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

Percentage Accurate: 97.8% → 100.0%

Time: 4.4s

Alternatives: 7

Speedup: 1.3×

• 21.6% 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: 97.8% 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 99.2%

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

   1. *-commutative 99.2%

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

   2. sub-neg 99.2%

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

   3. distribute-rgt-in 99.2%

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

   4. metadata-eval 99.2%

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

   5. neg-mul-1 99.2%

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

   6. associate-+r+ 99.2%

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

   7. unsub-neg 99.2%

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

   8. +-commutative 99.2%

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

   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. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto x \cdot \left(z + y\right) - z \]
6. Add Preprocessing

Alternative 2: 60.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-100}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-36}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+40} \lor \neg \left(x \leq 1.35 \cdot 10^{+101}\right) \land \left(x \leq 3.65 \cdot 10^{+140} \lor \neg \left(x \leq 3.8 \cdot 10^{+217}\right) \land x \leq 5.8 \cdot 10^{+278}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.2e+40)
   (* x z)
   (if (<= x -8.5e-100)
     (* x y)
     (if (<= x 9e-36)
       (- z)
       (if (or (<= x 7.8e+40)
               (and (not (<= x 1.35e+101))
                    (or (<= x 3.65e+140)
                        (and (not (<= x 3.8e+217)) (<= x 5.8e+278)))))
         (* x y)
         (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e+40) {
		tmp = x * z;
	} else if (x <= -8.5e-100) {
		tmp = x * y;
	} else if (x <= 9e-36) {
		tmp = -z;
	} else if ((x <= 7.8e+40) || (!(x <= 1.35e+101) && ((x <= 3.65e+140) || (!(x <= 3.8e+217) && (x <= 5.8e+278))))) {
		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 <= (-1.2d+40)) then
        tmp = x * z
    else if (x <= (-8.5d-100)) then
        tmp = x * y
    else if (x <= 9d-36) then
        tmp = -z
    else if ((x <= 7.8d+40) .or. (.not. (x <= 1.35d+101)) .and. (x <= 3.65d+140) .or. (.not. (x <= 3.8d+217)) .and. (x <= 5.8d+278)) 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 <= -1.2e+40) {
		tmp = x * z;
	} else if (x <= -8.5e-100) {
		tmp = x * y;
	} else if (x <= 9e-36) {
		tmp = -z;
	} else if ((x <= 7.8e+40) || (!(x <= 1.35e+101) && ((x <= 3.65e+140) || (!(x <= 3.8e+217) && (x <= 5.8e+278))))) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.2e+40:
		tmp = x * z
	elif x <= -8.5e-100:
		tmp = x * y
	elif x <= 9e-36:
		tmp = -z
	elif (x <= 7.8e+40) or (not (x <= 1.35e+101) and ((x <= 3.65e+140) or (not (x <= 3.8e+217) and (x <= 5.8e+278)))):
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.2e+40)
		tmp = Float64(x * z);
	elseif (x <= -8.5e-100)
		tmp = Float64(x * y);
	elseif (x <= 9e-36)
		tmp = Float64(-z);
	elseif ((x <= 7.8e+40) || (!(x <= 1.35e+101) && ((x <= 3.65e+140) || (!(x <= 3.8e+217) && (x <= 5.8e+278)))))
		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 <= -1.2e+40)
		tmp = x * z;
	elseif (x <= -8.5e-100)
		tmp = x * y;
	elseif (x <= 9e-36)
		tmp = -z;
	elseif ((x <= 7.8e+40) || (~((x <= 1.35e+101)) && ((x <= 3.65e+140) || (~((x <= 3.8e+217)) && (x <= 5.8e+278)))))
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.2e+40], N[(x * z), $MachinePrecision], If[LessEqual[x, -8.5e-100], N[(x * y), $MachinePrecision], If[LessEqual[x, 9e-36], (-z), If[Or[LessEqual[x, 7.8e+40], And[N[Not[LessEqual[x, 1.35e+101]], $MachinePrecision], Or[LessEqual[x, 3.65e+140], And[N[Not[LessEqual[x, 3.8e+217]], $MachinePrecision], LessEqual[x, 5.8e+278]]]]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2e40 or 7.8000000000000002e40 < x < 1.35000000000000003e101 or 3.6500000000000002e140 < x < 3.80000000000000002e217 or 5.7999999999999995e278 < x

   1. Initial program 98.1%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 65.3%

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

   4. Taylor expanded in x around inf 65.3%

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

   if -1.2e40 < x < -8.50000000000000017e-100 or 9.00000000000000047e-36 < x < 7.8000000000000002e40 or 1.35000000000000003e101 < x < 3.6500000000000002e140 or 3.80000000000000002e217 < x < 5.7999999999999995e278

