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

Percentage Accurate: 98.0% → 100.0%

Time: 5.0s

Alternatives: 7

Speedup: 1.3×

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

Specification

Math

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

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 99.2%

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

   1. sub-neg 99.2%

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

   2. +-commutative 99.2%

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

   3. distribute-lft1-in 99.2%

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

   4. associate-+r+ 99.2%

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

   5. +-commutative 99.2%

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

   6. *-commutative 99.2%

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

   7. neg-mul-1 99.2%

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

   8. associate-*r* 99.2%

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

   9. *-commutative 99.2%

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

   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: 56.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4500000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-144}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-167}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 60000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+248}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= x -7e+77)
     (* x y)
     (if (<= x -4500000000000.0)
       t_0
       (if (<= x -5.6e-144)
         (* x y)
         (if (<= x 1.3e-167)
           z
           (if (<= x 60000000000.0)
             (* x y)
             (if (<= x 7.6e+248) t_0 (* x y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (x <= -7e+77) {
		tmp = x * y;
	} else if (x <= -4500000000000.0) {
		tmp = t_0;
	} else if (x <= -5.6e-144) {
		tmp = x * y;
	} else if (x <= 1.3e-167) {
		tmp = z;
	} else if (x <= 60000000000.0) {
		tmp = x * y;
	} else if (x <= 7.6e+248) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * -z
    if (x <= (-7d+77)) then
        tmp = x * y
    else if (x <= (-4500000000000.0d0)) then
        tmp = t_0
    else if (x <= (-5.6d-144)) then
        tmp = x * y
    else if (x <= 1.3d-167) then
        tmp = z
    else if (x <= 60000000000.0d0) then
        tmp = x * y
    else if (x <= 7.6d+248) then
        tmp = t_0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (x <= -7e+77) {
		tmp = x * y;
	} else if (x <= -4500000000000.0) {
		tmp = t_0;
	} else if (x <= -5.6e-144) {
		tmp = x * y;
	} else if (x <= 1.3e-167) {
		tmp = z;
	} else if (x <= 60000000000.0) {
		tmp = x * y;
	} else if (x <= 7.6e+248) {
		tmp = t_0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if x <= -7e+77:
		tmp = x * y
	elif x <= -4500000000000.0:
		tmp = t_0
	elif x <= -5.6e-144:
		tmp = x * y
	elif x <= 1.3e-167:
		tmp = z
	elif x <= 60000000000.0:
		tmp = x * y
	elif x <= 7.6e+248:
		tmp = t_0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (x <= -7e+77)
		tmp = Float64(x * y);
	elseif (x <= -4500000000000.0)
		tmp = t_0;
	elseif (x <= -5.6e-144)
		tmp = Float64(x * y);
	elseif (x <= 1.3e-167)
		tmp = z;
	elseif (x <= 60000000000.0)
		tmp = Float64(x * y);
	elseif (x <= 7.6e+248)
		tmp = t_0;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (x <= -7e+77)
		tmp = x * y;
	elseif (x <= -4500000000000.0)
		tmp = t_0;
	elseif (x <= -5.6e-144)
		tmp = x * y;
	elseif (x <= 1.3e-167)
		tmp = z;
	elseif (x <= 60000000000.0)
		tmp = x * y;
	elseif (x <= 7.6e+248)
		tmp = t_0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[x, -7e+77], N[(x * y), $MachinePrecision], If[LessEqual[x, -4500000000000.0], t$95$0, If[LessEqual[x, -5.6e-144], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.3e-167], z, If[LessEqual[x, 60000000000.0], N[(x * y), $MachinePrecision], If[LessEqual[x, 7.6e+248], t$95$0, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.0000000000000003e77 or -4.5e12 < x < -5.59999999999999995e-144 or 1.2999999999999999e-167 < x < 6e10 or 7.6000000000000002e248 < x

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 65.2%

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

   if -7.0000000000000003e77 < x < -4.5e12 or 6e10 < x < 7.6000000000000002e248

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-rgt1-in 99.9%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.4%

