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

Percentage Accurate: 97.9% → 100.0%

Time: 7.4s

Alternatives: 7

Speedup: 1.3×

• 20.9% 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: 97.9% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. *-commutative 98.4%

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

   2. sub-neg 98.4%

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

   3. distribute-rgt-in 98.4%

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

   4. metadata-eval 98.4%

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

   5. neg-mul-1 98.4%

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

   6. associate-+r+ 98.4%

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

   7. unsub-neg 98.4%

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

   8. +-commutative 98.4%

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

   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. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. fma-neg 100.0%

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

   3. +-commutative 100.0%

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

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y + z, x, -z\right)} \]
7. Add Preprocessing

Alternative 2: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-66}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+256}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.6e-66)
   (* y x)
   (if (<= x 3e-79) (- z) (if (<= x 3.5e+256) (* y x) (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-66) {
		tmp = y * x;
	} else if (x <= 3e-79) {
		tmp = -z;
	} else if (x <= 3.5e+256) {
		tmp = y * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.6d-66)) then
        tmp = y * x
    else if (x <= 3d-79) then
        tmp = -z
    else if (x <= 3.5d+256) then
        tmp = y * x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-66) {
		tmp = y * x;
	} else if (x <= 3e-79) {
		tmp = -z;
	} else if (x <= 3.5e+256) {
		tmp = y * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.6e-66:
		tmp = y * x
	elif x <= 3e-79:
		tmp = -z
	elif x <= 3.5e+256:
		tmp = y * x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.6e-66)
		tmp = Float64(y * x);
	elseif (x <= 3e-79)
		tmp = Float64(-z);
	elseif (x <= 3.5e+256)
		tmp = Float64(y * x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.6e-66)
		tmp = y * x;
	elseif (x <= 3e-79)
		tmp = -z;
	elseif (x <= 3.5e+256)
		tmp = y * x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.6e-66], N[(y * x), $MachinePrecision], If[LessEqual[x, 3e-79], (-z), If[LessEqual[x, 3.5e+256], N[(y * x), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5999999999999999e-66 or 3e-79 < x < 3.4999999999999998e256

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf 61.3%

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

   if -2.5999999999999999e-66 < x < 3e-79

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.0%

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

      1. neg-mul-1 80.0%

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

   5. Simplified 80.0%

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

   if 3.4999999999999998e256 < 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 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 82.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-66}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+256}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.0155\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 0.0155))) (* (+ y z) x) (- (* y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.0155)) {
		tmp = (y + z) * x;
	} else {
		tmp = (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 <= (-1.0d0)) .or. (.not. (x <= 0.0155d0))) then
        tmp = (y + z) * x
    else
        tmp = (y * x) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.0155)) {
		tmp = (y + z) * x;
	} else {
		tmp = (y * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.0) or not (x <= 0.0155):
		tmp = (y + z) * x
	else:
		tmp = (y * x) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 0.0155))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = Float64(Float64(y * x) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 0.0155)))
		tmp = (y + z) * x;
	else
		tmp = (y * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 0.0155]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 0.0155 < x

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 99.5%

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

      1. +-commutative 99.5%

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

   5. Simplified 99.5%

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

   if -1 < x < 0.0155

   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 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.0155\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-65} \lor \neg \left(x \leq 4.8 \cdot 10^{-79}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.9e-65) (not (<= x 4.8e-79))) (* (+ y z) x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.9e-65) || !(x <= 4.8e-79)) {
		tmp = (y + z) * x;
	} 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-65)) .or. (.not. (x <= 4.8d-79))) then
        tmp = (y + z) * x
    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-65) || !(x <= 4.8e-79)) {
		tmp = (y + z) * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.9e-65) or not (x <= 4.8e-79):
		tmp = (y + z) * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.9e-65) || !(x <= 4.8e-79))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.9e-65) || ~((x <= 4.8e-79)))
		tmp = (y + z) * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.9e-65], N[Not[LessEqual[x, 4.8e-79]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -4.89999999999999964e-65 or 4.80000000000000011e-79 < x

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 91.8%

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

      1. +-commutative 91.8%

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

   5. Simplified 91.8%

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

   if -4.89999999999999964e-65 < x < 4.80000000000000011e-79

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.0%

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

      1. neg-mul-1 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-65} \lor \neg \left(x \leq 4.8 \cdot 10^{-79}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-63} \lor \neg \left(x \leq 4 \cdot 10^{-80}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.1e-63) (not (<= x 4e-80))) (* y x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.1e-63) || !(x <= 4e-80)) {
		tmp = y * x;
	} 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 <= (-3.1d-63)) .or. (.not. (x <= 4d-80))) then
        tmp = y * x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.1e-63) || !(x <= 4e-80)) {
		tmp = y * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.1e-63) or not (x <= 4e-80):
		tmp = y * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.1e-63) || !(x <= 4e-80))
		tmp = Float64(y * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.1e-63) || ~((x <= 4e-80)))
		tmp = y * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.1e-63], N[Not[LessEqual[x, 4e-80]], $MachinePrecision]], N[(y * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -3.09999999999999984e-63 or 3.99999999999999985e-80 < x

   1. Initial program 97.4%

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

   3. Taylor expanded in y around inf 59.6%

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

   if -3.09999999999999984e-63 < x < 3.99999999999999985e-80

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.0%

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

      1. neg-mul-1 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-63} \lor \neg \left(x \leq 4 \cdot 10^{-80}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. *-commutative 98.4%

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

   2. sub-neg 98.4%

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

   3. distribute-rgt-in 98.4%

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

   4. metadata-eval 98.4%

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

   5. neg-mul-1 98.4%

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

   6. associate-+r+ 98.4%

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

   7. unsub-neg 98.4%

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

   8. +-commutative 98.4%

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

   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%

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

Alternative 7: 36.4% 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 98.4%

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

3. Taylor expanded in x around 0 37.0%

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

   1. neg-mul-1 37.0%

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

5. Simplified 37.0%

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

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))