Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3

Percentage Accurate: 97.8% → 100.0%

Time: 5.4s

Alternatives: 6

Speedup: 1.3×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - 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 = (x * y) + ((1.0d0 - x) * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

Python

def code(x, y, z):
	return (x * y) + ((1.0 - x) * z)

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + ((1.0 - x) * z);
end

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - 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 = (x * y) + ((1.0d0 - x) * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

Python

def code(x, y, z):
	return (x * y) + ((1.0 - x) * z)

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + ((1.0 - x) * z);
end

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return z + (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 = z + (x * (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. +-commutative 99.2%

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

   2. *-commutative 99.2%

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

   3. distribute-rgt-out-- 99.2%

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

   4. *-lft-identity 99.2%

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

   5. associate-+l- 99.2%

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

   6. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 60.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-137}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-23}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3800000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.25e-95)
   (* x y)
   (if (<= x 2.05e-137)
     z
     (if (<= x 6.2e-124)
       (* x y)
       (if (<= x 6e-23) z (if (<= x 3800000.0) (* x y) (- (* z x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e-95) {
		tmp = x * y;
	} else if (x <= 2.05e-137) {
		tmp = z;
	} else if (x <= 6.2e-124) {
		tmp = x * y;
	} else if (x <= 6e-23) {
		tmp = z;
	} else if (x <= 3800000.0) {
		tmp = x * 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 <= (-2.25d-95)) then
        tmp = x * y
    else if (x <= 2.05d-137) then
        tmp = z
    else if (x <= 6.2d-124) then
        tmp = x * y
    else if (x <= 6d-23) then
        tmp = z
    else if (x <= 3800000.0d0) then
        tmp = x * 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 <= -2.25e-95) {
		tmp = x * y;
	} else if (x <= 2.05e-137) {
		tmp = z;
	} else if (x <= 6.2e-124) {
		tmp = x * y;
	} else if (x <= 6e-23) {
		tmp = z;
	} else if (x <= 3800000.0) {
		tmp = x * y;
	} else {
		tmp = -(z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.25e-95:
		tmp = x * y
	elif x <= 2.05e-137:
		tmp = z
	elif x <= 6.2e-124:
		tmp = x * y
	elif x <= 6e-23:
		tmp = z
	elif x <= 3800000.0:
		tmp = x * y
	else:
		tmp = -(z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.25e-95)
		tmp = Float64(x * y);
	elseif (x <= 2.05e-137)
		tmp = z;
	elseif (x <= 6.2e-124)
		tmp = Float64(x * y);
	elseif (x <= 6e-23)
		tmp = z;
	elseif (x <= 3800000.0)
		tmp = Float64(x * y);
	else
		tmp = Float64(-Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.25e-95)
		tmp = x * y;
	elseif (x <= 2.05e-137)
		tmp = z;
	elseif (x <= 6.2e-124)
		tmp = x * y;
	elseif (x <= 6e-23)
		tmp = z;
	elseif (x <= 3800000.0)
		tmp = x * y;
	else
		tmp = -(z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.25e-95], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.05e-137], z, If[LessEqual[x, 6.2e-124], N[(x * y), $MachinePrecision], If[LessEqual[x, 6e-23], z, If[LessEqual[x, 3800000.0], N[(x * y), $MachinePrecision], (-N[(z * x), $MachinePrecision])]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e-95 or 2.0499999999999999e-137 < x < 6.1999999999999996e-124 or 6.00000000000000006e-23 < x < 3.8e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 66.9%

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

   if -2.25e-95 < x < 2.0499999999999999e-137 or 6.1999999999999996e-124 < x < 6.00000000000000006e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.7%

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

   if 3.8e6 < x

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 99.1%

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

      1. neg-mul-1 99.1%

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

      2. unsub-neg 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in y around 0 67.2%

