdot 10^{-168}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e-78) (not (<= y 1.55e-168))) (* y (- 1.0 x)) (* x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-78) || !(y <= 1.55e-168)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.4d-78)) .or. (.not. (y <= 1.55d-168))) then
        tmp = y * (1.0d0 - x)
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-78) || !(y <= 1.55e-168)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e-78) or not (y <= 1.55e-168):
		tmp = y * (1.0 - x)
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e-78) || !(y <= 1.55e-168))
		tmp = Float64(y * Float64(1.0 - x));
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.4e-78) || ~((y <= 1.55e-168)))
		tmp = y * (1.0 - x);
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e-78], N[Not[LessEqual[y, 1.55e-168]], $MachinePrecision]], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(x * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000012e-78 or 1.55e-168 < y

   1. Initial program 97.9%

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

   2. Taylor expanded in y around inf 83.3%

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

   if -3.40000000000000012e-78 < y < 1.55e-168

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.2%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-78} \lor \neg \left(y \leq 1.55 \cdot 10^{-168}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 4: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+16} \lor \neg \left(x \leq 2500000000\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.5e+16) (not (<= x 2500000000.0)))
   (* x (- z y))
   (* y (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+16) || !(x <= 2500000000.0)) {
		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 <= (-9.5d+16)) .or. (.not. (x <= 2500000000.0d0))) 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 <= -9.5e+16) || !(x <= 2500000000.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.5e+16) or not (x <= 2500000000.0):
		tmp = x * (z - y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.5e+16) || !(x <= 2500000000.0))
		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 <= -9.5e+16) || ~((x <= 2500000000.0)))
		tmp = x * (z - y);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.5e+16], N[Not[LessEqual[x, 2500000000.0]], $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 < -9.5e16 or 2.5e9 < x

   1. Initial program 97.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   if -9.5e16 < x < 2.5e9

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+16} \lor \neg \left(x \leq 2500000000\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 97.1%

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

   2. Taylor expanded in x around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

   4. Simplified 98.9%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*r/ 100.0%

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

      4. metadata-eval 100.0%

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

   3. Applied egg-rr 100.0%

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

      1. associate-*l/ 100.0%

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

      2. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 100.0%

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

   7. Taylor expanded in z around inf 97.6%

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

4. Final simplification 98.3%

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

Alternative 6: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-33}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.5e+16) (* x z) (if (<= x 1.15e-33) y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e+16) {
		tmp = x * z;
	} else if (x <= 1.15e-33) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-9.5d+16)) then
        tmp = x * z
    else if (x <= 1.15d-33) then
        tmp = y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e+16) {
		tmp = x * z;
	} else if (x <= 1.15e-33) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.5e+16:
		tmp = x * z
	elif x <= 1.15e-33:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.5e+16)
		tmp = Float64(x * z);
	elseif (x <= 1.15e-33)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.5e+16)
		tmp = x * z;
	elseif (x <= 1.15e-33)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.5e+16], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.15e-33], y, N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5e16 or 1.14999999999999993e-33 < x

   1. Initial program 97.2%

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

   2. Taylor expanded in y around 0 52.3%

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

   if -9.5e16 < x < 1.14999999999999993e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.5%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-33}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 7: 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. flip-- 88.3%

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

   3. associate-*r/ 83.2%

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

   4. metadata-eval 83.2%

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

3. Applied egg-rr 83.2%

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

   1. associate-*l/ 85.7%

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

   2. +-commutative 85.7%

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

5. Simplified 85.7%

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

6. Taylor expanded in x around 0 100.0%

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

7. Final simplification 100.0%

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

Alternative 8: 36.0% 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 38.2%

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

3. Final simplification 38.2%

   \[\leadsto y \]

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 2023207 
(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)))