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

Percentage Accurate: 97.7% → 100.0%

Time: 7.0s

Alternatives: 7

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: 97.7% 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 98.4%

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

   1. *-commutative 98.4%

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

   2. distribute-lft-out-- 98.4%

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

   3. *-rgt-identity 98.4%

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

   4. cancel-sign-sub-inv 98.4%

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

   5. associate-+l+ 98.4%

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

   6. +-commutative 98.4%

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

   7. *-commutative 98.4%

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

   8. distribute-rgt-out 100.0%

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

   9. fma-define 100.0%

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

   10. +-commutative 100.0%

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

   11. 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 61.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+224}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-14}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-38}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-61}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+57} \lor \neg \left(x \leq 3.7 \cdot 10^{+142}\right) \land x \leq 2.1 \cdot 10^{+232}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -9.5e+224)
     t_0
     (if (<= x -5.4e+63)
       (* x z)
       (if (<= x -1.3e+43)
         t_0
         (if (<= x -1.36e-14)
           (* x z)
           (if (<= x -7e-38)
             y
             (if (<= x -3e-61)
               (* x z)
               (if (<= x 1.0)
                 y
                 (if (or (<= x 6.5e+57)
                         (and (not (<= x 3.7e+142)) (<= x 2.1e+232)))
                   t_0
                   (* x z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -9.5e+224) {
		tmp = t_0;
	} else if (x <= -5.4e+63) {
		tmp = x * z;
	} else if (x <= -1.3e+43) {
		tmp = t_0;
	} else if (x <= -1.36e-14) {
		tmp = x * z;
	} else if (x <= -7e-38) {
		tmp = y;
	} else if (x <= -3e-61) {
		tmp = x * z;
	} else if (x <= 1.0) {
		tmp = y;
	} else if ((x <= 6.5e+57) || (!(x <= 3.7e+142) && (x <= 2.1e+232))) {
		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 = x * -y
    if (x <= (-9.5d+224)) then
        tmp = t_0
    else if (x <= (-5.4d+63)) then
        tmp = x * z
    else if (x <= (-1.3d+43)) then
        tmp = t_0
    else if (x <= (-1.36d-14)) then
        tmp = x * z
    else if (x <= (-7d-38)) then
        tmp = y
    else if (x <= (-3d-61)) then
        tmp = x * z
    else if (x <= 1.0d0) then
        tmp = y
    else if ((x <= 6.5d+57) .or. (.not. (x <= 3.7d+142)) .and. (x <= 2.1d+232)) 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 = x * -y;
	double tmp;
	if (x <= -9.5e+224) {
		tmp = t_0;
	} else if (x <= -5.4e+63) {
		tmp = x * z;
	} else if (x <= -1.3e+43) {
		tmp = t_0;
	} else if (x <= -1.36e-14) {
		tmp = x * z;
	} else if (x <= -7e-38) {
		tmp = y;
	} else if (x <= -3e-61) {
		tmp = x * z;
	} else if (x <= 1.0) {
		tmp = y;
	} else if ((x <= 6.5e+57) || (!(x <= 3.7e+142) && (x <= 2.1e+232))) {
		tmp = t_0;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if x <= -9.5e+224:
		tmp = t_0
	elif x <= -5.4e+63:
		tmp = x * z
	elif x <= -1.3e+43:
		tmp = t_0
	elif x <= -1.36e-14:
		tmp = x * z
	elif x <= -7e-38:
		tmp = y
	elif x <= -3e-61:
		tmp = x * z
	elif x <= 1.0:
		tmp = y
	elif (x <= 6.5e+57) or (not (x <= 3.7e+142) and (x <= 2.1e+232)):
		tmp = t_0
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -9.5e+224)
		tmp = t_0;
	elseif (x <= -5.4e+63)
		tmp = Float64(x * z);
	elseif (x <= -1.3e+43)
		tmp = t_0;
	elseif (x <= -1.36e-14)
		tmp = Float64(x * z);
	elseif (x <= -7e-38)
		tmp = y;
	elseif (x <= -3e-61)
		tmp = Float64(x * z);
	elseif (x <= 1.0)
		tmp = y;
	elseif ((x <= 6.5e+57) || (!(x <= 3.7e+142) && (x <= 2.1e+232)))
		tmp = t_0;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -y;
	tmp = 0.0;
	if (x <= -9.5e+224)
		tmp = t_0;
	elseif (x <= -5.4e+63)
		tmp = x * z;
	elseif (x <= -1.3e+43)
		tmp = t_0;
	elseif (x <= -1.36e-14)
		tmp = x * z;
	elseif (x <= -7e-38)
		tmp = y;
	elseif (x <= -3e-61)
		tmp = x * z;
	elseif (x <= 1.0)
		tmp = y;
	elseif ((x <= 6.5e+57) || (~((x <= 3.7e+142)) && (x <= 2.1e+232)))
		tmp = t_0;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -9.5e+224], t$95$0, If[LessEqual[x, -5.4e+63], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.3e+43], t$95$0, If[LessEqual[x, -1.36e-14], N[(x * z), $MachinePrecision], If[LessEqual[x, -7e-38], y, If[LessEqual[x, -3e-61], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.0], y, If[Or[LessEqual[x, 6.5e+57], And[N[Not[LessEqual[x, 3.7e+142]], $MachinePrecision], LessEqual[x, 2.1e+232]]], t$95$0, N[(x * z), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5000000000000002e224 or -5.40000000000000035e63 < x < -1.3000000000000001e43 or 1 < x < 6.4999999999999997e57 or 3.6999999999999997e142 < x < 2.09999999999999991e232

