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

Percentage Accurate: 97.8% → 100.0%

Time: 2.7s

Alternatives: 6

Speedup: 1.3×

• 20.7% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $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. sub-neg 98.8%

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

   3. distribute-rgt-in 98.8%

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

   4. associate-+r+ 98.8%

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

   5. metadata-eval 98.8%

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

   6. mul-1-neg 98.8%

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

   7. unsub-neg 98.8%

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

   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%

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

Alternative 2: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+200}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -9.9 \cdot 10^{+61}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-8}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+58}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+208}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.2e+200)
   (* x z)
   (if (<= x -1.35e+95)
     (* x y)
     (if (<= x -9.9e+61)
       (* x z)
       (if (<= x -4.9e-95)
         (* x y)
         (if (<= x 8.5e-8)
           (- z)
           (if (<= x 1.05e+58)
             (* x y)
             (if (<= x 2.4e+208) (* x z) (* x y)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e+200) {
		tmp = x * z;
	} else if (x <= -1.35e+95) {
		tmp = x * y;
	} else if (x <= -9.9e+61) {
		tmp = x * z;
	} else if (x <= -4.9e-95) {
		tmp = x * y;
	} else if (x <= 8.5e-8) {
		tmp = -z;
	} else if (x <= 1.05e+58) {
		tmp = x * y;
	} else if (x <= 2.4e+208) {
		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 <= (-1.2d+200)) then
        tmp = x * z
    else if (x <= (-1.35d+95)) then
        tmp = x * y
    else if (x <= (-9.9d+61)) then
        tmp = x * z
    else if (x <= (-4.9d-95)) then
        tmp = x * y
    else if (x <= 8.5d-8) then
        tmp = -z
    else if (x <= 1.05d+58) then
        tmp = x * y
    else if (x <= 2.4d+208) 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 <= -1.2e+200) {
		tmp = x * z;
	} else if (x <= -1.35e+95) {
		tmp = x * y;
	} else if (x <= -9.9e+61) {
		tmp = x * z;
	} else if (x <= -4.9e-95) {
		tmp = x * y;
	} else if (x <= 8.5e-8) {
		tmp = -z;
	} else if (x <= 1.05e+58) {
		tmp = x * y;
	} else if (x <= 2.4e+208) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.2e+200:
		tmp = x * z
	elif x <= -1.35e+95:
		tmp = x * y
	elif x <= -9.9e+61:
		tmp = x * z
	elif x <= -4.9e-95:
		tmp = x * y
	elif x <= 8.5e-8:
		tmp = -z
	elif x <= 1.05e+58:
		tmp = x * y
	elif x <= 2.4e+208:
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.2e+200)
		tmp = Float64(x * z);
	elseif (x <= -1.35e+95)
		tmp = Float64(x * y);
	elseif (x <= -9.9e+61)
		tmp = Float64(x * z);
	elseif (x <= -4.9e-95)
		tmp = Float64(x * y);
	elseif (x <= 8.5e-8)
		tmp = Float64(-z);
	elseif (x <= 1.05e+58)
		tmp = Float64(x * y);
	elseif (x <= 2.4e+208)
		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 <= -1.2e+200)
		tmp = x * z;
	elseif (x <= -1.35e+95)
		tmp = x * y;
	elseif (x <= -9.9e+61)
		tmp = x * z;
	elseif (x <= -4.9e-95)
		tmp = x * y;
	elseif (x <= 8.5e-8)
		tmp = -z;
	elseif (x <= 1.05e+58)
		tmp = x * y;
	elseif (x <= 2.4e+208)
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.2e+200], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.35e+95], N[(x * y), $MachinePrecision], If[LessEqual[x, -9.9e+61], N[(x * z), $MachinePrecision], If[LessEqual[x, -4.9e-95], N[(x * y), $MachinePrecision], If[LessEqual[x, 8.5e-8], (-z), If[LessEqual[x, 1.05e+58], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.4e+208], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2e200 or -1.35e95 < x < -9.9000000000000004e61 or 1.05000000000000006e58 < x < 2.39999999999999987e208

