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

Percentage Accurate: 97.9% → 100.0%

Time: 3.9s

Alternatives: 8

Speedup: 1.3×

• 22.2% 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

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

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 97.6%

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

   1. *-commutative 97.6%

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

   2. sub-neg 97.6%

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

   3. distribute-rgt-in 97.6%

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

   4. associate-+r+ 97.6%

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

   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: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-38}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+46} \lor \neg \left(x \leq 3.05 \cdot 10^{+165}\right) \land x \leq 1.75 \cdot 10^{+239}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0)
   (* x z)
   (if (<= x 1.65e-38)
     (- z)
     (if (or (<= x 7e+46) (and (not (<= x 3.05e+165)) (<= x 1.75e+239)))
       (* 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 <= 1.65e-38) {
		tmp = -z;
	} else if ((x <= 7e+46) || (!(x <= 3.05e+165) && (x <= 1.75e+239))) {
		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 <= 1.65d-38) then
        tmp = -z
    else if ((x <= 7d+46) .or. (.not. (x <= 3.05d+165)) .and. (x <= 1.75d+239)) 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 <= 1.65e-38) {
		tmp = -z;
	} else if ((x <= 7e+46) || (!(x <= 3.05e+165) && (x <= 1.75e+239))) {
		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 <= 1.65e-38:
		tmp = -z
	elif (x <= 7e+46) or (not (x <= 3.05e+165) and (x <= 1.75e+239)):
		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 <= 1.65e-38)
		tmp = Float64(-z);
	elseif ((x <= 7e+46) || (!(x <= 3.05e+165) && (x <= 1.75e+239)))
		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 <= 1.65e-38)
		tmp = -z;
	elseif ((x <= 7e+46) || (~((x <= 3.05e+165)) && (x <= 1.75e+239)))
		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, 1.65e-38], (-z), If[Or[LessEqual[x, 7e+46], And[N[Not[LessEqual[x, 3.05e+165]], $MachinePrecision], LessEqual[x, 1.75e+239]]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 6.9999999999999997e46 < x < 3.04999999999999983e165 or 1.7500000000000001e239 < x

   1. Initial program 94.0%

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

   2. Taylor expanded in x around inf 99.6%

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

      1. +-commutative 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in z around inf 61.5%

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

   if -1 < x < 1.6500000000000001e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.7%

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

      1. mul-1-neg 72.7%

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

   4. Simplified 72.7%

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

   if 1.6500000000000001e-38 < x < 6.9999999999999997e46 or 3.04999999999999983e165 < x < 1.7500000000000001e239

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 61.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-38}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+46} \lor \neg \left(x \leq 3.05 \cdot 10^{+165}\right) \land x \leq 1.75 \cdot 10^{+239}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.31 \lor \neg \left(x \leq 7.5 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.31) (not (<= x 7.5e-38))) (* x (+ y z)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.31) || !(x <= 7.5e-38)) {
		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 <= (-0.31d0)) .or. (.not. (x <= 7.5d-38))) 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 <= -0.31) || !(x <= 7.5e-38)) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.31) or not (x <= 7.5e-38):
		tmp = x * (y + z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.31) || !(x <= 7.5e-38))
		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 <= -0.31) || ~((x <= 7.5e-38)))
		tmp = x * (y + z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.31], N[Not[LessEqual[x, 7.5e-38]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -0.309999999999999998 or 7.5e-38 < x

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf 95.0%

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

      1. +-commutative 95.0%

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

   4. Simplified 95.0%

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

   if -0.309999999999999998 < x < 7.5e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.7%

