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

Percentage Accurate: 97.9% → 100.0%

Time: 6.4s

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: 97.9% 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

\[\begin{array}{l} \\ \mathsf{fma}\left(z - y, x, y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- z y) x y))

C

double code(double x, double y, double z) {
	return fma((z - y), x, y);
}

Julia

function code(x, y, z)
	return fma(Float64(z - y), x, y)
end

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. *-commutative N/A

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

   2. cancel-sign-sub N/A

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

   3. distribute-lft-neg-out N/A

      \[\leadsto \left(1 - x\right) \cdot y - \left(\mathsf{neg}\left(z \cdot x\right)\right) \]

   4. distribute-rgt-neg-in N/A

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

   5. cancel-sign-sub-inv N/A

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

   6. *-commutative N/A

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

   7. sub-neg N/A

      \[\leadsto y \cdot \left(1 + \left(\mathsf{neg}\left(x\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   8. distribute-lft-in N/A

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

   9. *-rgt-identity N/A

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

   10. associate-+r+ N/A

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

   11. distribute-rgt-in N/A

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

   12. sub-neg N/A

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

   13. distribute-lft-neg-in N/A

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

   14. +-commutative N/A

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

   15. *-commutative N/A

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

   16. distribute-lft-neg-in N/A

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

   17. fma-define N/A

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

   18. fma-lowering-fma.f64 N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y - z\right)\right)\right), \color{blue}{x}, y\right) \]

   19. sub-neg N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x, y\right) \]

   20. +-commutative N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right), x, y\right) \]

   21. distribute-neg-in N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right), x, y\right) \]

   22. unsub-neg N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - y\right), x, y\right) \]

   23. remove-double-neg N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(z - y\right), x, y\right) \]

   24. --lowering--.f64 100.0%

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(z, y\right), x, y\right) \]

4. Applied egg-rr 100.0%

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

Alternative 2: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - y\right) \cdot x\\ \mathbf{if}\;x \leq -430000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;y + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z y) x)))
   (if (<= x -430000000000.0) t_0 (if (<= x 1.6e-6) (+ y (* z x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z - y) * x;
	double tmp;
	if (x <= -430000000000.0) {
		tmp = t_0;
	} else if (x <= 1.6e-6) {
		tmp = y + (z * x);
	} 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 = (z - y) * x
    if (x <= (-430000000000.0d0)) then
        tmp = t_0
    else if (x <= 1.6d-6) then
        tmp = y + (z * x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z - y) * x;
	double tmp;
	if (x <= -430000000000.0) {
		tmp = t_0;
	} else if (x <= 1.6e-6) {
		tmp = y + (z * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z - y) * x
	tmp = 0
	if x <= -430000000000.0:
		tmp = t_0
	elif x <= 1.6e-6:
		tmp = y + (z * x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z - y) * x)
	tmp = 0.0
	if (x <= -430000000000.0)
		tmp = t_0;
	elseif (x <= 1.6e-6)
		tmp = Float64(y + Float64(z * x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z - y) * x;
	tmp = 0.0;
	if (x <= -430000000000.0)
		tmp = t_0;
	elseif (x <= 1.6e-6)
		tmp = y + (z * x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -430000000000.0], t$95$0, If[LessEqual[x, 1.6e-6], N[(y + N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3e11 or 1.5999999999999999e-6 < x

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. distribute-lft-out-- N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y - \color{blue}{-1 \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y + z\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{-1 \cdot y}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z - \color{blue}{y}\right)\right) \]

      14. --lowering--.f64 99.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 99.8%

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

   if -4.3e11 < x < 1.5999999999999999e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(x, z\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 98.3%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -430000000000:\\ \;\;\;\;\left(z - y\right) \cdot x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;y + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - y\right) \cdot x\\ \mathbf{if}\;x \leq -1.8:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 10^{-18}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z y) x)))
   (if (<= x -1.8) t_0 (if (<= x 1e-18) (* y (- 1.0 x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z - y) * x;
	double tmp;
	if (x <= -1.8) {
		tmp = t_0;
	} else if (x <= 1e-18) {
		tmp = y * (1.0 - x);
	} 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 = (z - y) * x
    if (x <= (-1.8d0)) then
        tmp = t_0
    else if (x <= 1d-18) then
        tmp = y * (1.0d0 - x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z - y) * x;
	double tmp;
	if (x <= -1.8) {
		tmp = t_0;
	} else if (x <= 1e-18) {
		tmp = y * (1.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z - y) * x
	tmp = 0
	if x <= -1.8:
		tmp = t_0
	elif x <= 1e-18:
		tmp = y * (1.0 - x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z - y) * x)
	tmp = 0.0
	if (x <= -1.8)
		tmp = t_0;
	elseif (x <= 1e-18)
		tmp = Float64(y * Float64(1.0 - x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z - y) * x;
	tmp = 0.0;
	if (x <= -1.8)
		tmp = t_0;
	elseif (x <= 1e-18)
		tmp = y * (1.0 - x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.8], t$95$0, If[LessEqual[x, 1e-18], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000004 or 1.0000000000000001e-18 < x

