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

Percentage Accurate: 98.1% → 100.0%

Time: 4.1s

Alternatives: 7

Speedup: 1.3×

• 20.2% 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: 98.1% 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 98.8%

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

   1. *-commutative 98.8%

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

   2. distribute-rgt-out-- 98.8%

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

   3. cancel-sign-sub-inv 98.8%

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

   4. metadata-eval 98.8%

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

   5. neg-mul-1 98.8%

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

   6. associate-+r+ 98.8%

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

   7. unsub-neg 98.8%

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

   8. +-commutative 98.8%

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

   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: 59.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+159}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1860:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-135}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-39}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+96} \lor \neg \left(x \leq 2.8 \cdot 10^{+136}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.52e+159)
   (* x z)
   (if (<= x -1860.0)
     (* x y)
     (if (<= x -2.1e-79)
       (- z)
       (if (<= x -3.2e-135)
         (* x y)
         (if (<= x 5.7e-39)
           (- z)
           (if (or (<= x 2.35e+96) (not (<= x 2.8e+136)))
             (* x y)
             (* x z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.52e+159) {
		tmp = x * z;
	} else if (x <= -1860.0) {
		tmp = x * y;
	} else if (x <= -2.1e-79) {
		tmp = -z;
	} else if (x <= -3.2e-135) {
		tmp = x * y;
	} else if (x <= 5.7e-39) {
		tmp = -z;
	} else if ((x <= 2.35e+96) || !(x <= 2.8e+136)) {
		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 <= (-1.52d+159)) then
        tmp = x * z
    else if (x <= (-1860.0d0)) then
        tmp = x * y
    else if (x <= (-2.1d-79)) then
        tmp = -z
    else if (x <= (-3.2d-135)) then
        tmp = x * y
    else if (x <= 5.7d-39) then
        tmp = -z
    else if ((x <= 2.35d+96) .or. (.not. (x <= 2.8d+136))) 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 <= -1.52e+159) {
		tmp = x * z;
	} else if (x <= -1860.0) {
		tmp = x * y;
	} else if (x <= -2.1e-79) {
		tmp = -z;
	} else if (x <= -3.2e-135) {
		tmp = x * y;
	} else if (x <= 5.7e-39) {
		tmp = -z;
	} else if ((x <= 2.35e+96) || !(x <= 2.8e+136)) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.52e+159:
		tmp = x * z
	elif x <= -1860.0:
		tmp = x * y
	elif x <= -2.1e-79:
		tmp = -z
	elif x <= -3.2e-135:
		tmp = x * y
	elif x <= 5.7e-39:
		tmp = -z
	elif (x <= 2.35e+96) or not (x <= 2.8e+136):
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.52e+159)
		tmp = Float64(x * z);
	elseif (x <= -1860.0)
		tmp = Float64(x * y);
	elseif (x <= -2.1e-79)
		tmp = Float64(-z);
	elseif (x <= -3.2e-135)
		tmp = Float64(x * y);
	elseif (x <= 5.7e-39)
		tmp = Float64(-z);
	elseif ((x <= 2.35e+96) || !(x <= 2.8e+136))
		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 <= -1.52e+159)
		tmp = x * z;
	elseif (x <= -1860.0)
		tmp = x * y;
	elseif (x <= -2.1e-79)
		tmp = -z;
	elseif (x <= -3.2e-135)
		tmp = x * y;
	elseif (x <= 5.7e-39)
		tmp = -z;
	elseif ((x <= 2.35e+96) || ~((x <= 2.8e+136)))
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.52e+159], N[(x * z), $MachinePrecision], If[LessEqual[x, -1860.0], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.1e-79], (-z), If[LessEqual[x, -3.2e-135], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.7e-39], (-z), If[Or[LessEqual[x, 2.35e+96], N[Not[LessEqual[x, 2.8e+136]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5199999999999999e159 or 2.35e96 < x < 2.8000000000000002e136

   1. Initial program 93.2%

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

   3. Taylor expanded in y around 0 73.7%

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

   4. Taylor expanded in x around inf 73.7%

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

      1. *-commutative 73.7%

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

   6. Simplified 73.7%

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

   if -1.5199999999999999e159 < x < -1860 or -2.0999999999999999e-79 < x < -3.2e-135 or 5.6999999999999997e-39 < x < 2.35e96 or 2.8000000000000002e136 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 70.3%

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

   if -1860 < x < -2.0999999999999999e-79 or -3.2e-135 < x < 5.6999999999999997e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.5%

