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

Percentage Accurate: 98.0% → 99.0%

Time: 3.4s

Alternatives: 9

Speedup: 1.3×

• 20.1% 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: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

   3. sub-neg 100.0%

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

   4. metadata-eval 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-34}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-33}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+40}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+258}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.6e-34)
   (* x y)
   (if (<= x 3.1e-33)
     (- z)
     (if (<= x 1.45e+40) (* x y) (if (<= x 1.95e+258) (* x z) (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-34) {
		tmp = x * y;
	} else if (x <= 3.1e-33) {
		tmp = -z;
	} else if (x <= 1.45e+40) {
		tmp = x * y;
	} else if (x <= 1.95e+258) {
		tmp = x * 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 <= (-2.6d-34)) then
        tmp = x * y
    else if (x <= 3.1d-33) then
        tmp = -z
    else if (x <= 1.45d+40) then
        tmp = x * y
    else if (x <= 1.95d+258) then
        tmp = x * 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 <= -2.6e-34) {
		tmp = x * y;
	} else if (x <= 3.1e-33) {
		tmp = -z;
	} else if (x <= 1.45e+40) {
		tmp = x * y;
	} else if (x <= 1.95e+258) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.6e-34:
		tmp = x * y
	elif x <= 3.1e-33:
		tmp = -z
	elif x <= 1.45e+40:
		tmp = x * y
	elif x <= 1.95e+258:
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.6e-34)
		tmp = Float64(x * y);
	elseif (x <= 3.1e-33)
		tmp = Float64(-z);
	elseif (x <= 1.45e+40)
		tmp = Float64(x * y);
	elseif (x <= 1.95e+258)
		tmp = Float64(x * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.6e-34)
		tmp = x * y;
	elseif (x <= 3.1e-33)
		tmp = -z;
	elseif (x <= 1.45e+40)
		tmp = x * y;
	elseif (x <= 1.95e+258)
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.6e-34], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.1e-33], (-z), If[LessEqual[x, 1.45e+40], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.95e+258], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5999999999999999e-34 or 3.09999999999999997e-33 < x < 1.45000000000000009e40 or 1.95000000000000019e258 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 74.4%

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

   if -2.5999999999999999e-34 < x < 3.09999999999999997e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. neg-mul-1 77.8%

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

   4. Simplified 77.8%

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

   if 1.45000000000000009e40 < x < 1.95000000000000019e258

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 66.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-34}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-33}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+40}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+258}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-34} \lor \neg \left(x \leq 2.5 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e-34) (not (<= x 2.5e-34))) (* x (+ z y)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-34) || !(x <= 2.5e-34)) {
		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 <= (-5.8d-34)) .or. (.not. (x <= 2.5d-34))) 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 <= -5.8e-34) || !(x <= 2.5e-34)) {
		tmp = x * (z + y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e-34) or not (x <= 2.5e-34):
		tmp = x * (z + y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e-34) || !(x <= 2.5e-34))
		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 <= -5.8e-34) || ~((x <= 2.5e-34)))
		tmp = x * (z + y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e-34], N[Not[LessEqual[x, 2.5e-34]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -5.8000000000000004e-34 or 2.5000000000000001e-34 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 96.5%

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

      1. +-commutative 96.5%

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

   4. Simplified 96.5%

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

   if -5.8000000000000004e-34 < x < 2.5000000000000001e-34

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. neg-mul-1 77.8%

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

   4. Simplified 77.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-34} \lor \neg \left(x \leq 2.5 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-34} \lor \neg \left(x \leq 5.2 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.6e-34) (not (<= x 5.2e-8))) (* x (+ z y)) (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e-34) || !(x <= 5.2e-8)) {
		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 <= (-1.6d-34)) .or. (.not. (x <= 5.2d-8))) 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 <= -1.6e-34) || !(x <= 5.2e-8)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.6e-34) or not (x <= 5.2e-8):
		tmp = x * (z + y)
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.6e-34) || !(x <= 5.2e-8))
		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 <= -1.6e-34) || ~((x <= 5.2e-8)))
		tmp = x * (z + y);
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.6e-34], N[Not[LessEqual[x, 5.2e-8]], $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 < -1.60000000000000001e-34 or 5.2000000000000002e-8 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 98.7%

