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

Percentage Accurate: 98.0% → 100.0%

Time: 4.0s

Alternatives: 7

Speedup: 1.3×

• 21.5% 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 99.6%

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

   1. *-commutative 99.6%

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

   2. distribute-lft-out-- 99.6%

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

   3. *-rgt-identity 99.6%

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

   4. cancel-sign-sub-inv 99.6%

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

   5. +-commutative 99.6%

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

   6. +-commutative 99.6%

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

   7. associate-+l+ 99.6%

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

   8. +-commutative 99.6%

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

   9. *-commutative 99.6%

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

   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: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.04 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-72}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+21} \lor \neg \left(x \leq 6.2 \cdot 10^{+164}\right) \land x \leq 9.5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -3.5e+148)
     (* x z)
     (if (<= x -1.04e+39)
       t_0
       (if (<= x -3.6e-72)
         (* x z)
         (if (<= x 8.5e-25)
           y
           (if (or (<= x 8.8e+21) (and (not (<= x 6.2e+164)) (<= x 9.5e+233)))
             (* x z)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -3.5e+148) {
		tmp = x * z;
	} else if (x <= -1.04e+39) {
		tmp = t_0;
	} else if (x <= -3.6e-72) {
		tmp = x * z;
	} else if (x <= 8.5e-25) {
		tmp = y;
	} else if ((x <= 8.8e+21) || (!(x <= 6.2e+164) && (x <= 9.5e+233))) {
		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 <= (-3.5d+148)) then
        tmp = x * z
    else if (x <= (-1.04d+39)) then
        tmp = t_0
    else if (x <= (-3.6d-72)) then
        tmp = x * z
    else if (x <= 8.5d-25) then
        tmp = y
    else if ((x <= 8.8d+21) .or. (.not. (x <= 6.2d+164)) .and. (x <= 9.5d+233)) 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 <= -3.5e+148) {
		tmp = x * z;
	} else if (x <= -1.04e+39) {
		tmp = t_0;
	} else if (x <= -3.6e-72) {
		tmp = x * z;
	} else if (x <= 8.5e-25) {
		tmp = y;
	} else if ((x <= 8.8e+21) || (!(x <= 6.2e+164) && (x <= 9.5e+233))) {
		tmp = x * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if x <= -3.5e+148:
		tmp = x * z
	elif x <= -1.04e+39:
		tmp = t_0
	elif x <= -3.6e-72:
		tmp = x * z
	elif x <= 8.5e-25:
		tmp = y
	elif (x <= 8.8e+21) or (not (x <= 6.2e+164) and (x <= 9.5e+233)):
		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 <= -3.5e+148)
		tmp = Float64(x * z);
	elseif (x <= -1.04e+39)
		tmp = t_0;
	elseif (x <= -3.6e-72)
		tmp = Float64(x * z);
	elseif (x <= 8.5e-25)
		tmp = y;
	elseif ((x <= 8.8e+21) || (!(x <= 6.2e+164) && (x <= 9.5e+233)))
		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 <= -3.5e+148)
		tmp = x * z;
	elseif (x <= -1.04e+39)
		tmp = t_0;
	elseif (x <= -3.6e-72)
		tmp = x * z;
	elseif (x <= 8.5e-25)
		tmp = y;
	elseif ((x <= 8.8e+21) || (~((x <= 6.2e+164)) && (x <= 9.5e+233)))
		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, -3.5e+148], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.04e+39], t$95$0, If[LessEqual[x, -3.6e-72], N[(x * z), $MachinePrecision], If[LessEqual[x, 8.5e-25], y, If[Or[LessEqual[x, 8.8e+21], And[N[Not[LessEqual[x, 6.2e+164]], $MachinePrecision], LessEqual[x, 9.5e+233]]], N[(x * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4999999999999999e148 or -1.04e39 < x < -3.6e-72 or 8.49999999999999981e-25 < x < 8.8e21 or 6.2000000000000003e164 < x < 9.5000000000000001e233

   1. Initial program 98.6%

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

   2. Taylor expanded in y around 0 67.3%

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

   if -3.4999999999999999e148 < x < -1.04e39 or 8.8e21 < x < 6.2000000000000003e164 or 9.5000000000000001e233 < x

   1. Initial program 100.0%

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

   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. unsub-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 67.3%

