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

Percentage Accurate: 98.0% → 100.0%

Time: 5.3s

Alternatives: 8

Speedup: 1.3×

• 21.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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 98.0%

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

   1. *-commutative 98.0%

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

   2. sub-neg 98.0%

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

   3. distribute-rgt-in 98.0%

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

   4. metadata-eval 98.0%

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

   5. neg-mul-1 98.0%

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

   6. associate-+r+ 98.0%

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

   7. unsub-neg 98.0%

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

   8. +-commutative 98.0%

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

   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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 59.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+105}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-9} \lor \neg \left(x \leq 1.55 \cdot 10^{-114}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.3e+105)
   (* x z)
   (if (or (<= x -1.5e-9) (not (<= x 1.55e-114))) (* x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.3e+105) {
		tmp = x * z;
	} else if ((x <= -1.5e-9) || !(x <= 1.55e-114)) {
		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 <= (-4.3d+105)) then
        tmp = x * z
    else if ((x <= (-1.5d-9)) .or. (.not. (x <= 1.55d-114))) 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 <= -4.3e+105) {
		tmp = x * z;
	} else if ((x <= -1.5e-9) || !(x <= 1.55e-114)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.3e+105:
		tmp = x * z
	elif (x <= -1.5e-9) or not (x <= 1.55e-114):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.3e+105)
		tmp = Float64(x * z);
	elseif ((x <= -1.5e-9) || !(x <= 1.55e-114))
		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 <= -4.3e+105)
		tmp = x * z;
	elseif ((x <= -1.5e-9) || ~((x <= 1.55e-114)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.3e+105], N[(x * z), $MachinePrecision], If[Or[LessEqual[x, -1.5e-9], N[Not[LessEqual[x, 1.55e-114]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 3 regimes

2. if x < -4.3000000000000002e105

   1. Initial program 92.7%

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

   3. Taylor expanded in y around 0 62.6%

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

   4. Taylor expanded in x around inf 62.6%

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

      1. *-commutative 62.6%

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

   6. Simplified 62.6%

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

   if -4.3000000000000002e105 < x < -1.49999999999999999e-9 or 1.55e-114 < 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 57.7%

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

   if -1.49999999999999999e-9 < x < 1.55e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.2%

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

      1. neg-mul-1 78.2%

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

   5. Simplified 78.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+105}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-9} \lor \neg \left(x \leq 1.55 \cdot 10^{-114}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.022\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 0.022))) (* x (+ z y)) (- (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.022)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * y) - 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 <= (-1.0d0)) .or. (.not. (x <= 0.022d0))) then
        tmp = x * (z + y)
    else
        tmp = (x * y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.022)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.0) or not (x <= 0.022):
		tmp = x * (z + y)
	else:
		tmp = (x * y) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 0.022))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(x * y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 0.022)))
		tmp = x * (z + y);
	else
		tmp = (x * y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 0.022]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 0.021999999999999999 < x

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf 97.9%

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

      1. +-commutative 97.9%

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

   5. Simplified 97.9%

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

   if -1 < x < 0.021999999999999999

   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. 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. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.022\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-38} \lor \neg \left(z \leq 5.6 \cdot 10^{-21}\right):\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e-38) (not (<= z 5.6e-21))) (* z (+ x -1.0)) (* x (+ z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-38) || !(z <= 5.6e-21)) {
		tmp = z * (x + -1.0);
	} 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 ((z <= (-8.5d-38)) .or. (.not. (z <= 5.6d-21))) then
        tmp = z * (x + (-1.0d0))
    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 ((z <= -8.5e-38) || !(z <= 5.6e-21)) {
		tmp = z * (x + -1.0);
	} else {
		tmp = x * (z + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e-38) or not (z <= 5.6e-21):
		tmp = z * (x + -1.0)
	else:
		tmp = x * (z + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e-38) || !(z <= 5.6e-21))
		tmp = Float64(z * Float64(x + -1.0));
	else
		tmp = Float64(x * Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e-38) || ~((z <= 5.6e-21)))
		tmp = z * (x + -1.0);
	else
		tmp = x * (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e-38], N[Not[LessEqual[z, 5.6e-21]], $MachinePrecision]], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000046e-38 or 5.60000000000000008e-21 < z