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

      1. mul-1-neg 81.5%

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

   5. Simplified 81.5%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+159}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1860:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-135}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-39}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+96} \lor \neg \left(x \leq 2.8 \cdot 10^{+136}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -1950:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-37}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -1950.0)
     t_0
     (if (<= x -3e-77)
       (* z (+ x -1.0))
       (if (<= x -5.6e-135)
         t_0
         (if (<= x 1.8e-37) (- z) (+ (* x y) (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -1950.0) {
		tmp = t_0;
	} else if (x <= -3e-77) {
		tmp = z * (x + -1.0);
	} else if (x <= -5.6e-135) {
		tmp = t_0;
	} else if (x <= 1.8e-37) {
		tmp = -z;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (z + y)
    if (x <= (-1950.0d0)) then
        tmp = t_0
    else if (x <= (-3d-77)) then
        tmp = z * (x + (-1.0d0))
    else if (x <= (-5.6d-135)) then
        tmp = t_0
    else if (x <= 1.8d-37) then
        tmp = -z
    else
        tmp = (x * y) + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -1950.0) {
		tmp = t_0;
	} else if (x <= -3e-77) {
		tmp = z * (x + -1.0);
	} else if (x <= -5.6e-135) {
		tmp = t_0;
	} else if (x <= 1.8e-37) {
		tmp = -z;
	} else {
		tmp = (x * y) + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -1950.0:
		tmp = t_0
	elif x <= -3e-77:
		tmp = z * (x + -1.0)
	elif x <= -5.6e-135:
		tmp = t_0
	elif x <= 1.8e-37:
		tmp = -z
	else:
		tmp = (x * y) + (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -1950.0)
		tmp = t_0;
	elseif (x <= -3e-77)
		tmp = Float64(z * Float64(x + -1.0));
	elseif (x <= -5.6e-135)
		tmp = t_0;
	elseif (x <= 1.8e-37)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x * y) + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -1950.0)
		tmp = t_0;
	elseif (x <= -3e-77)
		tmp = z * (x + -1.0);
	elseif (x <= -5.6e-135)
		tmp = t_0;
	elseif (x <= 1.8e-37)
		tmp = -z;
	else
		tmp = (x * y) + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1950.0], t$95$0, If[LessEqual[x, -3e-77], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.6e-135], t$95$0, If[LessEqual[x, 1.8e-37], (-z), N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1950 or -3.00000000000000016e-77 < x < -5.60000000000000047e-135

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 96.4%

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

      1. +-commutative 96.4%

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

   5. Simplified 96.4%

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

   if -1950 < x < -3.00000000000000016e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.5%

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

   if -5.60000000000000047e-135 < x < 1.80000000000000004e-37

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 83.4%

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

      1. mul-1-neg 83.4%

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

   5. Simplified 83.4%

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

   if 1.80000000000000004e-37 < 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 98.3%

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

      1. *-commutative 98.3%

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

   5. Simplified 98.3%

      \[\leadsto x \cdot y + \color{blue}{z \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1950:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-37}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.58 \cdot 10^{-9} \lor \neg \left(x \leq -1.05 \cdot 10^{-79} \lor \neg \left(x \leq -5.6 \cdot 10^{-135}\right) \land x \leq 1.35 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.58e-9)
         (not
          (or (<= x -1.05e-79) (and (not (<= x -5.6e-135)) (<= x 1.35e-29)))))
   (* x (+ z y))
   (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.58e-9) || !((x <= -1.05e-79) || (!(x <= -5.6e-135) && (x <= 1.35e-29)))) {
		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 <= (-1.58d-9)) .or. (.not. (x <= (-1.05d-79)) .or. (.not. (x <= (-5.6d-135))) .and. (x <= 1.35d-29))) 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 <= -1.58e-9) || !((x <= -1.05e-79) || (!(x <= -5.6e-135) && (x <= 1.35e-29)))) {
		tmp = x * (z + y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.58e-9) or not ((x <= -1.05e-79) or (not (x <= -5.6e-135) and (x <= 1.35e-29))):
		tmp = x * (z + y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.58e-9) || !((x <= -1.05e-79) || (!(x <= -5.6e-135) && (x <= 1.35e-29))))
		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 <= -1.58e-9) || ~(((x <= -1.05e-79) || (~((x <= -5.6e-135)) && (x <= 1.35e-29)))))
		tmp = x * (z + y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.58e-9], N[Not[Or[LessEqual[x, -1.05e-79], And[N[Not[LessEqual[x, -5.6e-135]], $MachinePrecision], LessEqual[x, 1.35e-29]]]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.5799999999999999e-9 or -1.05e-79 < x < -5.60000000000000047e-135 or 1.35000000000000011e-29 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 97.0%

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

      1. +-commutative 97.0%

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

   5. Simplified 97.0%

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

   if -1.5799999999999999e-9 < x < -1.05e-79 or -5.60000000000000047e-135 < x < 1.35000000000000011e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.2%

