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

Percentage Accurate: 97.9% → 100.0%

Time: 3.9s

Alternatives: 7

Speedup: 1.3×

• 21.4% 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: 97.9% 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 98.4%

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

   1. +-commutative 98.4%

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

   2. *-commutative 98.4%

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

   3. distribute-rgt-out-- 98.4%

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

   4. *-lft-identity 98.4%

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

   5. associate-+l- 98.4%

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

   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. Final simplification 100.0%

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

Alternative 2: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -7.1 \cdot 10^{+59}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-51}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+47} \lor \neg \left(x \leq 1.9 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= x -7.1e+59)
     (* x y)
     (if (<= x -6.2e+17)
       t_0
       (if (<= x -2.05e-8)
         (* x y)
         (if (<= x 3e-51)
           z
           (if (or (<= x 9.6e+47) (not (<= x 1.9e+145))) (* x y) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (x <= -7.1e+59) {
		tmp = x * y;
	} else if (x <= -6.2e+17) {
		tmp = t_0;
	} else if (x <= -2.05e-8) {
		tmp = x * y;
	} else if (x <= 3e-51) {
		tmp = z;
	} else if ((x <= 9.6e+47) || !(x <= 1.9e+145)) {
		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 <= (-7.1d+59)) then
        tmp = x * y
    else if (x <= (-6.2d+17)) then
        tmp = t_0
    else if (x <= (-2.05d-8)) then
        tmp = x * y
    else if (x <= 3d-51) then
        tmp = z
    else if ((x <= 9.6d+47) .or. (.not. (x <= 1.9d+145))) 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 <= -7.1e+59) {
		tmp = x * y;
	} else if (x <= -6.2e+17) {
		tmp = t_0;
	} else if (x <= -2.05e-8) {
		tmp = x * y;
	} else if (x <= 3e-51) {
		tmp = z;
	} else if ((x <= 9.6e+47) || !(x <= 1.9e+145)) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if x <= -7.1e+59:
		tmp = x * y
	elif x <= -6.2e+17:
		tmp = t_0
	elif x <= -2.05e-8:
		tmp = x * y
	elif x <= 3e-51:
		tmp = z
	elif (x <= 9.6e+47) or not (x <= 1.9e+145):
		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 <= -7.1e+59)
		tmp = Float64(x * y);
	elseif (x <= -6.2e+17)
		tmp = t_0;
	elseif (x <= -2.05e-8)
		tmp = Float64(x * y);
	elseif (x <= 3e-51)
		tmp = z;
	elseif ((x <= 9.6e+47) || !(x <= 1.9e+145))
		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 <= -7.1e+59)
		tmp = x * y;
	elseif (x <= -6.2e+17)
		tmp = t_0;
	elseif (x <= -2.05e-8)
		tmp = x * y;
	elseif (x <= 3e-51)
		tmp = z;
	elseif ((x <= 9.6e+47) || ~((x <= 1.9e+145)))
		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, -7.1e+59], N[(x * y), $MachinePrecision], If[LessEqual[x, -6.2e+17], t$95$0, If[LessEqual[x, -2.05e-8], N[(x * y), $MachinePrecision], If[LessEqual[x, 3e-51], z, If[Or[LessEqual[x, 9.6e+47], N[Not[LessEqual[x, 1.9e+145]], $MachinePrecision]], N[(x * y), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.10000000000000003e59 or -6.2e17 < x < -2.05000000000000016e-8 or 3.00000000000000002e-51 < x < 9.60000000000000075e47 or 1.90000000000000006e145 < x

   1. Initial program 96.5%

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

   2. Taylor expanded in y around inf 66.1%

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

   if -7.10000000000000003e59 < x < -6.2e17 or 9.60000000000000075e47 < x < 1.90000000000000006e145