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

      1. +-commutative 98.7%

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

   4. Simplified 98.7%

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

   if -1.60000000000000001e-34 < x < 5.2000000000000002e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.4%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-34} \lor \neg \left(x \leq 5.2 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 5: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-34} \lor \neg \left(x \leq 1.02 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.5e-34) (not (<= x 1.02e-6))) (* x (+ z y)) (- (* x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e-34) || !(x <= 1.02e-6)) {
		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 <= (-6.5d-34)) .or. (.not. (x <= 1.02d-6))) 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 <= -6.5e-34) || !(x <= 1.02e-6)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * z) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.5e-34) or not (x <= 1.02e-6):
		tmp = x * (z + y)
	else:
		tmp = (x * z) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.5e-34) || !(x <= 1.02e-6))
		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 <= -6.5e-34) || ~((x <= 1.02e-6)))
		tmp = x * (z + y);
	else
		tmp = (x * z) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e-34], N[Not[LessEqual[x, 1.02e-6]], $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 < -6.49999999999999985e-34 or 1.02e-6 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 98.7%

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

      1. +-commutative 98.7%

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

   4. Simplified 98.7%

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

   if -6.49999999999999985e-34 < x < 1.02e-6

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. mul-1-neg 100.0%

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

      7. unsub-neg 100.0%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 76.4%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-34} \lor \neg \left(x \leq 1.02 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \]

Alternative 6: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-33}:\\ \;\;\;\;x \cdot z + x \cdot y\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-9}:\\ \;\;\;\;x \cdot z - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.8e-33)
   (+ (* x z) (* x y))
   (if (<= x 2.2e-9) (- (* x z) z) (* x (+ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e-33) {
		tmp = (x * z) + (x * y);
	} else if (x <= 2.2e-9) {
		tmp = (x * z) - z;
	} else {
		tmp = x * (z + 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 <= (-4.8d-33)) then
        tmp = (x * z) + (x * y)
    else if (x <= 2.2d-9) then
        tmp = (x * z) - z
    else
        tmp = x * (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e-33) {
		tmp = (x * z) + (x * y);
	} else if (x <= 2.2e-9) {
		tmp = (x * z) - z;
	} else {
		tmp = x * (z + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.8e-33:
		tmp = (x * z) + (x * y)
	elif x <= 2.2e-9:
		tmp = (x * z) - z
	else:
		tmp = x * (z + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.8e-33)
		tmp = Float64(Float64(x * z) + Float64(x * y));
	elseif (x <= 2.2e-9)
		tmp = Float64(Float64(x * z) - z);
	else
		tmp = Float64(x * Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.8e-33)
		tmp = (x * z) + (x * y);
	elseif (x <= 2.2e-9)
		tmp = (x * z) - z;
	else
		tmp = x * (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.8e-33], N[(N[(x * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-9], N[(N[(x * z), $MachinePrecision] - z), $MachinePrecision], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 98.5%

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

   if -4.8e-33 < x < 2.1999999999999998e-9

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. mul-1-neg 100.0%

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

      7. unsub-neg 100.0%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 76.4%

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

   if 2.1999999999999998e-9 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 98.9%

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

      1. +-commutative 98.9%

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

   4. Simplified 98.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-33}:\\ \;\;\;\;x \cdot z + x \cdot y\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-9}:\\ \;\;\;\;x \cdot z - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]

Alternative 7: 61.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-31}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-33}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.52e-31) (* x y) (if (<= x 1.9e-33) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.52e-31) {
		tmp = x * y;
	} else if (x <= 1.9e-33) {
		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 <= (-1.52d-31)) then
        tmp = x * y
    else if (x <= 1.9d-33) 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 <= -1.52e-31) {
		tmp = x * y;
	} else if (x <= 1.9e-33) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.52e-31:
		tmp = x * y
	elif x <= 1.9e-33:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.52e-31)
		tmp = Float64(x * y);
	elseif (x <= 1.9e-33)
		tmp = Float64(-z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.52e-31)
		tmp = x * y;
	elseif (x <= 1.9e-33)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.52e-31], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.9e-33], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.52000000000000003e-31 or 1.89999999999999997e-33 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 63.4%

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

   if -1.52000000000000003e-31 < x < 1.89999999999999997e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. neg-mul-1 77.8%

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

   4. Simplified 77.8%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-31}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-33}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 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 100.0%

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

   1. *-commutative 100.0%

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

   2. sub-neg 100.0%

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

   3. distribute-rgt-in 100.0%

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

   4. associate-+r+ 100.0%

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

   5. metadata-eval 100.0%

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

   6. mul-1-neg 100.0%

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

   7. unsub-neg 100.0%

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

   8. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 9: 35.8% 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 100.0%

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

2. Taylor expanded in x around 0 37.4%

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

   1. neg-mul-1 37.4%

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

4. Simplified 37.4%

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

5. Final simplification 37.4%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))