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 87.0%

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

   if -8.50000000000000046e-38 < z < 5.60000000000000008e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.0%

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

      1. +-commutative 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-38} \lor \neg \left(z \leq 5.6 \cdot 10^{-21}\right):\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-14} \lor \neg \left(x \leq 1.75 \cdot 10^{-113}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.2e-14) (not (<= x 1.75e-113))) (* x (+ z y)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e-14) || !(x <= 1.75e-113)) {
		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 <= (-7.2d-14)) .or. (.not. (x <= 1.75d-113))) 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 <= -7.2e-14) || !(x <= 1.75e-113)) {
		tmp = x * (z + y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.2e-14) or not (x <= 1.75e-113):
		tmp = x * (z + y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.2e-14) || !(x <= 1.75e-113))
		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 <= -7.2e-14) || ~((x <= 1.75e-113)))
		tmp = x * (z + y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.2e-14], N[Not[LessEqual[x, 1.75e-113]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -7.1999999999999996e-14 or 1.75000000000000014e-113 < x

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf 89.0%

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

      1. +-commutative 89.0%

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

   5. Simplified 89.0%

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

   if -7.1999999999999996e-14 < x < 1.75000000000000014e-113

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.2%

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

      1. neg-mul-1 78.2%

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

   5. Simplified 78.2%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-14} \lor \neg \left(x \leq 1.75 \cdot 10^{-113}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-14} \lor \neg \left(x \leq 5.6 \cdot 10^{-114}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.2e-14) (not (<= x 5.6e-114))) (* x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.2e-14) || !(x <= 5.6e-114)) {
		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 <= (-9.2d-14)) .or. (.not. (x <= 5.6d-114))) 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 <= -9.2e-14) || !(x <= 5.6e-114)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.2e-14) or not (x <= 5.6e-114):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.2e-14) || !(x <= 5.6e-114))
		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 <= -9.2e-14) || ~((x <= 5.6e-114)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.2e-14], N[Not[LessEqual[x, 5.6e-114]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -9.19999999999999993e-14 or 5.6000000000000003e-114 < x

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf 53.9%

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

   if -9.19999999999999993e-14 < x < 5.6000000000000003e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.2%

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

      1. neg-mul-1 78.2%

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

   5. Simplified 78.2%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-14} \lor \neg \left(x \leq 5.6 \cdot 10^{-114}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
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 98.0%

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

3. Taylor expanded in x around 0 40.1%

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

   1. neg-mul-1 40.1%

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

5. Simplified 40.1%

   \[\leadsto \color{blue}{-z} \]
6. Add Preprocessing

Alternative 8: 2.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

double code(double x, double y, double z) {
	return z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

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

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in x around 0 40.1%

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

   1. neg-mul-1 40.1%

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

5. Simplified 40.1%

   \[\leadsto \color{blue}{-z} \]
6. Step-by-step derivation

   1. neg-sub0 40.1%

      \[\leadsto \color{blue}{0 - z} \]

   2. sub-neg 40.1%

      \[\leadsto \color{blue}{0 + \left(-z\right)} \]

   3. add-sqr-sqrt 22.5%

      \[\leadsto 0 + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}} \]

   4. sqrt-unprod 15.6%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \]

   5. sqr-neg 15.6%

      \[\leadsto 0 + \sqrt{\color{blue}{z \cdot z}} \]

   6. sqrt-unprod 1.0%

      \[\leadsto 0 + \color{blue}{\sqrt{z} \cdot \sqrt{z}} \]

   7. add-sqr-sqrt 2.5%

      \[\leadsto 0 + \color{blue}{z} \]

7. Applied egg-rr 2.5%

   \[\leadsto \color{blue}{0 + z} \]
8. Step-by-step derivation

   1. +-lft-identity 2.5%

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

9. Simplified 2.5%

   \[\leadsto \color{blue}{z} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024116 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))