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

Percentage Accurate: 97.9% → 100.0%

Time: 4.9s

Alternatives: 6

Speedup: 1.4×

• 21.1% 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, 1.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return fma((z + y), x, -z);
}

Julia

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

Wolfram

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

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

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. +-commutative N/A

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

   5. lower-+.f64 N/A

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

   6. mul-1-neg N/A

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

   7. lower-neg.f64 100.0

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

5. Applied rewrites 100.0%

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

Alternative 2: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+203}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(z, x, z\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-61}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(z, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4e+203)
   (* y x)
   (if (<= x -5.5e+21)
     (fma z x z)
     (if (<= x -5.4e-61)
       (* y x)
       (if (<= x 1.0) (- z) (if (<= x 3.2e+160) (fma z x z) (* y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4e+203) {
		tmp = y * x;
	} else if (x <= -5.5e+21) {
		tmp = fma(z, x, z);
	} else if (x <= -5.4e-61) {
		tmp = y * x;
	} else if (x <= 1.0) {
		tmp = -z;
	} else if (x <= 3.2e+160) {
		tmp = fma(z, x, z);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4e+203)
		tmp = Float64(y * x);
	elseif (x <= -5.5e+21)
		tmp = fma(z, x, z);
	elseif (x <= -5.4e-61)
		tmp = Float64(y * x);
	elseif (x <= 1.0)
		tmp = Float64(-z);
	elseif (x <= 3.2e+160)
		tmp = fma(z, x, z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4e+203], N[(y * x), $MachinePrecision], If[LessEqual[x, -5.5e+21], N[(z * x + z), $MachinePrecision], If[LessEqual[x, -5.4e-61], N[(y * x), $MachinePrecision], If[LessEqual[x, 1.0], (-z), If[LessEqual[x, 3.2e+160], N[(z * x + z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4e203 or -5.5e21 < x < -5.39999999999999987e-61 or 3.1999999999999998e160 < x

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 6.1

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

   5. Applied rewrites 6.1%

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

   7. Applied rewrites 2.5%

      \[\leadsto z \]

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 69.8

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

   10. Applied rewrites 69.8%

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

   if -4e203 < x < -5.5e21 or 1 < x < 3.1999999999999998e160

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.4

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

   5. Applied rewrites 63.4%

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

   7. Applied rewrites 63.2%

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

   if -5.39999999999999987e-61 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 75.5

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

   5. Applied rewrites 75.5%

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

Alternative 3: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-61} \lor \neg \left(x \leq 1.6 \cdot 10^{-29}\right):\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.4e-61) (not (<= x 1.6e-29))) (* (+ z y) x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.4e-61) || !(x <= 1.6e-29)) {
		tmp = (z + 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 <= (-5.4d-61)) .or. (.not. (x <= 1.6d-29))) then
        tmp = (z + 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 <= -5.4e-61) || !(x <= 1.6e-29)) {
		tmp = (z + y) * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.4e-61) or not (x <= 1.6e-29):
		tmp = (z + y) * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.4e-61) || !(x <= 1.6e-29))
		tmp = Float64(Float64(z + y) * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.4e-61) || ~((x <= 1.6e-29)))
		tmp = (z + y) * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.4e-61], N[Not[LessEqual[x, 1.6e-29]], $MachinePrecision]], N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -5.39999999999999987e-61 or 1.6e-29 < x

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 96.6

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

   5. Applied rewrites 96.6%

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

   if -5.39999999999999987e-61 < x < 1.6e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 78.6

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

   5. Applied rewrites 78.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-61} \lor \neg \left(x \leq 1.6 \cdot 10^{-29}\right):\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-61} \lor \neg \left(x \leq 1.6 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.4e-61) (not (<= x 1.6e-29))) (* y x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.4e-61) || !(x <= 1.6e-29)) {
		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 <= (-5.4d-61)) .or. (.not. (x <= 1.6d-29))) 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 <= -5.4e-61) || !(x <= 1.6e-29)) {
		tmp = y * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.4e-61) or not (x <= 1.6e-29):
		tmp = y * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.4e-61) || !(x <= 1.6e-29))
		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 <= -5.4e-61) || ~((x <= 1.6e-29)))
		tmp = y * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.4e-61], N[Not[LessEqual[x, 1.6e-29]], $MachinePrecision]], N[(y * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -5.39999999999999987e-61 or 1.6e-29 < x

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 6.1

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

   5. Applied rewrites 6.1%

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

   7. Applied rewrites 2.9%

      \[\leadsto z \]

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 52.9

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

   10. Applied rewrites 52.9%

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

   if -5.39999999999999987e-61 < x < 1.6e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 78.6

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

   5. Applied rewrites 78.6%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-61} \lor \neg \left(x \leq 1.6 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.0% accurate, 5.7× 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

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. lower-neg.f64 37.9

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

5. Applied rewrites 37.9%

   \[\leadsto \color{blue}{-z} \]
6. Add Preprocessing

Alternative 6: 2.6% accurate, 17.0× 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 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

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. lower-neg.f64 37.9

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

5. Applied rewrites 37.9%

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

7. Applied rewrites 2.5%

   \[\leadsto z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024296 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))