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

Percentage Accurate: 97.9% → 100.0%

Time: 5.2s

Alternatives: 8

Speedup: 1.3×

• 20.3% 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 98.0%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
2. Add Preprocessing
3. 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-define 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 60.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+233}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -15500000000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 5.08 \cdot 10^{-85}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+109} \lor \neg \left(x \leq 6.2 \cdot 10^{+196}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e+233)
   (* y x)
   (if (<= x -15500000000000.0)
     (* z x)
     (if (<= x 5.08e-85)
       (- z)
       (if (or (<= x 7e+109) (not (<= x 6.2e+196))) (* y x) (* z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e+233) {
		tmp = y * x;
	} else if (x <= -15500000000000.0) {
		tmp = z * x;
	} else if (x <= 5.08e-85) {
		tmp = -z;
	} else if ((x <= 7e+109) || !(x <= 6.2e+196)) {
		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 <= (-1.25d+233)) then
        tmp = y * x
    else if (x <= (-15500000000000.0d0)) then
        tmp = z * x
    else if (x <= 5.08d-85) then
        tmp = -z
    else if ((x <= 7d+109) .or. (.not. (x <= 6.2d+196))) 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 <= -1.25e+233) {
		tmp = y * x;
	} else if (x <= -15500000000000.0) {
		tmp = z * x;
	} else if (x <= 5.08e-85) {
		tmp = -z;
	} else if ((x <= 7e+109) || !(x <= 6.2e+196)) {
		tmp = y * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e+233:
		tmp = y * x
	elif x <= -15500000000000.0:
		tmp = z * x
	elif x <= 5.08e-85:
		tmp = -z
	elif (x <= 7e+109) or not (x <= 6.2e+196):
		tmp = y * x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e+233)
		tmp = Float64(y * x);
	elseif (x <= -15500000000000.0)
		tmp = Float64(z * x);
	elseif (x <= 5.08e-85)
		tmp = Float64(-z);
	elseif ((x <= 7e+109) || !(x <= 6.2e+196))
		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 <= -1.25e+233)
		tmp = y * x;
	elseif (x <= -15500000000000.0)
		tmp = z * x;
	elseif (x <= 5.08e-85)
		tmp = -z;
	elseif ((x <= 7e+109) || ~((x <= 6.2e+196)))
		tmp = y * x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e+233], N[(y * x), $MachinePrecision], If[LessEqual[x, -15500000000000.0], N[(z * x), $MachinePrecision], If[LessEqual[x, 5.08e-85], (-z), If[Or[LessEqual[x, 7e+109], N[Not[LessEqual[x, 6.2e+196]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25000000000000002e233 or 5.0799999999999997e-85 < x < 6.99999999999999966e109 or 6.2000000000000002e196 < x

   1. Initial program 95.3%

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

   3. Taylor expanded in y around inf 65.2%

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

   if -1.25000000000000002e233 < x < -1.55e13 or 6.99999999999999966e109 < x < 6.2000000000000002e196

   1. Initial program 98.4%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 69.7%

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

   if -1.55e13 < x < 5.0799999999999997e-85

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.7%

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

      1. neg-mul-1 75.7%

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

   5. Simplified 75.7%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+233}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -15500000000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 5.08 \cdot 10^{-85}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+109} \lor \neg \left(x \leq 6.2 \cdot 10^{+196}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-5} \lor \neg \left(x \leq 5.08 \cdot 10^{-85}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3e-5) (not (<= x 5.08e-85))) (* (+ y z) x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e-5) || !(x <= 5.08e-85)) {
		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 <= (-3d-5)) .or. (.not. (x <= 5.08d-85))) 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 <= -3e-5) || !(x <= 5.08e-85)) {
		tmp = (y + z) * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3e-5) or not (x <= 5.08e-85):
		tmp = (y + z) * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3e-5) || !(x <= 5.08e-85))
		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 <= -3e-5) || ~((x <= 5.08e-85)))
		tmp = (y + z) * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3e-5], N[Not[LessEqual[x, 5.08e-85]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000008e-5 or 5.0799999999999997e-85 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 92.5%

