Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3

Percentage Accurate: 98.0% → 100.0%

Time: 3.5s

Alternatives: 7

Speedup: 1.3×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. *-commutative 96.4%

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

   2. sub-neg 96.4%

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

   3. distribute-rgt-in 96.5%

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

   4. metadata-eval 96.5%

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

   5. neg-mul-1 96.5%

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

   6. associate-+r+ 96.5%

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

   7. unsub-neg 96.5%

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

   8. +-commutative 96.5%

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

   9. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 61.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+190}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+128}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+96}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.15 \cdot 10^{-38}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+35} \lor \neg \left(x \leq 3.7 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.8e+190)
   (* x z)
   (if (<= x -1.5e+128)
     (* x y)
     (if (<= x -3.2e+96)
       (* x z)
       (if (<= x -3.1e-25)
         (* x y)
         (if (<= x 4.15e-38)
           (- z)
           (if (or (<= x 3e+35) (not (<= x 3.7e+122))) (* x y) (* x z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e+190) {
		tmp = x * z;
	} else if (x <= -1.5e+128) {
		tmp = x * y;
	} else if (x <= -3.2e+96) {
		tmp = x * z;
	} else if (x <= -3.1e-25) {
		tmp = x * y;
	} else if (x <= 4.15e-38) {
		tmp = -z;
	} else if ((x <= 3e+35) || !(x <= 3.7e+122)) {
		tmp = x * y;
	} else {
		tmp = 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 <= (-5.8d+190)) then
        tmp = x * z
    else if (x <= (-1.5d+128)) then
        tmp = x * y
    else if (x <= (-3.2d+96)) then
        tmp = x * z
    else if (x <= (-3.1d-25)) then
        tmp = x * y
    else if (x <= 4.15d-38) then
        tmp = -z
    else if ((x <= 3d+35) .or. (.not. (x <= 3.7d+122))) then
        tmp = x * y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e+190) {
		tmp = x * z;
	} else if (x <= -1.5e+128) {
		tmp = x * y;
	} else if (x <= -3.2e+96) {
		tmp = x * z;
	} else if (x <= -3.1e-25) {
		tmp = x * y;
	} else if (x <= 4.15e-38) {
		tmp = -z;
	} else if ((x <= 3e+35) || !(x <= 3.7e+122)) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.8e+190:
		tmp = x * z
	elif x <= -1.5e+128:
		tmp = x * y
	elif x <= -3.2e+96:
		tmp = x * z
	elif x <= -3.1e-25:
		tmp = x * y
	elif x <= 4.15e-38:
		tmp = -z
	elif (x <= 3e+35) or not (x <= 3.7e+122):
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.8e+190)
		tmp = Float64(x * z);
	elseif (x <= -1.5e+128)
		tmp = Float64(x * y);
	elseif (x <= -3.2e+96)
		tmp = Float64(x * z);
	elseif (x <= -3.1e-25)
		tmp = Float64(x * y);
	elseif (x <= 4.15e-38)
		tmp = Float64(-z);
	elseif ((x <= 3e+35) || !(x <= 3.7e+122))
		tmp = Float64(x * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.8e+190)
		tmp = x * z;
	elseif (x <= -1.5e+128)
		tmp = x * y;
	elseif (x <= -3.2e+96)
		tmp = x * z;
	elseif (x <= -3.1e-25)
		tmp = x * y;
	elseif (x <= 4.15e-38)
		tmp = -z;
	elseif ((x <= 3e+35) || ~((x <= 3.7e+122)))
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.8e+190], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.5e+128], N[(x * y), $MachinePrecision], If[LessEqual[x, -3.2e+96], N[(x * z), $MachinePrecision], If[LessEqual[x, -3.1e-25], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.15e-38], (-z), If[Or[LessEqual[x, 3e+35], N[Not[LessEqual[x, 3.7e+122]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.79999999999999979e190 or -1.4999999999999999e128 < x < -3.20000000000000006e96 or 2.99999999999999991e35 < x < 3.6999999999999997e122

   1. Initial program 94.0%

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

   2. Taylor expanded in y around 0 76.6%

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

   3. Taylor expanded in x around inf 76.6%

      \[\leadsto \color{blue}{x \cdot z} \]
   4. Step-by-step derivation

      1. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   if -5.79999999999999979e190 < x < -1.4999999999999999e128 or -3.20000000000000006e96 < x < -3.09999999999999995e-25 or 4.1499999999999998e-38 < x < 2.99999999999999991e35 or 3.6999999999999997e122 < x

   1. Initial program 93.9%

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

   2. Taylor expanded in y around inf 67.6%

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

   if -3.09999999999999995e-25 < x < 4.1499999999999998e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.9%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. neg-mul-1 75.9%

