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

Percentage Accurate: 97.9% → 100.0%

Time: 2.7s

Alternatives: 6

Speedup: 1.3×

• 20.7% 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, 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 99.2%

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

   1. *-commutative 99.2%

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

   2. sub-neg 99.2%

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

   3. distribute-rgt-in 99.2%

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

   4. associate-+r+ 99.2%

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

   5. metadata-eval 99.2%

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

   6. mul-1-neg 99.2%

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

   7. unsub-neg 99.2%

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

   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 2: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -17000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-23}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+238}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -17000000.0)
   (* x z)
   (if (<= x 1.25e-23)
     (- z)
     (if (<= x 3.2e+24) (* x y) (if (<= x 5.2e+238) (* x z) (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -17000000.0) {
		tmp = x * z;
	} else if (x <= 1.25e-23) {
		tmp = -z;
	} else if (x <= 3.2e+24) {
		tmp = x * y;
	} else if (x <= 5.2e+238) {
		tmp = x * 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 <= (-17000000.0d0)) then
        tmp = x * z
    else if (x <= 1.25d-23) then
        tmp = -z
    else if (x <= 3.2d+24) then
        tmp = x * y
    else if (x <= 5.2d+238) then
        tmp = x * 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 <= -17000000.0) {
		tmp = x * z;
	} else if (x <= 1.25e-23) {
		tmp = -z;
	} else if (x <= 3.2e+24) {
		tmp = x * y;
	} else if (x <= 5.2e+238) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -17000000.0:
		tmp = x * z
	elif x <= 1.25e-23:
		tmp = -z
	elif x <= 3.2e+24:
		tmp = x * y
	elif x <= 5.2e+238:
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -17000000.0)
		tmp = Float64(x * z);
	elseif (x <= 1.25e-23)
		tmp = Float64(-z);
	elseif (x <= 3.2e+24)
		tmp = Float64(x * y);
	elseif (x <= 5.2e+238)
		tmp = Float64(x * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -17000000.0)
		tmp = x * z;
	elseif (x <= 1.25e-23)
		tmp = -z;
	elseif (x <= 3.2e+24)
		tmp = x * y;
	elseif (x <= 5.2e+238)
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -17000000.0], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.25e-23], (-z), If[LessEqual[x, 3.2e+24], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.2e+238], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e7 or 3.1999999999999997e24 < x < 5.1999999999999999e238

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf 99.5%

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

      1. +-commutative 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in z around inf 63.7%

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

   if -1.7e7 < x < 1.2500000000000001e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 69.9%

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

      1. mul-1-neg 69.9%

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

   4. Simplified 69.9%

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

   if 1.2500000000000001e-23 < x < 3.1999999999999997e24 or 5.1999999999999999e238 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 73.2%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -17000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-23}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+238}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-11} \lor \neg \left(x \leq 3.8 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2e-11) (not (<= x 3.8e-25))) (* x (+ y z)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e-11) || !(x <= 3.8e-25)) {
		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 <= (-2d-11)) .or. (.not. (x <= 3.8d-25))) 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 <= -2e-11) || !(x <= 3.8e-25)) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2e-11) or not (x <= 3.8e-25):
		tmp = x * (y + z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2e-11) || !(x <= 3.8e-25))
		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 <= -2e-11) || ~((x <= 3.8e-25)))
		tmp = x * (y + z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2e-11], N[Not[LessEqual[x, 3.8e-25]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999988e-11 or 3.7999999999999998e-25 < x

   1. Initial program 98.3%

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

   2. Taylor expanded in x around inf 97.4%

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

      1. +-commutative 97.4%

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

   4. Simplified 97.4%

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

   if -1.99999999999999988e-11 < x < 3.7999999999999998e-25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.9%

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

      1. mul-1-neg 70.9%

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

   4. Simplified 70.9%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-11} \lor \neg \left(x \leq 3.8 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+72} \lor \neg \left(y \leq 5.5 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e+72) (not (<= y 5.5e-16))) (* x (+ y z)) (- (* x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+72) || !(y <= 5.5e-16)) {
		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 ((y <= (-5.2d+72)) .or. (.not. (y <= 5.5d-16))) 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 ((y <= -5.2e+72) || !(y <= 5.5e-16)) {
		tmp = x * (y + z);
	} else {
		tmp = (x * z) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+72) or not (y <= 5.5e-16):
		tmp = x * (y + z)
	else:
		tmp = (x * z) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+72) || !(y <= 5.5e-16))
		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 ((y <= -5.2e+72) || ~((y <= 5.5e-16)))
		tmp = x * (y + z);
	else
		tmp = (x * z) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+72], N[Not[LessEqual[y, 5.5e-16]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999963e72 or 5.49999999999999964e-16 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in x around inf 76.8%

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

      1. +-commutative 76.8%

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

   4. Simplified 76.8%

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

   if -5.19999999999999963e72 < y < 5.49999999999999964e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.6%

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

      1. *-commutative 89.6%

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

      2. distribute-lft-out-- 89.6%

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

      3. *-rgt-identity 89.6%

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

   4. Simplified 89.6%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+72} \lor \neg \left(y \leq 5.5 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \]

Alternative 5: 61.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.8e-11) (* x y) (if (<= x 2.1e-26) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.8e-11) {
		tmp = x * y;
	} else if (x <= 2.1e-26) {
		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 <= (-3.8d-11)) then
        tmp = x * y
    else if (x <= 2.1d-26) 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 <= -3.8e-11) {
		tmp = x * y;
	} else if (x <= 2.1e-26) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.8e-11:
		tmp = x * y
	elif x <= 2.1e-26:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.8e-11)
		tmp = Float64(x * y);
	elseif (x <= 2.1e-26)
		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 <= -3.8e-11)
		tmp = x * y;
	elseif (x <= 2.1e-26)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.8e-11], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.1e-26], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998e-11 or 2.10000000000000008e-26 < x

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 47.8%

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

   if -3.7999999999999998e-11 < x < 2.10000000000000008e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.9%

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

      1. mul-1-neg 70.9%

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

   4. Simplified 70.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 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 99.2%

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

2. Taylor expanded in x around 0 39.9%

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

   1. mul-1-neg 39.9%

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

4. Simplified 39.9%

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

5. Final simplification 39.9%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))