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

   5. Taylor expanded in y around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. distribute-rgt-neg-out 71.8%

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

   7. Simplified 71.8%

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

   if -5.59999999999999995e-144 < x < 1.2999999999999999e-167

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.7%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4500000000000:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-144}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-167}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 60000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+248}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105 \lor \neg \left(z \leq 2.2 \cdot 10^{+17} \lor \neg \left(z \leq 7 \cdot 10^{+66}\right) \land z \leq 6.5 \cdot 10^{+101}\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -105.0)
         (not (or (<= z 2.2e+17) (and (not (<= z 7e+66)) (<= z 6.5e+101)))))
   (* z (- 1.0 x))
   (* x (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -105.0) || !((z <= 2.2e+17) || (!(z <= 7e+66) && (z <= 6.5e+101)))) {
		tmp = z * (1.0 - x);
	} else {
		tmp = x * (y - 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 ((z <= (-105.0d0)) .or. (.not. (z <= 2.2d+17) .or. (.not. (z <= 7d+66)) .and. (z <= 6.5d+101))) then
        tmp = z * (1.0d0 - x)
    else
        tmp = x * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -105.0) || !((z <= 2.2e+17) || (!(z <= 7e+66) && (z <= 6.5e+101)))) {
		tmp = z * (1.0 - x);
	} else {
		tmp = x * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -105.0) or not ((z <= 2.2e+17) or (not (z <= 7e+66) and (z <= 6.5e+101))):
		tmp = z * (1.0 - x)
	else:
		tmp = x * (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -105.0) || !((z <= 2.2e+17) || (!(z <= 7e+66) && (z <= 6.5e+101))))
		tmp = Float64(z * Float64(1.0 - x));
	else
		tmp = Float64(x * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -105.0) || ~(((z <= 2.2e+17) || (~((z <= 7e+66)) && (z <= 6.5e+101)))))
		tmp = z * (1.0 - x);
	else
		tmp = x * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -105.0], N[Not[Or[LessEqual[z, 2.2e+17], And[N[Not[LessEqual[z, 7e+66]], $MachinePrecision], LessEqual[z, 6.5e+101]]]], $MachinePrecision]], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -105 or 2.2e17 < z < 6.9999999999999994e66 or 6.50000000000000016e101 < z

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 89.3%

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

   if -105 < z < 2.2e17 or 6.9999999999999994e66 < z < 6.50000000000000016e101

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-rgt1-in 100.0%

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

      4. associate-+r+ 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 85.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -105 \lor \neg \left(z \leq 2.2 \cdot 10^{+17} \lor \neg \left(z \leq 7 \cdot 10^{+66}\right) \land z \leq 6.5 \cdot 10^{+101}\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]

Alternative 4: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-64} \lor \neg \left(z \leq 1.25 \cdot 10^{-67}\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e-64) (not (<= z 1.25e-67))) (* z (- 1.0 x)) (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-64) || !(z <= 1.25e-67)) {
		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 ((z <= (-4.5d-64)) .or. (.not. (z <= 1.25d-67))) 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 ((z <= -4.5e-64) || !(z <= 1.25e-67)) {
		tmp = z * (1.0 - x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e-64) or not (z <= 1.25e-67):
		tmp = z * (1.0 - x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e-64) || !(z <= 1.25e-67))
		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 ((z <= -4.5e-64) || ~((z <= 1.25e-67)))
		tmp = z * (1.0 - x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e-64], N[Not[LessEqual[z, 1.25e-67]], $MachinePrecision]], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000001e-64 or 1.25e-67 < z

   1. Initial program 98.6%

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

   2. Taylor expanded in y around 0 82.1%

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

   if -4.5000000000000001e-64 < z < 1.25e-67

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 73.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-64} \lor \neg \left(z \leq 1.25 \cdot 10^{-67}\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 56.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-144}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-167}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.6e-144) (* x y) (if (<= x 1.3e-167) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.6e-144) {
		tmp = x * y;
	} else if (x <= 1.3e-167) {
		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 <= (-5.6d-144)) then
        tmp = x * y
    else if (x <= 1.3d-167) 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 <= -5.6e-144) {
		tmp = x * y;
	} else if (x <= 1.3e-167) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.6e-144:
		tmp = x * y
	elif x <= 1.3e-167:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.6e-144)
		tmp = Float64(x * y);
	elseif (x <= 1.3e-167)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.6e-144)
		tmp = x * y;
	elseif (x <= 1.3e-167)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.6e-144], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.3e-167], z, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.59999999999999995e-144 or 1.2999999999999999e-167 < x

   1. Initial program 99.0%

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

   2. Taylor expanded in y around inf 51.7%

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

   if -5.59999999999999995e-144 < x < 1.2999999999999999e-167

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.7%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-144}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-167}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

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 99.2%

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

   1. sub-neg 99.2%

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

   2. +-commutative 99.2%

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

   3. distribute-rgt1-in 99.2%

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

   4. associate-+r+ 99.2%

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

   5. cancel-sign-sub-inv 99.2%

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

   6. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in x around 0 100.0%

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

5. Final simplification 100.0%

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

Alternative 7: 36.6% 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. Taylor expanded in x around 0 29.7%

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

3. Final simplification 29.7%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023214 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))