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

   4. Simplified 75.9%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+190}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+128}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+96}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.15 \cdot 10^{-38}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+35} \lor \neg \left(x \leq 3.7 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-25} \lor \neg \left(x \leq 4.2 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e-25) (not (<= x 4.2e-38))) (* x (+ z y)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-25) || !(x <= 4.2e-38)) {
		tmp = x * (z + 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 <= (-2.1d-25)) .or. (.not. (x <= 4.2d-38))) then
        tmp = x * (z + 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 <= -2.1e-25) || !(x <= 4.2e-38)) {
		tmp = x * (z + y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e-25) or not (x <= 4.2e-38):
		tmp = x * (z + y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e-25) || !(x <= 4.2e-38))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.1e-25) || ~((x <= 4.2e-38)))
		tmp = x * (z + y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e-25], N[Not[LessEqual[x, 4.2e-38]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -2.10000000000000002e-25 or 4.20000000000000026e-38 < x

   1. Initial program 93.9%

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

   2. Taylor expanded in x around inf 93.6%

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

      1. +-commutative 93.6%

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

   4. Simplified 93.6%

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

   if -2.10000000000000002e-25 < x < 4.20000000000000026e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.9%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. neg-mul-1 75.9%

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

   4. Simplified 75.9%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-25} \lor \neg \left(x \leq 4.2 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0004 \lor \neg \left(x \leq 1.5 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0004) (not (<= x 1.5e-38))) (* x (+ z y)) (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0004) || !(x <= 1.5e-38)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (x + -1.0);
	}
	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) :: tmp
    if ((x <= (-0.0004d0)) .or. (.not. (x <= 1.5d-38))) then
        tmp = x * (z + y)
    else
        tmp = z * (x + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0004) || !(x <= 1.5e-38)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0004) or not (x <= 1.5e-38):
		tmp = x * (z + y)
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0004) || !(x <= 1.5e-38))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(z * Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.0004) || ~((x <= 1.5e-38)))
		tmp = x * (z + y);
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0004], N[Not[LessEqual[x, 1.5e-38]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000019e-4 or 1.49999999999999994e-38 < x

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 96.7%

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

      1. +-commutative 96.7%

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

   4. Simplified 96.7%

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

   if -4.00000000000000019e-4 < x < 1.49999999999999994e-38

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 73.8%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0004 \lor \neg \left(x \leq 1.5 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 5: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0011 \lor \neg \left(x \leq 3.6 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0011) (not (<= x 3.6e-38))) (* x (+ z y)) (- (* x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0011) || !(x <= 3.6e-38)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * z) - 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 <= (-0.0011d0)) .or. (.not. (x <= 3.6d-38))) then
        tmp = x * (z + y)
    else
        tmp = (x * z) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0011) || !(x <= 3.6e-38)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * z) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0011) or not (x <= 3.6e-38):
		tmp = x * (z + y)
	else:
		tmp = (x * z) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0011) || !(x <= 3.6e-38))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(x * z) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.0011) || ~((x <= 3.6e-38)))
		tmp = x * (z + y);
	else
		tmp = (x * z) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0011], N[Not[LessEqual[x, 3.6e-38]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00110000000000000007 or 3.6000000000000001e-38 < x

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 96.7%

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

      1. +-commutative 96.7%

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

   4. Simplified 96.7%

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

   if -0.00110000000000000007 < x < 3.6000000000000001e-38

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. associate-+r+ 100.0%

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

      7. unsub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 73.9%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0011 \lor \neg \left(x \leq 3.6 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \]

Alternative 6: 60.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-25} \lor \neg \left(x \leq 3.8 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.75e-25) (not (<= x 3.8e-38))) (* x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.75e-25) || !(x <= 3.8e-38)) {
		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 <= (-1.75d-25)) .or. (.not. (x <= 3.8d-38))) 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 <= -1.75e-25) || !(x <= 3.8e-38)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.75e-25) or not (x <= 3.8e-38):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.75e-25) || !(x <= 3.8e-38))
		tmp = Float64(x * y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.75e-25) || ~((x <= 3.8e-38)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.75e-25], N[Not[LessEqual[x, 3.8e-38]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.7500000000000001e-25 or 3.8e-38 < x

   1. Initial program 93.9%

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

   2. Taylor expanded in y around inf 54.8%

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

   if -1.7500000000000001e-25 < x < 3.8e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.9%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. neg-mul-1 75.9%

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

   4. Simplified 75.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-25} \lor \neg \left(x \leq 3.8 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 37.0% accurate, 4.5× 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 Float64(-z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 96.4%

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

2. Taylor expanded in x around 0 34.7%

   \[\leadsto \color{blue}{-1 \cdot z} \]
3. Step-by-step derivation

   1. neg-mul-1 34.7%

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

4. Simplified 34.7%

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

5. Final simplification 34.7%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))