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. sub-neg 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in z around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. distribute-rgt-neg-out 71.8%

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

   8. Simplified 71.8%

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

   if -9.5000000000000002e224 < x < -5.40000000000000035e63 or -1.3000000000000001e43 < x < -1.36e-14 or -7.0000000000000003e-38 < x < -3.00000000000000012e-61 or 6.4999999999999997e57 < x < 3.6999999999999997e142 or 2.09999999999999991e232 < x

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 70.0%

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

   if -1.36e-14 < x < -7.0000000000000003e-38 or -3.00000000000000012e-61 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.4%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-14}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-38}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-61}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+57} \lor \neg \left(x \leq 3.7 \cdot 10^{+142}\right) \land x \leq 2.1 \cdot 10^{+232}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-14} \lor \neg \left(x \leq -9.5 \cdot 10^{-36} \lor \neg \left(x \leq -1 \cdot 10^{-60}\right) \land x \leq 2.7 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e-14)
         (not (or (<= x -9.5e-36) (and (not (<= x -1e-60)) (<= x 2.7e-41)))))
   (* x (- z y))
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-14) || !((x <= -9.5e-36) || (!(x <= -1e-60) && (x <= 2.7e-41)))) {
		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 <= (-6d-14)) .or. (.not. (x <= (-9.5d-36)) .or. (.not. (x <= (-1d-60))) .and. (x <= 2.7d-41))) 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 <= -6e-14) || !((x <= -9.5e-36) || (!(x <= -1e-60) && (x <= 2.7e-41)))) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e-14) or not ((x <= -9.5e-36) or (not (x <= -1e-60) and (x <= 2.7e-41))):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e-14) || !((x <= -9.5e-36) || (!(x <= -1e-60) && (x <= 2.7e-41))))
		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 <= -6e-14) || ~(((x <= -9.5e-36) || (~((x <= -1e-60)) && (x <= 2.7e-41)))))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e-14], N[Not[Or[LessEqual[x, -9.5e-36], And[N[Not[LessEqual[x, -1e-60]], $MachinePrecision], LessEqual[x, 2.7e-41]]]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999997e-14 or -9.5000000000000003e-36 < x < -9.9999999999999997e-61 or 2.7e-41 < x

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 98.1%

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

      1. mul-1-neg 98.1%

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

      2. sub-neg 98.1%

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

   5. Simplified 98.1%

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

   if -5.9999999999999997e-14 < x < -9.5000000000000003e-36 or -9.9999999999999997e-61 < x < 2.7e-41

