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

Percentage Accurate: 98.0% → 100.0%

Time: 4.1s

Alternatives: 7

Speedup: 1.3×

• 20.4% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. *-commutative 96.8%

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

   2. sub-neg 96.8%

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

   3. distribute-rgt-in 96.8%

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

   4. associate-+r+ 96.8%

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

   5. distribute-lft-out 100.0%

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

   6. fma-def 100.0%

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

   7. metadata-eval 100.0%

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

   8. mul-1-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 61.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-48}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+71} \lor \neg \left(x \leq 7.8 \cdot 10^{+198}\right) \land x \leq 1.55 \cdot 10^{+255}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0)
   (* x z)
   (if (<= x 5.1e-48)
     (- z)
     (if (or (<= x 1.08e+71) (and (not (<= x 7.8e+198)) (<= x 1.55e+255)))
       (* x y)
       (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x * z;
	} else if (x <= 5.1e-48) {
		tmp = -z;
	} else if ((x <= 1.08e+71) || (!(x <= 7.8e+198) && (x <= 1.55e+255))) {
		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 <= (-1.0d0)) then
        tmp = x * z
    else if (x <= 5.1d-48) then
        tmp = -z
    else if ((x <= 1.08d+71) .or. (.not. (x <= 7.8d+198)) .and. (x <= 1.55d+255)) 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 <= -1.0) {
		tmp = x * z;
	} else if (x <= 5.1e-48) {
		tmp = -z;
	} else if ((x <= 1.08e+71) || (!(x <= 7.8e+198) && (x <= 1.55e+255))) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = x * z
	elif x <= 5.1e-48:
		tmp = -z
	elif (x <= 1.08e+71) or (not (x <= 7.8e+198) and (x <= 1.55e+255)):
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x * z);
	elseif (x <= 5.1e-48)
		tmp = Float64(-z);
	elseif ((x <= 1.08e+71) || (!(x <= 7.8e+198) && (x <= 1.55e+255)))
		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 <= -1.0)
		tmp = x * z;
	elseif (x <= 5.1e-48)
		tmp = -z;
	elseif ((x <= 1.08e+71) || (~((x <= 7.8e+198)) && (x <= 1.55e+255)))
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[x, 5.1e-48], (-z), If[Or[LessEqual[x, 1.08e+71], And[N[Not[LessEqual[x, 7.8e+198]], $MachinePrecision], LessEqual[x, 1.55e+255]]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 1.08e71 < x < 7.8e198 or 1.5500000000000001e255 < x

   1. Initial program 93.1%

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

   2. Taylor expanded in y around 0 66.2%

      \[\leadsto \color{blue}{\left(x - 1\right) \cdot z} \]
   3. Step-by-step derivation

      1. sub-neg 66.2%

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

      2. metadata-eval 66.2%

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

      3. *-commutative 66.2%

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

      4. distribute-rgt-in 66.2%

         \[\leadsto \color{blue}{x \cdot z + -1 \cdot z} \]

      5. mul-1-neg 66.2%

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

      6. sub-neg 66.2%

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

      7. *-commutative 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in x around inf 65.4%

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

   if -1 < x < 5.10000000000000011e-48

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 74.4%

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

      1. mul-1-neg 74.4%

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

   4. Simplified 74.4%

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

   if 5.10000000000000011e-48 < x < 1.08e71 or 7.8e198 < x < 1.5500000000000001e255

   1. Initial program 97.2%

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

   2. Taylor expanded in y around inf 64.1%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-48}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+71} \lor \neg \left(x \leq 7.8 \cdot 10^{+198}\right) \land x \leq 1.55 \cdot 10^{+255}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-71} \lor \neg \left(x \leq 4.9 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.9e-71) (not (<= x 4.9e-48))) (* x (+ y z)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.9e-71) || !(x <= 4.9e-48)) {
		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-71)) .or. (.not. (x <= 4.9d-48))) 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-71) || !(x <= 4.9e-48)) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.9e-71) or not (x <= 4.9e-48):
		tmp = x * (y + z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.9e-71) || !(x <= 4.9e-48))
		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-71) || ~((x <= 4.9e-48)))
		tmp = x * (y + z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.9e-71], N[Not[LessEqual[x, 4.9e-48]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -4.8999999999999997e-71 or 4.9000000000000002e-48 < x