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

      1. associate-*r* 67.2%

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

      2. mul-1-neg 67.2%

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

   8. Simplified 67.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-137}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-23}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3800000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{-95}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-16}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y z))))
   (if (<= x -2.25e-95)
     t_0
     (if (<= x 1.85e-137)
       z
       (if (<= x 6.1e-124) (* x y) (if (<= x 4.8e-16) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - z);
	double tmp;
	if (x <= -2.25e-95) {
		tmp = t_0;
	} else if (x <= 1.85e-137) {
		tmp = z;
	} else if (x <= 6.1e-124) {
		tmp = x * y;
	} else if (x <= 4.8e-16) {
		tmp = z;
	} 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 * (y - z)
    if (x <= (-2.25d-95)) then
        tmp = t_0
    else if (x <= 1.85d-137) then
        tmp = z
    else if (x <= 6.1d-124) then
        tmp = x * y
    else if (x <= 4.8d-16) then
        tmp = z
    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 * (y - z);
	double tmp;
	if (x <= -2.25e-95) {
		tmp = t_0;
	} else if (x <= 1.85e-137) {
		tmp = z;
	} else if (x <= 6.1e-124) {
		tmp = x * y;
	} else if (x <= 4.8e-16) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y - z)
	tmp = 0
	if x <= -2.25e-95:
		tmp = t_0
	elif x <= 1.85e-137:
		tmp = z
	elif x <= 6.1e-124:
		tmp = x * y
	elif x <= 4.8e-16:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y - z))
	tmp = 0.0
	if (x <= -2.25e-95)
		tmp = t_0;
	elseif (x <= 1.85e-137)
		tmp = z;
	elseif (x <= 6.1e-124)
		tmp = Float64(x * y);
	elseif (x <= 4.8e-16)
		tmp = z;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y - z);
	tmp = 0.0;
	if (x <= -2.25e-95)
		tmp = t_0;
	elseif (x <= 1.85e-137)
		tmp = z;
	elseif (x <= 6.1e-124)
		tmp = x * y;
	elseif (x <= 4.8e-16)
		tmp = z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.25e-95], t$95$0, If[LessEqual[x, 1.85e-137], z, If[LessEqual[x, 6.1e-124], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.8e-16], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e-95 or 4.8000000000000001e-16 < x

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf 95.4%

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

      1. neg-mul-1 95.4%

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

      2. unsub-neg 95.4%

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

   5. Simplified 95.4%

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

   if -2.25e-95 < x < 1.85e-137 or 6.0999999999999998e-124 < x < 4.8000000000000001e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.7%

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

   if 1.85e-137 < x < 6.0999999999999998e-124

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 82.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-16}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-95} \lor \neg \left(x \leq 7.5 \cdot 10^{-138} \lor \neg \left(x \leq 1.34 \cdot 10^{-123}\right) \land x \leq 6.2 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.25e-95)
         (not
          (or (<= x 7.5e-138) (and (not (<= x 1.34e-123)) (<= x 6.2e-16)))))
   (* x y)
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.25e-95) || !((x <= 7.5e-138) || (!(x <= 1.34e-123) && (x <= 6.2e-16)))) {
		tmp = x * y;
	} else {
		tmp = 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 <= (-2.25d-95)) .or. (.not. (x <= 7.5d-138) .or. (.not. (x <= 1.34d-123)) .and. (x <= 6.2d-16))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.25e-95) || !((x <= 7.5e-138) || (!(x <= 1.34e-123) && (x <= 6.2e-16)))) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.25e-95) or not ((x <= 7.5e-138) or (not (x <= 1.34e-123) and (x <= 6.2e-16))):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.25e-95) || !((x <= 7.5e-138) || (!(x <= 1.34e-123) && (x <= 6.2e-16))))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.25e-95) || ~(((x <= 7.5e-138) || (~((x <= 1.34e-123)) && (x <= 6.2e-16)))))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.25e-95], N[Not[Or[LessEqual[x, 7.5e-138], And[N[Not[LessEqual[x, 1.34e-123]], $MachinePrecision], LessEqual[x, 6.2e-16]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e-95 or 7.4999999999999995e-138 < x < 1.34e-123 or 6.2000000000000002e-16 < x

   1. Initial program 98.7%

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

   3. Taylor expanded in y around inf 53.0%

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

   if -2.25e-95 < x < 7.4999999999999995e-138 or 1.34e-123 < x < 6.2000000000000002e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.7%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-95} \lor \neg \left(x \leq 7.5 \cdot 10^{-138} \lor \neg \left(x \leq 1.34 \cdot 10^{-123}\right) \land x \leq 6.2 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+15} \lor \neg \left(x \leq 3 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.6e+15) (not (<= x 3e-15))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.6e+15) || !(x <= 3e-15)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (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 <= (-5.6d+15)) .or. (.not. (x <= 3d-15))) then
        tmp = x * (y - z)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.6e+15) || !(x <= 3e-15)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.6e+15) or not (x <= 3e-15):
		tmp = x * (y - z)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.6e+15) || !(x <= 3e-15))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.6e+15) || ~((x <= 3e-15)))
		tmp = x * (y - z);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.6e+15], N[Not[LessEqual[x, 3e-15]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.6e15 or 3e-15 < x

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

   5. Simplified 99.4%

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

   if -5.6e15 < x < 3e-15

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. *-lft-identity 100.0%

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

      5. associate-+l- 100.0%

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

      6. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 99.8%

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

      1. associate-*r* 99.8%

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

      2. neg-mul-1 99.8%

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

      3. *-commutative 99.8%

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

   7. Simplified 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-rgt-neg-out 99.8%

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

      4. remove-double-neg 99.8%

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

   9. Applied egg-rr 99.8%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+15} \lor \neg \left(x \leq 3 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = z
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in x around 0 33.7%

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

4. Final simplification 33.7%

   \[\leadsto z \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024026 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))