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

Percentage Accurate: 98.1% → 100.0%

Time: 4.6s

Alternatives: 8

Speedup: 0.6×

• 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: 98.1% 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 97.6%

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

   1. *-commutative 97.6%

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

   2. distribute-lft-out-- 97.6%

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

   3. *-rgt-identity 97.6%

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

   4. cancel-sign-sub-inv 97.6%

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

   5. associate-+l+ 97.6%

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

   6. +-commutative 97.6%

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

   7. *-commutative 97.6%

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

   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. Add Preprocessing

Alternative 2: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot z + y \cdot \left(1 - x\right)\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* x z) (* y (- 1.0 x)))))
   (if (<= t_0 2e+298) t_0 (* x (- z y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x * z) + (y * (1.0 - x));
	double tmp;
	if (t_0 <= 2e+298) {
		tmp = t_0;
	} else {
		tmp = x * (z - 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) :: t_0
    real(8) :: tmp
    t_0 = (x * z) + (y * (1.0d0 - x))
    if (t_0 <= 2d+298) then
        tmp = t_0
    else
        tmp = x * (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * z) + (y * (1.0 - x));
	double tmp;
	if (t_0 <= 2e+298) {
		tmp = t_0;
	} else {
		tmp = x * (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * z) + (y * (1.0 - x))
	tmp = 0
	if t_0 <= 2e+298:
		tmp = t_0
	else:
		tmp = x * (z - y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * z) + Float64(y * Float64(1.0 - x)))
	tmp = 0.0
	if (t_0 <= 2e+298)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * z) + (y * (1.0 - x));
	tmp = 0.0;
	if (t_0 <= 2e+298)
		tmp = t_0;
	else
		tmp = x * (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * z), $MachinePrecision] + N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e+298], t$95$0, N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (*.f64 x z)) < 1.9999999999999999e298

   1. Initial program 100.0%

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

   if 1.9999999999999999e298 < (+.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (*.f64 x z))

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot z + y \cdot \left(1 - x\right) \leq 2 \cdot 10^{+298}:\\ \;\;\;\;x \cdot z + y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{-9} \lor \neg \left(x \leq 2 \cdot 10^{-88}\right):\\ \;\;\;\;x \cdot \left(z + \left(\frac{y}{x} - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.7e-9) (not (<= x 2e-88)))
   (* x (+ z (- (/ y x) y)))
   (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.7e-9) || !(x <= 2e-88)) {
		tmp = x * (z + ((y / x) - 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 <= (-4.7d-9)) .or. (.not. (x <= 2d-88))) then
        tmp = x * (z + ((y / x) - 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 <= -4.7e-9) || !(x <= 2e-88)) {
		tmp = x * (z + ((y / x) - y));
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.7e-9) or not (x <= 2e-88):
		tmp = x * (z + ((y / x) - y))
	else:
		tmp = y + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.7e-9) || !(x <= 2e-88))
		tmp = Float64(x * Float64(z + Float64(Float64(y / x) - 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 <= -4.7e-9) || ~((x <= 2e-88)))
		tmp = x * (z + ((y / x) - y));
	else
		tmp = y + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.7e-9], N[Not[LessEqual[x, 2e-88]], $MachinePrecision]], N[(x * N[(z + N[(N[(y / x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6999999999999999e-9 or 1.99999999999999987e-88 < x

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   if -4.6999999999999999e-9 < x < 1.99999999999999987e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{-9} \lor \neg \left(x \leq 2 \cdot 10^{-88}\right):\\ \;\;\;\;x \cdot \left(z + \left(\frac{y}{x} - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -75 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -75.0) (not (<= x 1.0))) (* x (- z y)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -75.0) || !(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 <= (-75.0d0)) .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 <= -75.0) || !(x <= 1.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -75.0) 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 <= -75.0) || !(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 <= -75.0) || ~((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, -75.0], 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 < -75 or 1 < x

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

   5. Simplified 98.9%

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

   if -75 < 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 98.3%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -75 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-111} \lor \neg \left(x \leq 3.45 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.2e-111) (not (<= x 3.45e+15)))
   (* x (- z y))
   (* y (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e-111) || !(x <= 3.45e+15)) {
		tmp = x * (z - y);
	} else {
		tmp = y * (1.0 - 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 <= (-1.2d-111)) .or. (.not. (x <= 3.45d+15))) then
        tmp = x * (z - y)
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e-111) || !(x <= 3.45e+15)) {
		tmp = x * (z - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.2e-111) or not (x <= 3.45e+15):
		tmp = x * (z - y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.2e-111) || !(x <= 3.45e+15))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.2e-111) || ~((x <= 3.45e+15)))
		tmp = x * (z - y);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.2e-111], N[Not[LessEqual[x, 3.45e+15]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e-111 or 3.45e15 < 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 94.3%

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

      1. mul-1-neg 94.3%

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

      2. unsub-neg 94.3%

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

   5. Simplified 94.3%

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

   if -1.2e-111 < x < 3.45e15

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.6%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-111} \lor \neg \left(x \leq 3.45 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-117} \lor \neg \left(x \leq 1.7 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e-117) (not (<= x 1.7e-42))) (* x (- z y)) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-117) || !(x <= 1.7e-42)) {
		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 <= (-8.5d-117)) .or. (.not. (x <= 1.7d-42))) 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 <= -8.5e-117) || !(x <= 1.7e-42)) {
		tmp = x * (z - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e-117) or not (x <= 1.7e-42):
		tmp = x * (z - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e-117) || !(x <= 1.7e-42))
		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 <= -8.5e-117) || ~((x <= 1.7e-42)))
		tmp = x * (z - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-117], N[Not[LessEqual[x, 1.7e-42]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999981e-117 or 1.70000000000000011e-42 < 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 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

   5. Simplified 91.7%

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

   if -8.49999999999999981e-117 < x < 1.70000000000000011e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-117} \lor \neg \left(x \leq 1.7 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-111} \lor \neg \left(x \leq 3.1 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.2e-111) (not (<= x 3.1e-63))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e-111) || !(x <= 3.1e-63)) {
		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 <= (-1.2d-111)) .or. (.not. (x <= 3.1d-63))) 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 <= -1.2e-111) || !(x <= 3.1e-63)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.2e-111) or not (x <= 3.1e-63):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.2e-111) || !(x <= 3.1e-63))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.2e-111) || ~((x <= 3.1e-63)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.2e-111], N[Not[LessEqual[x, 3.1e-63]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e-111 or 3.09999999999999984e-63 < 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 49.3%

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

   if -1.2e-111 < x < 3.09999999999999984e-63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.9%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-111} \lor \neg \left(x \leq 3.1 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 97.6%

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

3. Taylor expanded in x around 0 34.4%

   \[\leadsto \color{blue}{y} \]
4. 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 2024098 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (- y (* x (- y z)))

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