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

Percentage Accurate: 97.4% → 100.0%

Time: 4.1s

Alternatives: 6

Speedup: 1.3×

• 21.6% 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: 97.4% 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

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (z + y)) - 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 * (z + y)) - z
end function

Java

public static double code(double x, double y, double z) {
	return (x * (z + y)) - z;
}

Python

def code(x, y, z):
	return (x * (z + y)) - z

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (z + y)) - z;
end

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. *-commutative 97.2%

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

   2. distribute-rgt-out-- 97.2%

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

   3. cancel-sign-sub-inv 97.2%

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

   4. metadata-eval 97.2%

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

   5. neg-mul-1 97.2%

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

   6. associate-+r+ 97.2%

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

   7. unsub-neg 97.2%

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

   8. +-commutative 97.2%

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

   9. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+121}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-9}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-44}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+214}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.8e+121)
   (* x z)
   (if (<= x -2.3e-9)
     (* x y)
     (if (<= x 5e-44) (- z) (if (<= x 2.7e+214) (* x y) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e+121) {
		tmp = x * z;
	} else if (x <= -2.3e-9) {
		tmp = x * y;
	} else if (x <= 5e-44) {
		tmp = -z;
	} else if (x <= 2.7e+214) {
		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 <= (-2.8d+121)) then
        tmp = x * z
    else if (x <= (-2.3d-9)) then
        tmp = x * y
    else if (x <= 5d-44) then
        tmp = -z
    else if (x <= 2.7d+214) 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 <= -2.8e+121) {
		tmp = x * z;
	} else if (x <= -2.3e-9) {
		tmp = x * y;
	} else if (x <= 5e-44) {
		tmp = -z;
	} else if (x <= 2.7e+214) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.8e+121:
		tmp = x * z
	elif x <= -2.3e-9:
		tmp = x * y
	elif x <= 5e-44:
		tmp = -z
	elif x <= 2.7e+214:
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.8e+121)
		tmp = Float64(x * z);
	elseif (x <= -2.3e-9)
		tmp = Float64(x * y);
	elseif (x <= 5e-44)
		tmp = Float64(-z);
	elseif (x <= 2.7e+214)
		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 <= -2.8e+121)
		tmp = x * z;
	elseif (x <= -2.3e-9)
		tmp = x * y;
	elseif (x <= 5e-44)
		tmp = -z;
	elseif (x <= 2.7e+214)
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.8e+121], N[(x * z), $MachinePrecision], If[LessEqual[x, -2.3e-9], N[(x * y), $MachinePrecision], If[LessEqual[x, 5e-44], (-z), If[LessEqual[x, 2.7e+214], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.80000000000000006e121 or 2.70000000000000009e214 < x

   1. Initial program 93.5%

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

   3. Taylor expanded in y around 0 73.2%

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

   4. Taylor expanded in x around inf 73.2%

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

      1. *-commutative 73.2%

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

   6. Simplified 73.2%

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

   if -2.80000000000000006e121 < x < -2.2999999999999999e-9 or 5.00000000000000039e-44 < x < 2.70000000000000009e214

   1. Initial program 96.4%

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

   3. Taylor expanded in y around inf 66.6%

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

   if -2.2999999999999999e-9 < x < 5.00000000000000039e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.7%

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

      1. mul-1-neg 76.7%

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

   5. Simplified 76.7%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+121}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-9}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-44}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+214}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-11} \lor \neg \left(x \leq 6.8 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8e-11) (not (<= x 6.8e-46))) (* x (+ z y)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e-11) || !(x <= 6.8e-46)) {
		tmp = x * (z + y);
	} 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 <= (-8d-11)) .or. (.not. (x <= 6.8d-46))) then
        tmp = x * (z + y)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e-11) || !(x <= 6.8e-46)) {
		tmp = x * (z + y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8e-11) or not (x <= 6.8e-46):
		tmp = x * (z + y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8e-11) || !(x <= 6.8e-46))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8e-11) || ~((x <= 6.8e-46)))
		tmp = x * (z + y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8e-11], N[Not[LessEqual[x, 6.8e-46]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -7.99999999999999952e-11 or 6.79999999999999992e-46 < x

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 99.0%

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

      1. +-commutative 99.0%

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

   5. Simplified 99.0%

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

   if -7.99999999999999952e-11 < x < 6.79999999999999992e-46

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.7%

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

      1. mul-1-neg 76.7%

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

   5. Simplified 76.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-11} \lor \neg \left(x \leq 6.8 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-10} \lor \neg \left(x \leq 1.55 \cdot 10^{-47}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e-10) (not (<= x 1.55e-47)))
   (* x (+ z y))
   (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e-10) || !(x <= 1.55e-47)) {
		tmp = x * (z + y);
	} 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 <= (-1.7d-10)) .or. (.not. (x <= 1.55d-47))) then
        tmp = x * (z + y)
    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 <= -1.7e-10) || !(x <= 1.55e-47)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e-10) or not (x <= 1.55e-47):
		tmp = x * (z + y)
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e-10) || !(x <= 1.55e-47))
		tmp = Float64(x * Float64(z + y));
	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 <= -1.7e-10) || ~((x <= 1.55e-47)))
		tmp = x * (z + y);
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e-10], N[Not[LessEqual[x, 1.55e-47]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000007e-10 or 1.5499999999999999e-47 < x

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 99.0%

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

      1. +-commutative 99.0%

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

   5. Simplified 99.0%

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

   if -1.70000000000000007e-10 < x < 1.5499999999999999e-47

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.4%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-10} \lor \neg \left(x \leq 1.55 \cdot 10^{-47}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-9} \lor \neg \left(x \leq 1.5 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.3e-9) (not (<= x 1.5e-43))) (* x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.3e-9) || !(x <= 1.5e-43)) {
		tmp = x * y;
	} 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 <= (-1.3d-9)) .or. (.not. (x <= 1.5d-43))) then
        tmp = x * y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.3e-9) || !(x <= 1.5e-43)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.3e-9) or not (x <= 1.5e-43):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.3e-9) || !(x <= 1.5e-43))
		tmp = Float64(x * y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.3e-9) || ~((x <= 1.5e-43)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.3e-9], N[Not[LessEqual[x, 1.5e-43]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.3000000000000001e-9 or 1.50000000000000002e-43 < x

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 53.5%

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

   if -1.3000000000000001e-9 < x < 1.50000000000000002e-43

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.7%

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

      1. mul-1-neg 76.7%

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

   5. Simplified 76.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-9} \lor \neg \left(x \leq 1.5 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

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 97.2%

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

3. Taylor expanded in x around 0 34.7%

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

   1. mul-1-neg 34.7%

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

5. Simplified 34.7%

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

6. Final simplification 34.7%

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

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))