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

      1. mul-1-neg 72.7%

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

   4. Simplified 72.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.31 \lor \neg \left(x \leq 7.5 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+15} \lor \neg \left(x \leq 7.5 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e+15) (not (<= x 7.5e-38))) (* x (+ y z)) (* z (- x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+15) || !(x <= 7.5e-38)) {
		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 <= (-1.9d+15)) .or. (.not. (x <= 7.5d-38))) 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 <= -1.9e+15) || !(x <= 7.5e-38)) {
		tmp = x * (y + z);
	} else {
		tmp = z * (x - 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e+15) or not (x <= 7.5e-38):
		tmp = x * (y + z)
	else:
		tmp = z * (x - 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e+15) || !(x <= 7.5e-38))
		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 <= -1.9e+15) || ~((x <= 7.5e-38)))
		tmp = x * (y + z);
	else
		tmp = z * (x - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e+15], N[Not[LessEqual[x, 7.5e-38]], $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 < -1.9e15 or 7.5e-38 < x

   1. Initial program 95.6%

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

   2. Taylor expanded in x around inf 95.3%

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

      1. +-commutative 95.3%

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

   4. Simplified 95.3%

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

   if -1.9e15 < x < 7.5e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.5%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+15} \lor \neg \left(x \leq 7.5 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - 1\right)\\ \end{array} \]

Alternative 5: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+15} \lor \neg \left(x \leq 4.1 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e+15) (not (<= x 4.1e-38))) (* x (+ y z)) (- (* x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+15) || !(x <= 4.1e-38)) {
		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 <= (-1.9d+15)) .or. (.not. (x <= 4.1d-38))) 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 <= -1.9e+15) || !(x <= 4.1e-38)) {
		tmp = x * (y + z);
	} else {
		tmp = (x * z) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e+15) or not (x <= 4.1e-38):
		tmp = x * (y + z)
	else:
		tmp = (x * z) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e+15) || !(x <= 4.1e-38))
		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 <= -1.9e+15) || ~((x <= 4.1e-38)))
		tmp = x * (y + z);
	else
		tmp = (x * z) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e+15], N[Not[LessEqual[x, 4.1e-38]], $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 < -1.9e15 or 4.0999999999999998e-38 < x

   1. Initial program 95.6%

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

   2. Taylor expanded in x around inf 95.3%

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

      1. +-commutative 95.3%

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

   4. Simplified 95.3%

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

   if -1.9e15 < x < 4.0999999999999998e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.5%

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

      1. sub-neg 74.5%

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

      2. metadata-eval 74.5%

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

      3. *-commutative 74.5%

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

      4. distribute-rgt-in 74.5%

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

      5. mul-1-neg 74.5%

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

      6. sub-neg 74.5%

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

      7. *-commutative 74.5%

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

   4. Simplified 74.5%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+15} \lor \neg \left(x \leq 4.1 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \]

Alternative 6: 59.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+15}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-38}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e+15) (* x y) (if (<= x 5.5e-38) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e+15) {
		tmp = x * y;
	} else if (x <= 5.5e-38) {
		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 <= (-1.9d+15)) then
        tmp = x * y
    else if (x <= 5.5d-38) 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 <= -1.9e+15) {
		tmp = x * y;
	} else if (x <= 5.5e-38) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.9e+15:
		tmp = x * y
	elif x <= 5.5e-38:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e+15)
		tmp = Float64(x * y);
	elseif (x <= 5.5e-38)
		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 <= -1.9e+15)
		tmp = x * y;
	elseif (x <= 5.5e-38)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e+15], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.5e-38], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e15 or 5.50000000000000005e-38 < x

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 48.2%

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

   if -1.9e15 < x < 5.50000000000000005e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 71.6%

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

      1. mul-1-neg 71.6%

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

   4. Simplified 71.6%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+15}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-38}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 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 97.6%

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

   1. *-commutative 97.6%

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

   2. sub-neg 97.6%

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

   3. distribute-rgt-in 97.6%

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

   4. associate-+r+ 97.6%

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

   5. metadata-eval 97.6%

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

   6. mul-1-neg 97.6%

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

   7. unsub-neg 97.6%

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

   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 8: 35.9% 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 97.6%

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

2. Taylor expanded in x around 0 35.8%

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

   1. mul-1-neg 35.8%

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

4. Simplified 35.8%

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

5. Final simplification 35.8%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023176 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))