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

      1. mul-1-neg 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.58 \cdot 10^{-9} \lor \neg \left(x \leq -1.05 \cdot 10^{-79} \lor \neg \left(x \leq -5.6 \cdot 10^{-135}\right) \land x \leq 1.35 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -2550:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-135} \lor \neg \left(x \leq 2 \cdot 10^{-26}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -2550.0)
     t_0
     (if (<= x -1.1e-79)
       (* z (+ x -1.0))
       (if (or (<= x -5.6e-135) (not (<= x 2e-26))) t_0 (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -2550.0) {
		tmp = t_0;
	} else if (x <= -1.1e-79) {
		tmp = z * (x + -1.0);
	} else if ((x <= -5.6e-135) || !(x <= 2e-26)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (z + y)
    if (x <= (-2550.0d0)) then
        tmp = t_0
    else if (x <= (-1.1d-79)) then
        tmp = z * (x + (-1.0d0))
    else if ((x <= (-5.6d-135)) .or. (.not. (x <= 2d-26))) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -2550.0) {
		tmp = t_0;
	} else if (x <= -1.1e-79) {
		tmp = z * (x + -1.0);
	} else if ((x <= -5.6e-135) || !(x <= 2e-26)) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -2550.0:
		tmp = t_0
	elif x <= -1.1e-79:
		tmp = z * (x + -1.0)
	elif (x <= -5.6e-135) or not (x <= 2e-26):
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -2550.0)
		tmp = t_0;
	elseif (x <= -1.1e-79)
		tmp = Float64(z * Float64(x + -1.0));
	elseif ((x <= -5.6e-135) || !(x <= 2e-26))
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -2550.0)
		tmp = t_0;
	elseif (x <= -1.1e-79)
		tmp = z * (x + -1.0);
	elseif ((x <= -5.6e-135) || ~((x <= 2e-26)))
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2550.0], t$95$0, If[LessEqual[x, -1.1e-79], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5.6e-135], N[Not[LessEqual[x, 2e-26]], $MachinePrecision]], t$95$0, (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2550 or -1.0999999999999999e-79 < x < -5.60000000000000047e-135 or 2.0000000000000001e-26 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 97.4%

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

      1. +-commutative 97.4%

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

   5. Simplified 97.4%

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

   if -2550 < x < -1.0999999999999999e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.5%

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

   if -5.60000000000000047e-135 < x < 2.0000000000000001e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 83.4%

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

      1. mul-1-neg 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2550:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-135} \lor \neg \left(x \leq 2 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1860 \lor \neg \left(x \leq -1.55 \cdot 10^{-78} \lor \neg \left(x \leq -5.5 \cdot 10^{-135}\right) \land x \leq 3.1 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1860.0)
         (not
          (or (<= x -1.55e-78) (and (not (<= x -5.5e-135)) (<= x 3.1e-28)))))
   (* x y)
   (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1860.0) || !((x <= -1.55e-78) || (!(x <= -5.5e-135) && (x <= 3.1e-28)))) {
		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 <= (-1860.0d0)) .or. (.not. (x <= (-1.55d-78)) .or. (.not. (x <= (-5.5d-135))) .and. (x <= 3.1d-28))) 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 <= -1860.0) || !((x <= -1.55e-78) || (!(x <= -5.5e-135) && (x <= 3.1e-28)))) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1860.0) or not ((x <= -1.55e-78) or (not (x <= -5.5e-135) and (x <= 3.1e-28))):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1860.0) || !((x <= -1.55e-78) || (!(x <= -5.5e-135) && (x <= 3.1e-28))))
		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 <= -1860.0) || ~(((x <= -1.55e-78) || (~((x <= -5.5e-135)) && (x <= 3.1e-28)))))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1860.0], N[Not[Or[LessEqual[x, -1.55e-78], And[N[Not[LessEqual[x, -5.5e-135]], $MachinePrecision], LessEqual[x, 3.1e-28]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1860 or -1.55000000000000009e-78 < x < -5.4999999999999999e-135 or 3.09999999999999992e-28 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in y around inf 58.8%

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

   if -1860 < x < -1.55000000000000009e-78 or -5.4999999999999999e-135 < x < 3.09999999999999992e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.5%

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

      1. mul-1-neg 81.5%

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

   5. Simplified 81.5%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1860 \lor \neg \left(x \leq -1.55 \cdot 10^{-78} \lor \neg \left(x \leq -5.5 \cdot 10^{-135}\right) \land x \leq 3.1 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.9% 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 98.8%

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

3. Taylor expanded in x around 0 34.4%

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

   1. mul-1-neg 34.4%

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

5. Simplified 34.4%

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

6. Final simplification 34.4%

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

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))