   1. Initial program 99.9%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 70.2%

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

   if -8.50000000000000017e-100 < x < 9.00000000000000047e-36

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.7%

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

      1. neg-mul-1 76.7%

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

   5. Simplified 76.7%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-100}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-36}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+40} \lor \neg \left(x \leq 1.35 \cdot 10^{+101}\right) \land \left(x \leq 3.65 \cdot 10^{+140} \lor \neg \left(x \leq 3.8 \cdot 10^{+217}\right) \land x \leq 5.8 \cdot 10^{+278}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 245:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e-109)
   (* x (+ z y))
   (if (<= x 245.0) (* z (+ x -1.0)) (+ (* x y) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e-109) {
		tmp = x * (z + y);
	} else if (x <= 245.0) {
		tmp = z * (x + -1.0);
	} else {
		tmp = (x * y) + (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 <= (-1.45d-109)) then
        tmp = x * (z + y)
    else if (x <= 245.0d0) then
        tmp = z * (x + (-1.0d0))
    else
        tmp = (x * y) + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e-109) {
		tmp = x * (z + y);
	} else if (x <= 245.0) {
		tmp = z * (x + -1.0);
	} else {
		tmp = (x * y) + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e-109:
		tmp = x * (z + y)
	elif x <= 245.0:
		tmp = z * (x + -1.0)
	else:
		tmp = (x * y) + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e-109)
		tmp = Float64(x * Float64(z + y));
	elseif (x <= 245.0)
		tmp = Float64(z * Float64(x + -1.0));
	else
		tmp = Float64(Float64(x * y) + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e-109)
		tmp = x * (z + y);
	elseif (x <= 245.0)
		tmp = z * (x + -1.0);
	else
		tmp = (x * y) + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e-109], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 245.0], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45e-109

   1. Initial program 97.8%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 90.9%

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

      1. +-commutative 90.9%

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

   5. Simplified 90.9%

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

   if -1.45e-109 < x < 245

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.3%

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

   if 245 < x

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 245:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-111} \lor \neg \left(x \leq 4.6 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e-111) (not (<= x 4.6e-33))) (* x (+ z y)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e-111) || !(x <= 4.6e-33)) {
		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 <= (-4d-111)) .or. (.not. (x <= 4.6d-33))) 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 <= -4e-111) || !(x <= 4.6e-33)) {
		tmp = x * (z + y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e-111) or not (x <= 4.6e-33):
		tmp = x * (z + y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e-111) || !(x <= 4.6e-33))
		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 <= -4e-111) || ~((x <= 4.6e-33)))
		tmp = x * (z + y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e-111], N[Not[LessEqual[x, 4.6e-33]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000035e-111 or 4.59999999999999971e-33 < x

   1. Initial program 98.8%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 91.0%

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

      1. +-commutative 91.0%

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

   5. Simplified 91.0%

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

   if -4.00000000000000035e-111 < x < 4.59999999999999971e-33

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 77.9%

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

      1. neg-mul-1 77.9%

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

   5. Simplified 77.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-111} \lor \neg \left(x \leq 4.6 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-109} \lor \neg \left(x \leq 425\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3e-109) (not (<= x 425.0))) (* x (+ z y)) (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e-109) || !(x <= 425.0)) {
		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 <= (-3d-109)) .or. (.not. (x <= 425.0d0))) 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 <= -3e-109) || !(x <= 425.0)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3e-109) or not (x <= 425.0):
		tmp = x * (z + y)
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3e-109) || !(x <= 425.0))
		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 <= -3e-109) || ~((x <= 425.0)))
		tmp = x * (z + y);
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3e-109], N[Not[LessEqual[x, 425.0]], $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 < -3.00000000000000021e-109 or 425 < x

   1. Initial program 98.7%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.8%

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

      1. +-commutative 94.8%

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

   5. Simplified 94.8%

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

   if -3.00000000000000021e-109 < x < 425

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-109} \lor \neg \left(x \leq 425\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-100} \lor \neg \left(x \leq 1.15 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e-100) (not (<= x 1.15e-40))) (* x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-100) || !(x <= 1.15e-40)) {
		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-100)) .or. (.not. (x <= 1.15d-40))) 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-100) || !(x <= 1.15e-40)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e-100) or not (x <= 1.15e-40):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e-100) || !(x <= 1.15e-40))
		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 <= -8.5e-100) || ~((x <= 1.15e-40)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-100], N[Not[LessEqual[x, 1.15e-40]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -8.50000000000000017e-100 or 1.15e-40 < x

   1. Initial program 98.8%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 50.7%

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

   if -8.50000000000000017e-100 < x < 1.15e-40

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.7%

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

      1. neg-mul-1 76.7%

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

   5. Simplified 76.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-100} \lor \neg \left(x \leq 1.15 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.3% 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 99.2%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0 30.9%

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

   1. neg-mul-1 30.9%

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

5. Simplified 30.9%

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

6. Final simplification 30.9%

   \[\leadsto -z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))