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

Percentage Accurate: 97.6% → 98.7%

Time: 7.7s

Alternatives: 8

Speedup: 1.3×

• 20.9% 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: 97.6% 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: 98.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return fma(x, z, ((1.0 - x) * y));
}

Julia

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

Wolfram

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

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 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. sub-neg 99.6%

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

   3. distribute-lft-in 99.6%

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

   4. associate-+l+ 99.6%

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

   5. *-rgt-identity 99.6%

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

   6. +-commutative 99.6%

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

   7. distribute-rgt-neg-out 99.6%

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

   8. distribute-lft-neg-out 99.6%

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

   9. *-commutative 99.6%

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

   10. distribute-lft-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 3: 60.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-89}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-31}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+14} \lor \neg \left(x \leq 10^{+36}\right) \land \left(x \leq 3.8 \cdot 10^{+143} \lor \neg \left(x \leq 3.9 \cdot 10^{+261}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.32e-89)
   (* x z)
   (if (<= x 1.42e-31)
     y
     (if (or (<= x 1.65e+14)
             (and (not (<= x 1e+36))
                  (or (<= x 3.8e+143) (not (<= x 3.9e+261)))))
       (* x z)
       (* x (- y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.32e-89) {
		tmp = x * z;
	} else if (x <= 1.42e-31) {
		tmp = y;
	} else if ((x <= 1.65e+14) || (!(x <= 1e+36) && ((x <= 3.8e+143) || !(x <= 3.9e+261)))) {
		tmp = x * z;
	} else {
		tmp = x * -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 <= (-1.32d-89)) then
        tmp = x * z
    else if (x <= 1.42d-31) then
        tmp = y
    else if ((x <= 1.65d+14) .or. (.not. (x <= 1d+36)) .and. (x <= 3.8d+143) .or. (.not. (x <= 3.9d+261))) then
        tmp = x * z
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.32e-89) {
		tmp = x * z;
	} else if (x <= 1.42e-31) {
		tmp = y;
	} else if ((x <= 1.65e+14) || (!(x <= 1e+36) && ((x <= 3.8e+143) || !(x <= 3.9e+261)))) {
		tmp = x * z;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.32e-89:
		tmp = x * z
	elif x <= 1.42e-31:
		tmp = y
	elif (x <= 1.65e+14) or (not (x <= 1e+36) and ((x <= 3.8e+143) or not (x <= 3.9e+261))):
		tmp = x * z
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.32e-89)
		tmp = Float64(x * z);
	elseif (x <= 1.42e-31)
		tmp = y;
	elseif ((x <= 1.65e+14) || (!(x <= 1e+36) && ((x <= 3.8e+143) || !(x <= 3.9e+261))))
		tmp = Float64(x * z);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.32e-89)
		tmp = x * z;
	elseif (x <= 1.42e-31)
		tmp = y;
	elseif ((x <= 1.65e+14) || (~((x <= 1e+36)) && ((x <= 3.8e+143) || ~((x <= 3.9e+261)))))
		tmp = x * z;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.32e-89], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.42e-31], y, If[Or[LessEqual[x, 1.65e+14], And[N[Not[LessEqual[x, 1e+36]], $MachinePrecision], Or[LessEqual[x, 3.8e+143], N[Not[LessEqual[x, 3.9e+261]], $MachinePrecision]]]], N[(x * z), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.32e-89 or 1.4200000000000001e-31 < x < 1.65e14 or 1.00000000000000004e36 < x < 3.8e143 or 3.89999999999999994e261 < x

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 60.8%

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

   if -1.32e-89 < x < 1.4200000000000001e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.2%

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

   if 1.65e14 < x < 1.00000000000000004e36 or 3.8e143 < x < 3.89999999999999994e261

   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. sub-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 73.3%

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

      1. mul-1-neg 73.3%

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

      2. distribute-rgt-neg-out 73.3%

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

   7. Simplified 73.3%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-89}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-31}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+14} \lor \neg \left(x \leq 10^{+36}\right) \land \left(x \leq 3.8 \cdot 10^{+143} \lor \neg \left(x \leq 3.9 \cdot 10^{+261}\right)\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 4: 83.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-92} \lor \neg \left(x \leq 6.5 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.8e-92) (not (<= x 6.5e-31))) (* x (- z y)) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.8e-92) || !(x <= 6.5e-31)) {
		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 <= (-7.8d-92)) .or. (.not. (x <= 6.5d-31))) 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 <= -7.8e-92) || !(x <= 6.5e-31)) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.8e-92) or not (x <= 6.5e-31):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.8e-92) || !(x <= 6.5e-31))
		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 <= -7.8e-92) || ~((x <= 6.5e-31)))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.8e-92], N[Not[LessEqual[x, 6.5e-31]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -7.7999999999999993e-92 or 6.49999999999999967e-31 < x

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. sub-neg 93.6%

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

   4. Simplified 93.6%

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

   if -7.7999999999999993e-92 < x < 6.49999999999999967e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.2%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-92} \lor \neg \left(x \leq 6.5 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -19 \lor \neg \left(x \leq 0.0072\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -19.0) (not (<= x 0.0072))) (* x (- z y)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -19.0) || !(x <= 0.0072)) {
		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 <= (-19.0d0)) .or. (.not. (x <= 0.0072d0))) 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 <= -19.0) || !(x <= 0.0072)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -19.0) or not (x <= 0.0072):
		tmp = x * (z - y)
	else:
		tmp = y + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -19.0) || !(x <= 0.0072))
		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 <= -19.0) || ~((x <= 0.0072)))
		tmp = x * (z - y);
	else
		tmp = y + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -19.0], N[Not[LessEqual[x, 0.0072]], $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 < -19 or 0.0071999999999999998 < x

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 98.4%

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

      1. mul-1-neg 98.4%

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

      2. sub-neg 98.4%

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

   4. Simplified 98.4%

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

   if -19 < x < 0.0071999999999999998

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. associate-+l+ 100.0%

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

      5. *-rgt-identity 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. distribute-lft-neg-out 100.0%

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

      9. *-commutative 100.0%

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

      10. distribute-lft-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. Step-by-step derivation

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -19 \lor \neg \left(x \leq 0.0072\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]

Alternative 6: 60.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-90} \lor \neg \left(x \leq 1.4 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e-90) (not (<= x 1.4e-34))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-90) || !(x <= 1.4e-34)) {
		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 <= (-3.8d-90)) .or. (.not. (x <= 1.4d-34))) 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 <= -3.8e-90) || !(x <= 1.4e-34)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e-90) or not (x <= 1.4e-34):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e-90) || !(x <= 1.4e-34))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.8e-90) || ~((x <= 1.4e-34)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e-90], N[Not[LessEqual[x, 1.4e-34]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -3.8e-90 or 1.39999999999999998e-34 < x

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 54.8%

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

   if -3.8e-90 < x < 1.39999999999999998e-34

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-90} \lor \neg \left(x \leq 1.4 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. sub-neg 99.6%

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

   3. distribute-lft-in 99.6%

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

   4. associate-+l+ 99.6%

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

   5. *-rgt-identity 99.6%

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

   6. +-commutative 99.6%

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

   7. distribute-rgt-neg-out 99.6%

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

   8. distribute-lft-neg-out 99.6%

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

   9. *-commutative 99.6%

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

   10. distribute-lft-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. Step-by-step derivation

   1. fma-udef 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 8: 36.2% 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 36.4%

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

3. Final simplification 36.4%

   \[\leadsto y \]

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 2023301 
(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)))