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

Percentage Accurate: 98.0% → 100.0%

Time: 3.7s

Alternatives: 7

Speedup: 1.3×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 98.0% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. sub-neg 98.0%

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

   2. +-commutative 98.0%

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

   3. distribute-lft1-in 98.0%

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

   4. associate-+r+ 98.0%

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

   5. +-commutative 98.0%

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

   6. *-commutative 98.0%

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

   7. neg-mul-1 98.0%

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

   8. associate-*r* 98.0%

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

   9. *-commutative 98.0%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+146}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -27:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 60000000000 \lor \neg \left(x \leq 5.8 \cdot 10^{+178}\right) \land x \leq 3.35 \cdot 10^{+271}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= x -3.1e+146)
     (* x y)
     (if (<= x -5.8e+87)
       t_0
       (if (<= x -27.0)
         (* x y)
         (if (<= x 3.7e-60)
           z
           (if (or (<= x 60000000000.0)
                   (and (not (<= x 5.8e+178)) (<= x 3.35e+271)))
             (* x y)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -3.1e+146) {
		tmp = x * y;
	} else if (x <= -5.8e+87) {
		tmp = t_0;
	} else if (x <= -27.0) {
		tmp = x * y;
	} else if (x <= 3.7e-60) {
		tmp = z;
	} else if ((x <= 60000000000.0) || (!(x <= 5.8e+178) && (x <= 3.35e+271))) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (x <= (-3.1d+146)) then
        tmp = x * y
    else if (x <= (-5.8d+87)) then
        tmp = t_0
    else if (x <= (-27.0d0)) then
        tmp = x * y
    else if (x <= 3.7d-60) then
        tmp = z
    else if ((x <= 60000000000.0d0) .or. (.not. (x <= 5.8d+178)) .and. (x <= 3.35d+271)) then
        tmp = x * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -3.1e+146) {
		tmp = x * y;
	} else if (x <= -5.8e+87) {
		tmp = t_0;
	} else if (x <= -27.0) {
		tmp = x * y;
	} else if (x <= 3.7e-60) {
		tmp = z;
	} else if ((x <= 60000000000.0) || (!(x <= 5.8e+178) && (x <= 3.35e+271))) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if x <= -3.1e+146:
		tmp = x * y
	elif x <= -5.8e+87:
		tmp = t_0
	elif x <= -27.0:
		tmp = x * y
	elif x <= 3.7e-60:
		tmp = z
	elif (x <= 60000000000.0) or (not (x <= 5.8e+178) and (x <= 3.35e+271)):
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (x <= -3.1e+146)
		tmp = Float64(x * y);
	elseif (x <= -5.8e+87)
		tmp = t_0;
	elseif (x <= -27.0)
		tmp = Float64(x * y);
	elseif (x <= 3.7e-60)
		tmp = z;
	elseif ((x <= 60000000000.0) || (!(x <= 5.8e+178) && (x <= 3.35e+271)))
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (x <= -3.1e+146)
		tmp = x * y;
	elseif (x <= -5.8e+87)
		tmp = t_0;
	elseif (x <= -27.0)
		tmp = x * y;
	elseif (x <= 3.7e-60)
		tmp = z;
	elseif ((x <= 60000000000.0) || (~((x <= 5.8e+178)) && (x <= 3.35e+271)))
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[x, -3.1e+146], N[(x * y), $MachinePrecision], If[LessEqual[x, -5.8e+87], t$95$0, If[LessEqual[x, -27.0], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.7e-60], z, If[Or[LessEqual[x, 60000000000.0], And[N[Not[LessEqual[x, 5.8e+178]], $MachinePrecision], LessEqual[x, 3.35e+271]]], N[(x * y), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.1000000000000002e146 or -5.7999999999999996e87 < x < -27 or 3.70000000000000025e-60 < x < 6e10 or 5.8000000000000001e178 < x < 3.35e271

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 66.6%

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

   if -3.1000000000000002e146 < x < -5.7999999999999996e87 or 6e10 < x < 5.8000000000000001e178 or 3.35e271 < x

