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

Percentage Accurate: 97.9% → 100.0%

Time: 6.8s

Alternatives: 6

Speedup: 1.3×

• 20.7% 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: 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

\[\begin{array}{l} \\ \mathsf{fma}\left(y - z, 0 - x, y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y z) (- 0.0 x) y))

C

double code(double x, double y, double z) {
	return fma((y - z), (0.0 - x), y);
}

Julia

function code(x, y, z)
	return fma(Float64(y - z), Float64(0.0 - x), y)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - z), $MachinePrecision] * N[(0.0 - x), $MachinePrecision] + y), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

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

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

   5. fma-define N/A

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

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

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

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

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

   8. neg-sub0 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(0 - \color{blue}{x}\right), y\right) \]

   9. --lowering--.f64 100.0%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(0, \color{blue}{x}\right), y\right) \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, 0 - x, y\right)} \]
7. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 100.0%

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

8. Applied egg-rr 100.0%

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

9. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y - z, 0 - x, y\right) \]
10. Add Preprocessing

Alternative 2: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-9}:\\ \;\;\;\;y + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -1.8e+33) t_0 (if (<= x 1.8e-9) (+ y (* z x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -1.8e+33) {
		tmp = t_0;
	} else if (x <= 1.8e-9) {
		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 = x * (z - y)
    if (x <= (-1.8d+33)) then
        tmp = t_0
    else if (x <= 1.8d-9) 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 = x * (z - y);
	double tmp;
	if (x <= -1.8e+33) {
		tmp = t_0;
	} else if (x <= 1.8e-9) {
		tmp = y + (z * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -1.8e+33:
		tmp = t_0
	elif x <= 1.8e-9:
		tmp = y + (z * x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -1.8e+33)
		tmp = t_0;
	elseif (x <= 1.8e-9)
		tmp = Float64(y + Float64(z * x));
	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 <= -1.8e+33)
		tmp = t_0;
	elseif (x <= 1.8e-9)
		tmp = y + (z * x);
	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, -1.8e+33], t$95$0, If[LessEqual[x, 1.8e-9], N[(y + N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8000000000000001e33 or 1.8e-9 < x

   1. Initial program 98.1%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 99.5%

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

   5. Simplified 99.5%

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

   if -1.8000000000000001e33 < x < 1.8e-9

   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 99.4%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-9}:\\ \;\;\;\;y + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-115}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-20}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -1.2e-115) t_0 (if (<= x 4.4e-20) y t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -1.2e-115) {
		tmp = t_0;
	} else if (x <= 4.4e-20) {
		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 <= (-1.2d-115)) then
        tmp = t_0
    else if (x <= 4.4d-20) 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 <= -1.2e-115) {
		tmp = t_0;
	} else if (x <= 4.4e-20) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -1.2e-115:
		tmp = t_0
	elif x <= 4.4e-20:
		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 <= -1.2e-115)
		tmp = t_0;
	elseif (x <= 4.4e-20)
		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 <= -1.2e-115)
		tmp = t_0;
	elseif (x <= 4.4e-20)
		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, -1.2e-115], t$95$0, If[LessEqual[x, 4.4e-20], y, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000011e-115 or 4.39999999999999982e-20 < x

   1. Initial program 98.5%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   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 93.5%

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

   5. Simplified 93.5%

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

   if -1.20000000000000011e-115 < x < 4.39999999999999982e-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 78.1%

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

Alternative 4: 61.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-114}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{-21}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.1e-114) (* z x) (if (<= x 1.66e-21) y (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.1e-114) {
		tmp = z * x;
	} else if (x <= 1.66e-21) {
		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 <= (-3.1d-114)) then
        tmp = z * x
    else if (x <= 1.66d-21) 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 <= -3.1e-114) {
		tmp = z * x;
	} else if (x <= 1.66e-21) {
		tmp = y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.1e-114:
		tmp = z * x
	elif x <= 1.66e-21:
		tmp = y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.1e-114)
		tmp = Float64(z * x);
	elseif (x <= 1.66e-21)
		tmp = y;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.1e-114)
		tmp = z * x;
	elseif (x <= 1.66e-21)
		tmp = y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.1e-114], N[(z * x), $MachinePrecision], If[LessEqual[x, 1.66e-21], y, N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e-114 or 1.65999999999999993e-21 < x

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 63.0%

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

   5. Simplified 63.0%

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

   if -3.1e-114 < x < 1.65999999999999993e-21

   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 78.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-114}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{-21}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 99.2%

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

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

Alternative 6: 36.5% 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. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Simplified 38.9%

   \[\leadsto \color{blue}{y} \]
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 2024163 
(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)))