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

Percentage Accurate: 98.1% → 100.0%

Time: 3.4s

Alternatives: 7

Speedup: 1.3×

• 21.1% 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, 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 98.0%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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. metadata-eval 98.0%

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

   4. distribute-rgt-in 98.0%

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

   5. neg-mul-1 98.0%

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

   6. associate-+l+ 98.0%

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

   7. distribute-lft-in 100.0%

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

   8. *-commutative 100.0%

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

   9. fma-def 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 61.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+173}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{+49}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-25}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.4e+173)
   (* z x)
   (if (<= x -1.08e+49)
     (* y x)
     (if (<= x -1.0) (* z x) (if (<= x 8.6e-25) (- z) (* y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.4e+173) {
		tmp = z * x;
	} else if (x <= -1.08e+49) {
		tmp = y * x;
	} else if (x <= -1.0) {
		tmp = z * x;
	} else if (x <= 8.6e-25) {
		tmp = -z;
	} else {
		tmp = y * 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 <= (-4.4d+173)) then
        tmp = z * x
    else if (x <= (-1.08d+49)) then
        tmp = y * x
    else if (x <= (-1.0d0)) then
        tmp = z * x
    else if (x <= 8.6d-25) then
        tmp = -z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.4e+173) {
		tmp = z * x;
	} else if (x <= -1.08e+49) {
		tmp = y * x;
	} else if (x <= -1.0) {
		tmp = z * x;
	} else if (x <= 8.6e-25) {
		tmp = -z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.4e+173:
		tmp = z * x
	elif x <= -1.08e+49:
		tmp = y * x
	elif x <= -1.0:
		tmp = z * x
	elif x <= 8.6e-25:
		tmp = -z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.4e+173)
		tmp = Float64(z * x);
	elseif (x <= -1.08e+49)
		tmp = Float64(y * x);
	elseif (x <= -1.0)
		tmp = Float64(z * x);
	elseif (x <= 8.6e-25)
		tmp = Float64(-z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.4e+173)
		tmp = z * x;
	elseif (x <= -1.08e+49)
		tmp = y * x;
	elseif (x <= -1.0)
		tmp = z * x;
	elseif (x <= 8.6e-25)
		tmp = -z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.4e+173], N[(z * x), $MachinePrecision], If[LessEqual[x, -1.08e+49], N[(y * x), $MachinePrecision], If[LessEqual[x, -1.0], N[(z * x), $MachinePrecision], If[LessEqual[x, 8.6e-25], (-z), N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.4e173 or -1.08000000000000001e49 < x < -1

   1. Initial program 97.5%

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

   2. Taylor expanded in x around inf 99.4%

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

      1. +-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in z around inf 76.6%

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

   if -4.4e173 < x < -1.08000000000000001e49 or 8.59999999999999953e-25 < x

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 64.3%

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

   if -1 < x < 8.59999999999999953e-25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.2%

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

      1. neg-mul-1 74.2%

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

   4. Simplified 74.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+173}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{+49}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-25}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-13} \lor \neg \left(x \leq 1.15 \cdot 10^{-24}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9e-13) (not (<= x 1.15e-24))) (* (+ y z) x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e-13) || !(x <= 1.15e-24)) {
		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 <= (-9d-13)) .or. (.not. (x <= 1.15d-24))) 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 <= -9e-13) || !(x <= 1.15e-24)) {
		tmp = (y + z) * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9e-13) or not (x <= 1.15e-24):
		tmp = (y + z) * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9e-13) || !(x <= 1.15e-24))
		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 <= -9e-13) || ~((x <= 1.15e-24)))
		tmp = (y + z) * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9e-13], N[Not[LessEqual[x, 1.15e-24]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -9e-13 or 1.1500000000000001e-24 < x

   1. Initial program 96.7%

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

   2. Taylor expanded in x around inf 97.4%

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

      1. +-commutative 97.4%

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

   4. Simplified 97.4%

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

   if -9e-13 < x < 1.1500000000000001e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.1%

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

      1. neg-mul-1 76.1%

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

   4. Simplified 76.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-13} \lor \neg \left(x \leq 1.15 \cdot 10^{-24}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000165 \lor \neg \left(x \leq 1.7 \cdot 10^{-25}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.000165) (not (<= x 1.7e-25))) (* (+ y z) x) (- (* z x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.000165) || !(x <= 1.7e-25)) {
		tmp = (y + z) * x;
	} else {
		tmp = (z * 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 <= (-0.000165d0)) .or. (.not. (x <= 1.7d-25))) then
        tmp = (y + z) * x
    else
        tmp = (z * x) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.000165) || !(x <= 1.7e-25)) {
		tmp = (y + z) * x;
	} else {
		tmp = (z * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.000165) or not (x <= 1.7e-25):
		tmp = (y + z) * x
	else:
		tmp = (z * x) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.000165) || !(x <= 1.7e-25))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = Float64(Float64(z * x) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.000165) || ~((x <= 1.7e-25)))
		tmp = (y + z) * x;
	else
		tmp = (z * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.000165], N[Not[LessEqual[x, 1.7e-25]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(N[(z * x), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e-4 or 1.70000000000000001e-25 < x

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 99.2%

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

      1. +-commutative 99.2%

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

   4. Simplified 99.2%

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

   if -1.65e-4 < x < 1.70000000000000001e-25

   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. distribute-rgt-out-- 100.0%

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

      3. cancel-sign-sub-inv 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. 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. Taylor expanded in y around 0 75.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000165 \lor \neg \left(x \leq 1.7 \cdot 10^{-25}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z\\ \end{array} \]

Alternative 5: 62.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-12} \lor \neg \left(x \leq 1.16 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.2e-12) (not (<= x 1.16e-24))) (* y x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e-12) || !(x <= 1.16e-24)) {
		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 <= (-1.2d-12)) .or. (.not. (x <= 1.16d-24))) 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 <= -1.2e-12) || !(x <= 1.16e-24)) {
		tmp = y * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.2e-12) or not (x <= 1.16e-24):
		tmp = y * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.2e-12) || !(x <= 1.16e-24))
		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 <= -1.2e-12) || ~((x <= 1.16e-24)))
		tmp = y * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.2e-12], N[Not[LessEqual[x, 1.16e-24]], $MachinePrecision]], N[(y * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999994e-12 or 1.16e-24 < x

   1. Initial program 96.7%

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

   2. Taylor expanded in y around inf 55.4%

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

   if -1.19999999999999994e-12 < x < 1.16e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.1%

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

      1. neg-mul-1 76.1%

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

   4. Simplified 76.1%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-12} \lor \neg \left(x \leq 1.16 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

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 98.0%

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

   1. *-commutative 98.0%

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

   2. distribute-rgt-out-- 98.0%

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

   3. cancel-sign-sub-inv 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. 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%

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

Alternative 7: 36.5% 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. Taylor expanded in x around 0 33.4%

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

   1. neg-mul-1 33.4%

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

4. Simplified 33.4%

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

5. Final simplification 33.4%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023334 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))