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0 67.9%

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

   3. Taylor expanded in x around inf 67.3%

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

      1. mul-1-neg 67.3%

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

      2. distribute-rgt-neg-out 67.3%

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

   5. Simplified 67.3%

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

   if -27 < x < 3.70000000000000025e-60

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.3%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+146}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -27:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 60000000000 \lor \neg \left(x \leq 5.8 \cdot 10^{+178}\right) \land x \leq 3.35 \cdot 10^{+271}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1100000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+102} \lor \neg \left(y \leq 1.25 \cdot 10^{+205}\right) \land y \leq 1.16 \cdot 10^{+227}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1100000.0)
   (* x y)
   (if (or (<= y 3.2e+102) (and (not (<= y 1.25e+205)) (<= y 1.16e+227)))
     (* z (- 1.0 x))
     (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1100000.0) {
		tmp = x * y;
	} else if ((y <= 3.2e+102) || (!(y <= 1.25e+205) && (y <= 1.16e+227))) {
		tmp = z * (1.0 - x);
	} 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 (y <= (-1100000.0d0)) then
        tmp = x * y
    else if ((y <= 3.2d+102) .or. (.not. (y <= 1.25d+205)) .and. (y <= 1.16d+227)) then
        tmp = z * (1.0d0 - x)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1100000.0) {
		tmp = x * y;
	} else if ((y <= 3.2e+102) || (!(y <= 1.25e+205) && (y <= 1.16e+227))) {
		tmp = z * (1.0 - x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1100000.0:
		tmp = x * y
	elif (y <= 3.2e+102) or (not (y <= 1.25e+205) and (y <= 1.16e+227)):
		tmp = z * (1.0 - x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1100000.0)
		tmp = Float64(x * y);
	elseif ((y <= 3.2e+102) || (!(y <= 1.25e+205) && (y <= 1.16e+227)))
		tmp = Float64(z * Float64(1.0 - x));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1100000.0)
		tmp = x * y;
	elseif ((y <= 3.2e+102) || (~((y <= 1.25e+205)) && (y <= 1.16e+227)))
		tmp = z * (1.0 - x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1100000.0], N[(x * y), $MachinePrecision], If[Or[LessEqual[y, 3.2e+102], And[N[Not[LessEqual[y, 1.25e+205]], $MachinePrecision], LessEqual[y, 1.16e+227]]], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e6 or 3.1999999999999999e102 < y < 1.25e205 or 1.1599999999999999e227 < y

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf 71.8%

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

   if -1.1e6 < y < 3.1999999999999999e102 or 1.25e205 < y < 1.1599999999999999e227

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1100000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+102} \lor \neg \left(y \leq 1.25 \cdot 10^{+205}\right) \land y \leq 1.16 \cdot 10^{+227}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 83.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -28 \lor \neg \left(x \leq 6.2 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -28.0) (not (<= x 6.2e-65))) (* x (- y z)) (* z (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -28.0) || !(x <= 6.2e-65)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (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 <= (-28.0d0)) .or. (.not. (x <= 6.2d-65))) then
        tmp = x * (y - z)
    else
        tmp = z * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -28.0) || !(x <= 6.2e-65)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -28.0) or not (x <= 6.2e-65):
		tmp = x * (y - z)
	else:
		tmp = z * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -28.0) || !(x <= 6.2e-65))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -28.0) || ~((x <= 6.2e-65)))
		tmp = x * (y - z);
	else
		tmp = z * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -28.0], N[Not[LessEqual[x, 6.2e-65]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -28 or 6.20000000000000032e-65 < x

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 96.1%

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

      1. neg-mul-1 96.1%

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

      2. +-commutative 96.1%

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

      3. unsub-neg 96.1%

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

   4. Simplified 96.1%

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

   if -28 < x < 6.20000000000000032e-65

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.4%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -28 \lor \neg \left(x \leq 6.2 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 60.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -27:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-60}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -27.0) (* x y) (if (<= x 2.5e-60) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -27.0) {
		tmp = x * y;
	} else if (x <= 2.5e-60) {
		tmp = 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 <= (-27.0d0)) then
        tmp = x * y
    else if (x <= 2.5d-60) then
        tmp = 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 <= -27.0) {
		tmp = x * y;
	} else if (x <= 2.5e-60) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -27.0:
		tmp = x * y
	elif x <= 2.5e-60:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -27.0)
		tmp = Float64(x * y);
	elseif (x <= 2.5e-60)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -27.0)
		tmp = x * y;
	elseif (x <= 2.5e-60)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -27.0], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.5e-60], z, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -27 or 2.5000000000000001e-60 < x

   1. Initial program 96.1%

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

   2. Taylor expanded in y around inf 54.1%

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

   if -27 < x < 2.5000000000000001e-60

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.3%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -27:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-60}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 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 98.0%

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

2. Taylor expanded in x around 0 100.0%

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

3. Taylor expanded in z around 0 98.0%

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

   1. *-commutative 98.0%

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

   2. neg-mul-1 98.0%

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

   3. distribute-lft-in 98.0%

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

   4. *-rgt-identity 98.0%

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

   5. associate-+l+ 98.0%

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

   6. distribute-rgt-neg-out 98.0%

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

   7. mul-1-neg 98.0%

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

   8. associate-*r* 98.0%

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

   9. distribute-rgt-in 100.0%

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

   10. +-commutative 100.0%

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

   11. mul-1-neg 100.0%

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

   12. unsub-neg 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 7: 36.4% 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 98.0%

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

2. Taylor expanded in x around 0 38.9%

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

3. Final simplification 38.9%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))