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

Percentage Accurate: 97.7% → 100.0%

Time: 4.0s

Alternatives: 7

Speedup: 1.0×

• 21.1% 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: 97.7% 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 99.2%

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

   1. sub-neg 99.2%

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

   2. +-commutative 99.2%

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

   3. distribute-rgt1-in 99.2%

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

   4. associate-+l+ 99.2%

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

   5. +-commutative 99.2%

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

   6. *-commutative 99.2%

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

   7. neg-mul-1 99.2%

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

   8. associate-*r* 99.2%

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

   9. *-commutative 99.2%

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

   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: 60.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -5.9 \cdot 10^{+174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+140}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-31}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-128}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-109}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+69}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= x -5.9e+174)
     t_0
     (if (<= x -5.8e+140)
       (* x z)
       (if (<= x -2.2e+50)
         t_0
         (if (<= x -1.3e-31)
           (* x z)
           (if (<= x 1.4e-128)
             y
             (if (<= x 6.5e-109)
               (* x z)
               (if (<= x 4.9e-22)
                 y
                 (if (<= x 2.2e+69)
                   (* x z)
                   (if (<= x 2.4e+101) t_0 (* x z))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -5.9e+174) {
		tmp = t_0;
	} else if (x <= -5.8e+140) {
		tmp = x * z;
	} else if (x <= -2.2e+50) {
		tmp = t_0;
	} else if (x <= -1.3e-31) {
		tmp = x * z;
	} else if (x <= 1.4e-128) {
		tmp = y;
	} else if (x <= 6.5e-109) {
		tmp = x * z;
	} else if (x <= 4.9e-22) {
		tmp = y;
	} else if (x <= 2.2e+69) {
		tmp = x * z;
	} else if (x <= 2.4e+101) {
		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 <= (-5.9d+174)) then
        tmp = t_0
    else if (x <= (-5.8d+140)) then
        tmp = x * z
    else if (x <= (-2.2d+50)) then
        tmp = t_0
    else if (x <= (-1.3d-31)) then
        tmp = x * z
    else if (x <= 1.4d-128) then
        tmp = y
    else if (x <= 6.5d-109) then
        tmp = x * z
    else if (x <= 4.9d-22) then
        tmp = y
    else if (x <= 2.2d+69) then
        tmp = x * z
    else if (x <= 2.4d+101) 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 <= -5.9e+174) {
		tmp = t_0;
	} else if (x <= -5.8e+140) {
		tmp = x * z;
	} else if (x <= -2.2e+50) {
		tmp = t_0;
	} else if (x <= -1.3e-31) {
		tmp = x * z;
	} else if (x <= 1.4e-128) {
		tmp = y;
	} else if (x <= 6.5e-109) {
		tmp = x * z;
	} else if (x <= 4.9e-22) {
		tmp = y;
	} else if (x <= 2.2e+69) {
		tmp = x * z;
	} else if (x <= 2.4e+101) {
		tmp = t_0;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if x <= -5.9e+174:
		tmp = t_0
	elif x <= -5.8e+140:
		tmp = x * z
	elif x <= -2.2e+50:
		tmp = t_0
	elif x <= -1.3e-31:
		tmp = x * z
	elif x <= 1.4e-128:
		tmp = y
	elif x <= 6.5e-109:
		tmp = x * z
	elif x <= 4.9e-22:
		tmp = y
	elif x <= 2.2e+69:
		tmp = x * z
	elif x <= 2.4e+101:
		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 <= -5.9e+174)
		tmp = t_0;
	elseif (x <= -5.8e+140)
		tmp = Float64(x * z);
	elseif (x <= -2.2e+50)
		tmp = t_0;
	elseif (x <= -1.3e-31)
		tmp = Float64(x * z);
	elseif (x <= 1.4e-128)
		tmp = y;
	elseif (x <= 6.5e-109)
		tmp = Float64(x * z);
	elseif (x <= 4.9e-22)
		tmp = y;
	elseif (x <= 2.2e+69)
		tmp = Float64(x * z);
	elseif (x <= 2.4e+101)
		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 <= -5.9e+174)
		tmp = t_0;
	elseif (x <= -5.8e+140)
		tmp = x * z;
	elseif (x <= -2.2e+50)
		tmp = t_0;
	elseif (x <= -1.3e-31)
		tmp = x * z;
	elseif (x <= 1.4e-128)
		tmp = y;
	elseif (x <= 6.5e-109)
		tmp = x * z;
	elseif (x <= 4.9e-22)
		tmp = y;
	elseif (x <= 2.2e+69)
		tmp = x * z;
	elseif (x <= 2.4e+101)
		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, -5.9e+174], t$95$0, If[LessEqual[x, -5.8e+140], N[(x * z), $MachinePrecision], If[LessEqual[x, -2.2e+50], t$95$0, If[LessEqual[x, -1.3e-31], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.4e-128], y, If[LessEqual[x, 6.5e-109], N[(x * z), $MachinePrecision], If[LessEqual[x, 4.9e-22], y, If[LessEqual[x, 2.2e+69], N[(x * z), $MachinePrecision], If[LessEqual[x, 2.4e+101], t$95$0, N[(x * z), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.8999999999999999e174 or -5.7999999999999998e140 < x < -2.20000000000000017e50 or 2.2000000000000002e69 < x < 2.39999999999999988e101