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. distribute-lft-out-- N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y - \color{blue}{-1 \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y + z\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{-1 \cdot y}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z - \color{blue}{y}\right)\right) \]

      14. --lowering--.f64 98.4%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 98.4%

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

   if -1.80000000000000004 < x < 1.0000000000000001e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(1 - x\right)}\right) \]

      2. --lowering--.f64 75.3%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{x}\right)\right) \]

   5. Simplified 75.3%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8:\\ \;\;\;\;\left(z - y\right) \cdot x\\ \mathbf{elif}\;x \leq 10^{-18}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - y\right) \cdot x\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-22}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-18}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z y) x)))
   (if (<= x -5.5e-22) t_0 (if (<= x 7.6e-18) y t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z - y) * x;
	double tmp;
	if (x <= -5.5e-22) {
		tmp = t_0;
	} else if (x <= 7.6e-18) {
		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 = (z - y) * x
    if (x <= (-5.5d-22)) then
        tmp = t_0
    else if (x <= 7.6d-18) 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 = (z - y) * x;
	double tmp;
	if (x <= -5.5e-22) {
		tmp = t_0;
	} else if (x <= 7.6e-18) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z - y) * x
	tmp = 0
	if x <= -5.5e-22:
		tmp = t_0
	elif x <= 7.6e-18:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z - y) * x)
	tmp = 0.0
	if (x <= -5.5e-22)
		tmp = t_0;
	elseif (x <= 7.6e-18)
		tmp = y;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z - y) * x;
	tmp = 0.0;
	if (x <= -5.5e-22)
		tmp = t_0;
	elseif (x <= 7.6e-18)
		tmp = y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -5.5e-22], t$95$0, If[LessEqual[x, 7.6e-18], y, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000001e-22 or 7.5999999999999996e-18 < x

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. distribute-lft-out-- N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y - \color{blue}{-1 \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot y + z\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{-1 \cdot y}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z - \color{blue}{y}\right)\right) \]

      14. --lowering--.f64 96.6%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 96.6%

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

   if -5.5000000000000001e-22 < x < 7.5999999999999996e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Simplified 75.9%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-22}:\\ \;\;\;\;\left(z - y\right) \cdot x\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-18}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-22}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-20}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5e-22) (* z x) (if (<= x 6.8e-20) y (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e-22) {
		tmp = z * x;
	} else if (x <= 6.8e-20) {
		tmp = y;
	} else {
		tmp = z * 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 <= (-5.5d-22)) then
        tmp = z * x
    else if (x <= 6.8d-20) then
        tmp = y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e-22) {
		tmp = z * x;
	} else if (x <= 6.8e-20) {
		tmp = y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5e-22:
		tmp = z * x
	elif x <= 6.8e-20:
		tmp = y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5e-22)
		tmp = Float64(z * x);
	elseif (x <= 6.8e-20)
		tmp = y;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5e-22)
		tmp = z * x;
	elseif (x <= 6.8e-20)
		tmp = y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5e-22], N[(z * x), $MachinePrecision], If[LessEqual[x, 6.8e-20], y, N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000001e-22 or 6.7999999999999994e-20 < x

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 49.5%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{z}\right) \]

   5. Simplified 49.5%

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

   if -5.5000000000000001e-22 < x < 6.7999999999999994e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Simplified 75.9%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-22}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-20}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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 + ((z - y) * x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. *-commutative N/A

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

   2. distribute-rgt-out-- N/A

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

   3. *-lft-identity N/A

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

   4. associate-+l- N/A

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

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(y, \color{blue}{\left(x \cdot y - x \cdot z\right)}\right) \]

   6. distribute-lft-out-- N/A

      \[\leadsto \mathsf{\_.f64}\left(y, \left(x \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y - z\right)}\right)\right) \]

   8. --lowering--.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 7: 36.6% 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 98.0%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{y} \]
4. Step-by-step derivation

5. Simplified 36.9%

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

Developer Target 1: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024164 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (! :herbie-platform default (- y (* x (- y z))))

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