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 92.2%

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

      1. +-commutative 92.2%

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

   4. Simplified 92.2%

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

   if -4.8999999999999997e-71 < x < 4.9000000000000002e-48

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.0%

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

      1. mul-1-neg 79.0%

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

   4. Simplified 79.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-71} \lor \neg \left(x \leq 4.9 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-71} \lor \neg \left(x \leq 2.4 \cdot 10^{-49}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e-71) (not (<= x 2.4e-49))) (* x (+ y z)) (- (* x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-71) || !(x <= 2.4e-49)) {
		tmp = x * (y + z);
	} else {
		tmp = (x * z) - 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 <= (-2.8d-71)) .or. (.not. (x <= 2.4d-49))) then
        tmp = x * (y + z)
    else
        tmp = (x * z) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-71) || !(x <= 2.4e-49)) {
		tmp = x * (y + z);
	} else {
		tmp = (x * z) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e-71) or not (x <= 2.4e-49):
		tmp = x * (y + z)
	else:
		tmp = (x * z) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e-71) || !(x <= 2.4e-49))
		tmp = Float64(x * Float64(y + z));
	else
		tmp = Float64(Float64(x * z) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.8e-71) || ~((x <= 2.4e-49)))
		tmp = x * (y + z);
	else
		tmp = (x * z) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e-71], N[Not[LessEqual[x, 2.4e-49]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8e-71 or 2.39999999999999992e-49 < x

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 92.2%

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

      1. +-commutative 92.2%

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

   4. Simplified 92.2%

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

   if -2.8e-71 < x < 2.39999999999999992e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.0%

      \[\leadsto \color{blue}{\left(x - 1\right) \cdot z} \]
   3. Step-by-step derivation

      1. sub-neg 79.0%

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

      2. metadata-eval 79.0%

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

      3. *-commutative 79.0%

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

      4. distribute-rgt-in 79.0%

         \[\leadsto \color{blue}{x \cdot z + -1 \cdot z} \]

      5. mul-1-neg 79.0%

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

      6. sub-neg 79.0%

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

      7. *-commutative 79.0%

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

   4. Simplified 79.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-71} \lor \neg \left(x \leq 2.4 \cdot 10^{-49}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \]

Alternative 5: 61.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-48}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e-71) (* x y) (if (<= x 3.6e-48) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e-71) {
		tmp = x * y;
	} else if (x <= 3.6e-48) {
		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 <= (-4.2d-71)) then
        tmp = x * y
    else if (x <= 3.6d-48) 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 <= -4.2e-71) {
		tmp = x * y;
	} else if (x <= 3.6e-48) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e-71:
		tmp = x * y
	elif x <= 3.6e-48:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e-71)
		tmp = Float64(x * y);
	elseif (x <= 3.6e-48)
		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 <= -4.2e-71)
		tmp = x * y;
	elseif (x <= 3.6e-48)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e-71], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.6e-48], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000002e-71 or 3.6000000000000002e-48 < x

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 45.9%

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

   if -4.2000000000000002e-71 < x < 3.6000000000000002e-48

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.0%

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

      1. mul-1-neg 79.0%

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

   4. Simplified 79.0%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-48}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 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 96.8%

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

   1. *-commutative 96.8%

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

   2. sub-neg 96.8%

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

   3. distribute-rgt-in 96.8%

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

   4. associate-+r+ 96.8%

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

   5. metadata-eval 96.8%

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

   6. mul-1-neg 96.8%

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

   7. unsub-neg 96.8%

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

   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 7: 36.8% 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 96.8%

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

2. Taylor expanded in x around 0 37.2%

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

   1. mul-1-neg 37.2%

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

4. Simplified 37.2%

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

5. Final simplification 37.2%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))