   1. Initial program 97.7%

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

   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%

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

   5. Taylor expanded in z around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. distribute-rgt-neg-out 74.4%

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

   7. Simplified 74.4%

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

   if -5.8999999999999999e174 < x < -5.7999999999999998e140 or -2.20000000000000017e50 < x < -1.29999999999999998e-31 or 1.3999999999999999e-128 < x < 6.49999999999999959e-109 or 4.8999999999999998e-22 < x < 2.2000000000000002e69 or 2.39999999999999988e101 < x

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 72.8%

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

   if -1.29999999999999998e-31 < x < 1.3999999999999999e-128 or 6.49999999999999959e-109 < x < 4.8999999999999998e-22

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+140}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-31}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-128}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-109}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+69}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 84.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-128}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-105}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-23}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -7.8e-32)
     t_0
     (if (<= x 3.4e-128)
       y
       (if (<= x 1.8e-105) (* x z) (if (<= x 4.7e-23) y t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -7.8e-32) {
		tmp = t_0;
	} else if (x <= 3.4e-128) {
		tmp = y;
	} else if (x <= 1.8e-105) {
		tmp = x * z;
	} else if (x <= 4.7e-23) {
		tmp = y;
	} 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 * (z - y)
    if (x <= (-7.8d-32)) then
        tmp = t_0
    else if (x <= 3.4d-128) then
        tmp = y
    else if (x <= 1.8d-105) then
        tmp = x * z
    else if (x <= 4.7d-23) then
        tmp = y
    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 * (z - y);
	double tmp;
	if (x <= -7.8e-32) {
		tmp = t_0;
	} else if (x <= 3.4e-128) {
		tmp = y;
	} else if (x <= 1.8e-105) {
		tmp = x * z;
	} else if (x <= 4.7e-23) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -7.8e-32:
		tmp = t_0
	elif x <= 3.4e-128:
		tmp = y
	elif x <= 1.8e-105:
		tmp = x * z
	elif x <= 4.7e-23:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -7.8e-32)
		tmp = t_0;
	elseif (x <= 3.4e-128)
		tmp = y;
	elseif (x <= 1.8e-105)
		tmp = Float64(x * z);
	elseif (x <= 4.7e-23)
		tmp = y;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z - y);
	tmp = 0.0;
	if (x <= -7.8e-32)
		tmp = t_0;
	elseif (x <= 3.4e-128)
		tmp = y;
	elseif (x <= 1.8e-105)
		tmp = x * z;
	elseif (x <= 4.7e-23)
		tmp = y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e-32], t$95$0, If[LessEqual[x, 3.4e-128], y, If[LessEqual[x, 1.8e-105], N[(x * z), $MachinePrecision], If[LessEqual[x, 4.7e-23], y, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.8000000000000003e-32 or 4.7000000000000001e-23 < x

   1. Initial program 98.5%

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

   2. Taylor expanded in x around inf 98.1%

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

      1. mul-1-neg 98.1%

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

      2. unsub-neg 98.1%

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

   4. Simplified 98.1%

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

   if -7.8000000000000003e-32 < x < 3.39999999999999975e-128 or 1.79999999999999982e-105 < x < 4.7000000000000001e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.5%