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-14} \lor \neg \left(x \leq -9.5 \cdot 10^{-36} \lor \neg \left(x \leq -1 \cdot 10^{-60}\right) \land x \leq 2.7 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-17} \lor \neg \left(x \leq -1.9 \cdot 10^{-38} \lor \neg \left(x \leq -3.5 \cdot 10^{-63}\right) \land x \leq 3.1 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.8e-17)
         (not (or (<= x -1.9e-38) (and (not (<= x -3.5e-63)) (<= x 3.1e-41)))))
   (* x z)
   y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e-17) || !((x <= -1.9e-38) || (!(x <= -3.5e-63) && (x <= 3.1e-41)))) {
		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 <= (-4.8d-17)) .or. (.not. (x <= (-1.9d-38)) .or. (.not. (x <= (-3.5d-63))) .and. (x <= 3.1d-41))) 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 <= -4.8e-17) || !((x <= -1.9e-38) || (!(x <= -3.5e-63) && (x <= 3.1e-41)))) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.8e-17) or not ((x <= -1.9e-38) or (not (x <= -3.5e-63) and (x <= 3.1e-41))):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.8e-17) || !((x <= -1.9e-38) || (!(x <= -3.5e-63) && (x <= 3.1e-41))))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.8e-17) || ~(((x <= -1.9e-38) || (~((x <= -3.5e-63)) && (x <= 3.1e-41)))))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.8e-17], N[Not[Or[LessEqual[x, -1.9e-38], And[N[Not[LessEqual[x, -3.5e-63]], $MachinePrecision], LessEqual[x, 3.1e-41]]]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999973e-17 or -1.9e-38 < x < -3.50000000000000003e-63 or 3.10000000000000001e-41 < x

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 54.8%

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

   if -4.79999999999999973e-17 < x < -1.9e-38 or -3.50000000000000003e-63 < x < 3.10000000000000001e-41

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-17} \lor \neg \left(x \leq -1.9 \cdot 10^{-38} \lor \neg \left(x \leq -3.5 \cdot 10^{-63}\right) \land x \leq 3.1 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -70000000000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -70000000000000.0) (not (<= x 1.0)))
   (* x (- z y))
   (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -70000000000000.0) || !(x <= 1.0)) {
		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 <= (-70000000000000.0d0)) .or. (.not. (x <= 1.0d0))) 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 <= -70000000000000.0) || !(x <= 1.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -70000000000000.0) or not (x <= 1.0):
		tmp = x * (z - y)
	else:
		tmp = y + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -70000000000000.0) || !(x <= 1.0))
		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 <= -70000000000000.0) || ~((x <= 1.0)))
		tmp = x * (z - y);
	else
		tmp = y + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -70000000000000.0], N[Not[LessEqual[x, 1.0]], $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 < -7e13 or 1 < x

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. sub-neg 99.1%

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

   5. Simplified 99.1%

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

   if -7e13 < x < 1

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

      4. neg-sub0 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-lft-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. *-lft-identity 100.0%

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

      10. associate-+l- 100.0%

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

      11. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.6%

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

      1. neg-mul-1 99.6%

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

      2. *-commutative 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

   7. Simplified 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. distribute-rgt-neg-out 99.6%

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

      4. remove-double-neg 99.6%

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

   9. Applied egg-rr 99.6%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -70000000000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. remove-double-neg 98.4%

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

   2. distribute-rgt-neg-out 98.4%

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

   3. neg-sub0 98.4%

      \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-y\right)\right)} + x \cdot z \]

   4. neg-sub0 98.4%

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

   5. *-commutative 98.4%

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

   6. distribute-lft-neg-in 98.4%

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

   7. remove-double-neg 98.4%

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

   8. distribute-rgt-out-- 98.4%

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

   9. *-lft-identity 98.4%

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

   10. associate-+l- 98.4%

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

   11. distribute-lft-out-- 100.0%

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

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 7: 36.7% 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 98.4%

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

3. Taylor expanded in x around 0 38.8%

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

4. Final simplification 38.8%

   \[\leadsto y \]
5. Add Preprocessing

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 2024044 
(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)))