Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.8% → 96.9%

Time: 8.0s

Alternatives: 5

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))

C

double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (y - z)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))

C

double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (y - z)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y - z}{t - z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (/ (- y z) (- t z))))

C

double code(double x, double y, double z, double t) {
	return x * ((y - z) / (t - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y - z) / (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.5%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. *-commutative 85.5%

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

   2. associate-*l/ 98.4%

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

   3. *-commutative 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Final simplification 98.4%

   \[\leadsto x \cdot \frac{y - z}{t - z} \]
6. Add Preprocessing

Alternative 2: 53.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y}{t - z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (/ y (- t z))))

C

double code(double x, double y, double z, double t) {
	return x * (y / (t - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * (y / (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.5%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. *-commutative 85.5%

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

   2. associate-*l/ 98.4%

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

   3. *-commutative 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 53.8%

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

6. Final simplification 53.8%

   \[\leadsto x \cdot \frac{y}{t - z} \]
7. Add Preprocessing

Alternative 3: 53.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{z}{z - t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (/ z (- z t))))

C

double code(double x, double y, double z, double t) {
	return x * (z / (z - t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * (z / (z - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.5%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. *-commutative 85.5%

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

   2. associate-*l/ 98.4%

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

   3. *-commutative 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 56.4%

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

   1. neg-mul-1 56.4%

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

   2. distribute-neg-frac 56.4%

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

7. Simplified 56.4%

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

   1. frac-2neg 56.4%

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

   2. div-inv 56.4%

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

   3. remove-double-neg 56.4%

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

   4. sub-neg 56.4%

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

   5. distribute-neg-in 56.4%

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

   6. remove-double-neg 56.4%

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

9. Applied egg-rr 56.4%

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

    1. associate-*r/ 56.4%

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

    2. *-rgt-identity 56.4%

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

    3. +-commutative 56.4%

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

    4. unsub-neg 56.4%

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

11. Simplified 56.4%

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

12. Final simplification 56.4%

    \[\leadsto x \cdot \frac{z}{z - t} \]
13. Add Preprocessing

Alternative 4: 40.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (/ y t)))

C

double code(double x, double y, double z, double t) {
	return x * (y / t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * (y / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (y / t);
}

Python

def code(x, y, z, t):
	return x * (y / t)

Julia

function code(x, y, z, t)
	return Float64(x * Float64(y / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (y / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.5%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. *-commutative 85.5%

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

   2. associate-*l/ 98.4%

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

   3. *-commutative 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 39.9%

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

6. Final simplification 39.9%

   \[\leadsto x \cdot \frac{y}{t} \]
7. Add Preprocessing

Alternative 5: 34.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 85.5%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. *-commutative 85.5%

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

   2. associate-*l/ 98.4%

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

   3. *-commutative 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 37.5%

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

6. Final simplification 37.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x (/ (- t z) (- y z))))

C

double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / ((t - z) / (y - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - z));
}

Python

def code(x, y, z, t):
	return x / ((t - z) / (y - z))

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(t - z) / Float64(y - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((t - z) / (y - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024033 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))