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 66.2%

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

      1. associate-*r* 66.2%

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

      2. mul-1-neg 66.2%

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

   7. Simplified 66.2%

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

   if -2.05000000000000016e-8 < x < 3.00000000000000002e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.1 \cdot 10^{+59}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-51}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+47} \lor \neg \left(x \leq 1.9 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-10} \lor \neg \left(x \leq 2.45 \cdot 10^{-51}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.4e-10) (not (<= x 2.45e-51))) (* x (- y z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.4e-10) || !(x <= 2.45e-51)) {
		tmp = x * (y - z);
	} 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 <= (-6.4d-10)) .or. (.not. (x <= 2.45d-51))) then
        tmp = x * (y - z)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.4e-10) || !(x <= 2.45e-51)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.4e-10) or not (x <= 2.45e-51):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.4e-10) || !(x <= 2.45e-51))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.4e-10) || ~((x <= 2.45e-51)))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.4e-10], N[Not[LessEqual[x, 2.45e-51]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -6.39999999999999961e-10 or 2.44999999999999987e-51 < x

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 98.1%

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

      1. mul-1-neg 98.1%

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

      2. sub-neg 98.1%

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

   4. Simplified 98.1%

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

   if -6.39999999999999961e-10 < x < 2.44999999999999987e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.6%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-10} \lor \neg \left(x \leq 2.45 \cdot 10^{-51}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-9} \lor \neg \left(x \leq 8.6 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e-9) (not (<= x 8.6e-52))) (* x (- y z)) (* z (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-9) || !(x <= 8.6e-52)) {
		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 <= (-5.5d-9)) .or. (.not. (x <= 8.6d-52))) 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 <= -5.5e-9) || !(x <= 8.6e-52)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e-9) or not (x <= 8.6e-52):
		tmp = x * (y - z)
	else:
		tmp = z * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e-9) || !(x <= 8.6e-52))
		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 <= -5.5e-9) || ~((x <= 8.6e-52)))
		tmp = x * (y - z);
	else
		tmp = z * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e-9], N[Not[LessEqual[x, 8.6e-52]], $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 < -5.4999999999999996e-9 or 8.6000000000000007e-52 < x

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 98.1%

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

      1. mul-1-neg 98.1%

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

      2. sub-neg 98.1%

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

   4. Simplified 98.1%

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

   if -5.4999999999999996e-9 < x < 8.6000000000000007e-52

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.1%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-9} \lor \neg \left(x \leq 8.6 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -15.5 \lor \neg \left(x \leq 1.9 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -15.5) (not (<= x 1.9e-7))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -15.5) || !(x <= 1.9e-7)) {
		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 <= (-15.5d0)) .or. (.not. (x <= 1.9d-7))) 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 <= -15.5) || !(x <= 1.9e-7)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -15.5) or not (x <= 1.9e-7):
		tmp = x * (y - z)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -15.5) || !(x <= 1.9e-7))
		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 <= -15.5) || ~((x <= 1.9e-7)))
		tmp = x * (y - z);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -15.5], N[Not[LessEqual[x, 1.9e-7]], $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 < -15.5 or 1.90000000000000007e-7 < x

   1. Initial program 97.1%

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

   2. Taylor expanded in x around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. sub-neg 99.4%

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

   4. Simplified 99.4%

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

   if -15.5 < x < 1.90000000000000007e-7

   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. Taylor expanded in z around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. *-commutative 99.5%

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

      3. distribute-rgt-neg-in 99.5%

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

   6. Simplified 99.5%

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

      1. sub-neg 99.5%

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

      2. +-commutative 99.5%

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

      3. distribute-rgt-neg-out 99.5%

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

      4. remove-double-neg 99.5%

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

   8. Applied egg-rr 99.5%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -15.5 \lor \neg \left(x \leq 1.9 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 6: 61.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-10} \lor \neg \left(x \leq 4.1 \cdot 10^{-53}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e-10) (not (<= x 4.1e-53))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-10) || !(x <= 4.1e-53)) {
		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 <= (-8.5d-10)) .or. (.not. (x <= 4.1d-53))) 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 <= -8.5e-10) || !(x <= 4.1e-53)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e-10) or not (x <= 4.1e-53):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e-10) || !(x <= 4.1e-53))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.5e-10) || ~((x <= 4.1e-53)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-10], N[Not[LessEqual[x, 4.1e-53]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -8.4999999999999996e-10 or 4.1000000000000001e-53 < x

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf 59.4%

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

   if -8.4999999999999996e-10 < x < 4.1000000000000001e-53

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-10} \lor \neg \left(x \leq 4.1 \cdot 10^{-53}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 36.2% 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 98.4%

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

2. Taylor expanded in x around 0 31.9%

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

3. Final simplification 31.9%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))