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

      1. +-commutative 92.5%

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

   5. Simplified 92.5%

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

   if -3.00000000000000008e-5 < x < 5.0799999999999997e-85

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.1%

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

      1. neg-mul-1 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-5} \lor \neg \left(x \leq 5.08 \cdot 10^{-85}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.45 \lor \neg \left(x \leq 1.45 \cdot 10^{-5}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.45) (not (<= x 1.45e-5))) (* (+ y z) x) (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.45) || !(x <= 1.45e-5)) {
		tmp = (y + z) * x;
	} 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 <= (-0.45d0)) .or. (.not. (x <= 1.45d-5))) then
        tmp = (y + z) * x
    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 <= -0.45) || !(x <= 1.45e-5)) {
		tmp = (y + z) * x;
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.45) or not (x <= 1.45e-5):
		tmp = (y + z) * x
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.45) || !(x <= 1.45e-5))
		tmp = Float64(Float64(y + z) * x);
	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 <= -0.45) || ~((x <= 1.45e-5)))
		tmp = (y + z) * x;
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.45], N[Not[LessEqual[x, 1.45e-5]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.450000000000000011 or 1.45e-5 < x

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 99.4%

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

      1. +-commutative 99.4%

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

   5. Simplified 99.4%

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

   if -0.450000000000000011 < x < 1.45e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 72.8%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.45 \lor \neg \left(x \leq 1.45 \cdot 10^{-5}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \lor \neg \left(x \leq 4.8 \cdot 10^{-5}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.0) (not (<= x 4.8e-5))) (* (+ y z) x) (- (* z x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.0) || !(x <= 4.8e-5)) {
		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 <= (-4.0d0)) .or. (.not. (x <= 4.8d-5))) 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 <= -4.0) || !(x <= 4.8e-5)) {
		tmp = (y + z) * x;
	} else {
		tmp = (z * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.0) or not (x <= 4.8e-5):
		tmp = (y + z) * x
	else:
		tmp = (z * x) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.0) || !(x <= 4.8e-5))
		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 <= -4.0) || ~((x <= 4.8e-5)))
		tmp = (y + z) * x;
	else
		tmp = (z * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.0], N[Not[LessEqual[x, 4.8e-5]], $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 < -4 or 4.8000000000000001e-5 < x

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 99.4%

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

      1. +-commutative 99.4%

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

   5. Simplified 99.4%

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

   if -4 < x < 4.8000000000000001e-5

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      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. 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. Add Preprocessing

   5. Taylor expanded in y around 0 72.8%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \lor \neg \left(x \leq 4.8 \cdot 10^{-5}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-5} \lor \neg \left(x \leq 5.08 \cdot 10^{-85}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3e-5) (not (<= x 5.08e-85))) (* y x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e-5) || !(x <= 5.08e-85)) {
		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 <= (-3d-5)) .or. (.not. (x <= 5.08d-85))) 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 <= -3e-5) || !(x <= 5.08e-85)) {
		tmp = y * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3e-5) or not (x <= 5.08e-85):
		tmp = y * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3e-5) || !(x <= 5.08e-85))
		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 <= -3e-5) || ~((x <= 5.08e-85)))
		tmp = y * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3e-5], N[Not[LessEqual[x, 5.08e-85]], $MachinePrecision]], N[(y * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000008e-5 or 5.0799999999999997e-85 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf 52.0%

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

   if -3.00000000000000008e-5 < x < 5.0799999999999997e-85

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.1%

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

      1. neg-mul-1 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-5} \lor \neg \left(x \leq 5.08 \cdot 10^{-85}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. sub-neg 98.0%

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

   3. distribute-rgt-in 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 8: 36.3% 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 98.0%

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

3. Taylor expanded in x around 0 36.2%

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

   1. neg-mul-1 36.2%

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

5. Simplified 36.2%

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

6. Final simplification 36.2%

   \[\leadsto -z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))