   1. Initial program 97.1%

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

   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 68.9%

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

   if -1.2e200 < x < -1.35e95 or -9.9000000000000004e61 < x < -4.9e-95 or 8.49999999999999935e-8 < x < 1.05000000000000006e58 or 2.39999999999999987e208 < x

   1. Initial program 98.9%

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

   2. Taylor expanded in y around inf 64.4%

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

   if -4.9e-95 < x < 8.49999999999999935e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.1%

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

      1. neg-mul-1 78.1%

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

   4. Simplified 78.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+200}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -9.9 \cdot 10^{+61}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-8}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+58}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+208}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 83.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-95} \lor \neg \left(x \leq 4.4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.9e-95) (not (<= x 4.4e-7))) (* x (+ y z)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.9e-95) || !(x <= 4.4e-7)) {
		tmp = x * (y + z);
	} 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 <= (-4.9d-95)) .or. (.not. (x <= 4.4d-7))) then
        tmp = x * (y + z)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.9e-95) || !(x <= 4.4e-7)) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.9e-95) or not (x <= 4.4e-7):
		tmp = x * (y + z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.9e-95) || !(x <= 4.4e-7))
		tmp = Float64(x * Float64(y + z));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.9e-95) || ~((x <= 4.4e-7)))
		tmp = x * (y + z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.9e-95], N[Not[LessEqual[x, 4.4e-7]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -4.9e-95 or 4.4000000000000002e-7 < x

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf 93.9%

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

      1. +-commutative 93.9%

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

   4. Simplified 93.9%

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

   if -4.9e-95 < x < 4.4000000000000002e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.1%

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

      1. neg-mul-1 78.1%

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

   4. Simplified 78.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-95} \lor \neg \left(x \leq 4.4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 83.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-95} \lor \neg \left(x \leq 5.8 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.3e-95) (not (<= x 5.8e-5))) (* x (+ y z)) (* z (- x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e-95) || !(x <= 5.8e-5)) {
		tmp = x * (y + z);
	} 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 <= (-3.3d-95)) .or. (.not. (x <= 5.8d-5))) then
        tmp = x * (y + z)
    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 <= -3.3e-95) || !(x <= 5.8e-5)) {
		tmp = x * (y + z);
	} else {
		tmp = z * (x - 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.3e-95) or not (x <= 5.8e-5):
		tmp = x * (y + z)
	else:
		tmp = z * (x - 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.3e-95) || !(x <= 5.8e-5))
		tmp = Float64(x * Float64(y + z));
	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 <= -3.3e-95) || ~((x <= 5.8e-5)))
		tmp = x * (y + z);
	else
		tmp = z * (x - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.3e-95], N[Not[LessEqual[x, 5.8e-5]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3e-95 or 5.8e-5 < x

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf 93.9%

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

      1. +-commutative 93.9%

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

   4. Simplified 93.9%

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

   if -3.3e-95 < x < 5.8e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-95} \lor \neg \left(x \leq 5.8 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - 1\right)\\ \end{array} \]

Alternative 5: 60.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-8}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.3e-95) (* x y) (if (<= x 9.5e-8) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e-95) {
		tmp = x * y;
	} else if (x <= 9.5e-8) {
		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 <= (-2.3d-95)) then
        tmp = x * y
    else if (x <= 9.5d-8) 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 <= -2.3e-95) {
		tmp = x * y;
	} else if (x <= 9.5e-8) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.3e-95:
		tmp = x * y
	elif x <= 9.5e-8:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.3e-95)
		tmp = Float64(x * y);
	elseif (x <= 9.5e-8)
		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 <= -2.3e-95)
		tmp = x * y;
	elseif (x <= 9.5e-8)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.3e-95], N[(x * y), $MachinePrecision], If[LessEqual[x, 9.5e-8], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.29999999999999999e-95 or 9.50000000000000036e-8 < x

   1. Initial program 98.1%

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

   2. Taylor expanded in y around inf 53.0%

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

   if -2.29999999999999999e-95 < x < 9.50000000000000036e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.1%

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

      1. neg-mul-1 78.1%

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

   4. Simplified 78.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-8}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 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 98.8%

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

2. Taylor expanded in x around 0 33.9%

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

   1. neg-mul-1 33.9%

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

4. Simplified 33.9%

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

5. Final simplification 33.9%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))