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

Percentage Accurate: 97.9% → 100.0%

Time: 6.3s

Alternatives: 7

Speedup: 1.3×

• 20.9% 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 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. distribute-rgt-out-- 98.0%

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

   3. cancel-sign-sub-inv 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. distribute-lft-out 100.0%

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

   8. fma-def 100.0%

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

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: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -19:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 45:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+143}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -19.0)
   (* x y)
   (if (<= x 45.0) (- z) (if (<= x 2.8e+143) (* x z) (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -19.0) {
		tmp = x * y;
	} else if (x <= 45.0) {
		tmp = -z;
	} else if (x <= 2.8e+143) {
		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 <= (-19.0d0)) then
        tmp = x * y
    else if (x <= 45.0d0) then
        tmp = -z
    else if (x <= 2.8d+143) 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 <= -19.0) {
		tmp = x * y;
	} else if (x <= 45.0) {
		tmp = -z;
	} else if (x <= 2.8e+143) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -19.0:
		tmp = x * y
	elif x <= 45.0:
		tmp = -z
	elif x <= 2.8e+143:
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -19.0)
		tmp = Float64(x * y);
	elseif (x <= 45.0)
		tmp = Float64(-z);
	elseif (x <= 2.8e+143)
		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 <= -19.0)
		tmp = x * y;
	elseif (x <= 45.0)
		tmp = -z;
	elseif (x <= 2.8e+143)
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -19.0], N[(x * y), $MachinePrecision], If[LessEqual[x, 45.0], (-z), If[LessEqual[x, 2.8e+143], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -19 or 2.79999999999999998e143 < x

   1. Initial program 95.9%

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

   2. Taylor expanded in y around inf 54.4%

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

   if -19 < x < 45

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.6%

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

      1. mul-1-neg 75.6%

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

   4. Simplified 75.6%

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

   if 45 < x < 2.79999999999999998e143

   1. Initial program 96.8%

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

   2. Taylor expanded in x around inf 95.0%

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

      1. +-commutative 95.0%

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

   4. Simplified 95.0%

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

   5. Taylor expanded in z around inf 63.2%

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

      1. *-commutative 63.2%

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

   7. Simplified 63.2%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -19:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 45:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+143}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-8} \lor \neg \left(x \leq 0.0085\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.8e-8) (not (<= x 0.0085))) (* x (+ y z)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.8e-8) || !(x <= 0.0085)) {
		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 <= (-8.8d-8)) .or. (.not. (x <= 0.0085d0))) 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 <= -8.8e-8) || !(x <= 0.0085)) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.8e-8) or not (x <= 0.0085):
		tmp = x * (y + z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.8e-8) || !(x <= 0.0085))
		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 <= -8.8e-8) || ~((x <= 0.0085)))
		tmp = x * (y + z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.8e-8], N[Not[LessEqual[x, 0.0085]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -8.7999999999999994e-8 or 0.0085000000000000006 < x

   1. Initial program 96.2%

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

   2. Taylor expanded in x around inf 97.8%

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

      1. +-commutative 97.8%

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

   4. Simplified 97.8%

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

   if -8.7999999999999994e-8 < x < 0.0085000000000000006

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.7%

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

      1. mul-1-neg 76.7%

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

   4. Simplified 76.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-8} \lor \neg \left(x \leq 0.0085\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -22 \lor \neg \left(x \leq 1800000000000\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -22.0) (not (<= x 1800000000000.0)))
   (* x (+ y z))
   (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -22.0) || !(x <= 1800000000000.0)) {
		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 <= (-22.0d0)) .or. (.not. (x <= 1800000000000.0d0))) 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 <= -22.0) || !(x <= 1800000000000.0)) {
		tmp = x * (y + z);
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -22.0) or not (x <= 1800000000000.0):
		tmp = x * (y + z)
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -22.0) || !(x <= 1800000000000.0))
		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 <= -22.0) || ~((x <= 1800000000000.0)))
		tmp = x * (y + z);
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -22.0], N[Not[LessEqual[x, 1800000000000.0]], $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 < -22 or 1.8e12 < x

   1. Initial program 96.0%

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

   2. Taylor expanded in x around inf 99.5%

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

      1. +-commutative 99.5%

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

   4. Simplified 99.5%

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

   if -22 < x < 1.8e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -22 \lor \neg \left(x \leq 1800000000000\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 5: 61.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -19 \lor \neg \left(x \leq 0.0075\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -19.0) (not (<= x 0.0075))) (* x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -19.0) || !(x <= 0.0075)) {
		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 <= (-19.0d0)) .or. (.not. (x <= 0.0075d0))) 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 <= -19.0) || !(x <= 0.0075)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -19.0) or not (x <= 0.0075):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -19.0) || !(x <= 0.0075))
		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 <= -19.0) || ~((x <= 0.0075)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -19.0], N[Not[LessEqual[x, 0.0075]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -19 or 0.0074999999999999997 < x

   1. Initial program 96.1%

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

   2. Taylor expanded in y around inf 49.3%

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

   if -19 < x < 0.0074999999999999997

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.2%

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

      1. mul-1-neg 76.2%

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

   4. Simplified 76.2%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -19 \lor \neg \left(x \leq 0.0075\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

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 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. distribute-rgt-out-- 98.0%

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

   3. cancel-sign-sub-inv 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. unsub-neg 98.0%

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

   7. associate-+r- 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. Final simplification 100.0%

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

Alternative 7: 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 98.0%

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

2. Taylor expanded in x around 0 39.0%

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

   1. mul-1-neg 39.0%

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

4. Simplified 39.0%

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

5. Final simplification 39.0%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))