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

   if 3.39999999999999975e-128 < x < 1.79999999999999982e-105

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-128}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-105}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-23}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 4: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-128}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-100}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -7.5e-32)
     t_0
     (if (<= x 3.3e-128)
       y
       (if (<= x 4.1e-100) (* x z) (if (<= x 4.8e-24) (- y (* x y)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -7.5e-32) {
		tmp = t_0;
	} else if (x <= 3.3e-128) {
		tmp = y;
	} else if (x <= 4.1e-100) {
		tmp = x * z;
	} else if (x <= 4.8e-24) {
		tmp = y - (x * y);
	} 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 * (z - y)
    if (x <= (-7.5d-32)) then
        tmp = t_0
    else if (x <= 3.3d-128) then
        tmp = y
    else if (x <= 4.1d-100) then
        tmp = x * z
    else if (x <= 4.8d-24) then
        tmp = y - (x * y)
    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 * (z - y);
	double tmp;
	if (x <= -7.5e-32) {
		tmp = t_0;
	} else if (x <= 3.3e-128) {
		tmp = y;
	} else if (x <= 4.1e-100) {
		tmp = x * z;
	} else if (x <= 4.8e-24) {
		tmp = y - (x * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -7.5e-32:
		tmp = t_0
	elif x <= 3.3e-128:
		tmp = y
	elif x <= 4.1e-100:
		tmp = x * z
	elif x <= 4.8e-24:
		tmp = y - (x * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -7.5e-32)
		tmp = t_0;
	elseif (x <= 3.3e-128)
		tmp = y;
	elseif (x <= 4.1e-100)
		tmp = Float64(x * z);
	elseif (x <= 4.8e-24)
		tmp = Float64(y - Float64(x * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z - y);
	tmp = 0.0;
	if (x <= -7.5e-32)
		tmp = t_0;
	elseif (x <= 3.3e-128)
		tmp = y;
	elseif (x <= 4.1e-100)
		tmp = x * z;
	elseif (x <= 4.8e-24)
		tmp = y - (x * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e-32], t$95$0, If[LessEqual[x, 3.3e-128], y, If[LessEqual[x, 4.1e-100], N[(x * z), $MachinePrecision], If[LessEqual[x, 4.8e-24], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.49999999999999953e-32 or 4.7999999999999996e-24 < x

   1. Initial program 98.5%

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

   2. Taylor expanded in x around inf 98.1%

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

      1. mul-1-neg 98.1%

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

      2. unsub-neg 98.1%

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

   4. Simplified 98.1%

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

   if -7.49999999999999953e-32 < x < 3.3e-128

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.4%

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

   if 3.3e-128 < x < 4.0999999999999999e-100

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

   if 4.0999999999999999e-100 < x < 4.7999999999999996e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 73.2%

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

      1. sub-neg 73.2%

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

      2. distribute-lft-in 73.2%

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

      3. *-rgt-identity 73.2%

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

      4. distribute-rgt-neg-out 73.2%

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

      5. sub-neg 73.2%

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

   4. Simplified 73.2%

      \[\leadsto \color{blue}{y - y \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-128}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-100}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;y - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 5: 59.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-32}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-128}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-104}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-23}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2e-32)
   (* x z)
   (if (<= x 2.7e-128)
     y
     (if (<= x 1.55e-104) (* x z) (if (<= x 3.2e-23) y (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e-32) {
		tmp = x * z;
	} else if (x <= 2.7e-128) {
		tmp = y;
	} else if (x <= 1.55e-104) {
		tmp = x * z;
	} else if (x <= 3.2e-23) {
		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 <= (-2d-32)) then
        tmp = x * z
    else if (x <= 2.7d-128) then
        tmp = y
    else if (x <= 1.55d-104) then
        tmp = x * z
    else if (x <= 3.2d-23) 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 <= -2e-32) {
		tmp = x * z;
	} else if (x <= 2.7e-128) {
		tmp = y;
	} else if (x <= 1.55e-104) {
		tmp = x * z;
	} else if (x <= 3.2e-23) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2e-32:
		tmp = x * z
	elif x <= 2.7e-128:
		tmp = y
	elif x <= 1.55e-104:
		tmp = x * z
	elif x <= 3.2e-23:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2e-32)
		tmp = Float64(x * z);
	elseif (x <= 2.7e-128)
		tmp = y;
	elseif (x <= 1.55e-104)
		tmp = Float64(x * z);
	elseif (x <= 3.2e-23)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2e-32)
		tmp = x * z;
	elseif (x <= 2.7e-128)
		tmp = y;
	elseif (x <= 1.55e-104)
		tmp = x * z;
	elseif (x <= 3.2e-23)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2e-32], N[(x * z), $MachinePrecision], If[LessEqual[x, 2.7e-128], y, If[LessEqual[x, 1.55e-104], N[(x * z), $MachinePrecision], If[LessEqual[x, 3.2e-23], y, N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.00000000000000011e-32 or 2.70000000000000006e-128 < x < 1.54999999999999988e-104 or 3.19999999999999976e-23 < x

   1. Initial program 98.6%

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

   2. Taylor expanded in y around 0 59.5%

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

   if -2.00000000000000011e-32 < x < 2.70000000000000006e-128 or 1.54999999999999988e-104 < x < 3.19999999999999976e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-32}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-128}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-104}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-23}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 6: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (y * (1.0 - x)) + (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 * (1.0d0 - x)) + (x * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

2. Final simplification 99.2%

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

Alternative 7: 35.7% 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 99.2%

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

2. Taylor expanded in x around 0 33.9%

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

3. Final simplification 33.9%

   \[\leadsto y \]

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 2023171 
(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)))