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

      1. mul-1-neg 67.3%

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

      2. distribute-lft-neg-out 67.3%

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

      3. *-commutative 67.3%

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

   7. Simplified 67.3%

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

   if -3.6e-72 < x < 8.49999999999999981e-25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.04 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-72}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-25}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+21} \lor \neg \left(x \leq 6.2 \cdot 10^{+164}\right) \land x \leq 9.5 \cdot 10^{+233}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-72} \lor \neg \left(x \leq 3.6 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.6e-72) (not (<= x 3.6e-23))) (* x (- z y)) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.6e-72) || !(x <= 3.6e-23)) {
		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 <= (-3.6d-72)) .or. (.not. (x <= 3.6d-23))) 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 <= -3.6e-72) || !(x <= 3.6e-23)) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.6e-72) or not (x <= 3.6e-23):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.6e-72) || !(x <= 3.6e-23))
		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 <= -3.6e-72) || ~((x <= 3.6e-23)))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.6e-72], N[Not[LessEqual[x, 3.6e-23]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -3.6e-72 or 3.5999999999999998e-23 < x

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 95.6%

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

      1. mul-1-neg 95.6%

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

      2. unsub-neg 95.6%

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

   4. Simplified 95.6%

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

   if -3.6e-72 < x < 3.5999999999999998e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-72} \lor \neg \left(x \leq 3.6 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -33000000000 \lor \neg \left(x \leq 2.3 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -33000000000.0) (not (<= x 2.3e-8)))
   (* x (- z y))
   (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -33000000000.0) || !(x <= 2.3e-8)) {
		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 <= (-33000000000.0d0)) .or. (.not. (x <= 2.3d-8))) 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 <= -33000000000.0) || !(x <= 2.3e-8)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -33000000000.0) or not (x <= 2.3e-8):
		tmp = x * (z - y)
	else:
		tmp = y + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -33000000000.0) || !(x <= 2.3e-8))
		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 <= -33000000000.0) || ~((x <= 2.3e-8)))
		tmp = x * (z - y);
	else
		tmp = y + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -33000000000.0], N[Not[LessEqual[x, 2.3e-8]], $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 < -3.3e10 or 2.3000000000000001e-8 < x

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

   4. Simplified 99.5%

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

   if -3.3e10 < x < 2.3000000000000001e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. distribute-lft-neg-out 100.0%

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

      5. mul-1-neg 100.0%

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

      6. *-lft-identity 100.0%

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

      7. associate-+r+ 100.0%

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

      8. mul-1-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. distribute-lft-out-- 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around inf 99.3%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -33000000000 \lor \neg \left(x \leq 2.3 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]

Alternative 5: 61.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{-73} \lor \neg \left(x \leq 2.35 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.3e-73) (not (<= x 2.35e-23))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.3e-73) || !(x <= 2.35e-23)) {
		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 <= (-5.3d-73)) .or. (.not. (x <= 2.35d-23))) 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 <= -5.3e-73) || !(x <= 2.35e-23)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.3e-73) or not (x <= 2.35e-23):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.3e-73) || !(x <= 2.35e-23))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.3e-73) || ~((x <= 2.35e-23)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.3e-73], N[Not[LessEqual[x, 2.35e-23]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -5.29999999999999972e-73 or 2.35e-23 < x

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 52.9%

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

   if -5.29999999999999972e-73 < x < 2.35e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.2%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{-73} \lor \neg \left(x \leq 2.35 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

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 99.6%

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

2. Taylor expanded in x around 0 100.0%

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

   1. mul-1-neg 100.0%

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

4. Simplified 100.0%

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

5. Taylor expanded in y around 0 99.6%

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

   1. neg-mul-1 99.6%

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

   2. +-commutative 99.6%

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

   3. distribute-rgt-in 99.6%

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

   4. distribute-lft-neg-out 99.6%

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

   5. mul-1-neg 99.6%

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

   6. *-lft-identity 99.6%

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

   7. associate-+r+ 99.6%

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

   8. mul-1-neg 99.6%

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

   9. sub-neg 99.6%

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

   10. +-commutative 99.6%

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

   11. distribute-lft-out-- 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 7: 36.9% 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 99.6%

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

2. Taylor expanded in x around 0 41.6%

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

3. Final simplification 41.6%

   \[\leadsto y \]

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 2023306 
(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)))