Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 97.2% → 99.6%

Time: 10.7s

Alternatives: 14

Speedup: 1.1×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{a}{\frac{-1 - \left(t - z\right)}{z - y}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ a (/ (- -1.0 (- t z)) (- z y)))))

C

double code(double x, double y, double z, double t, double a) {
	return x - (a / ((-1.0 - (t - z)) / (z - y)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - (a / (((-1.0d0) - (t - z)) / (z - y)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (a / ((-1.0 - (t - z)) / (z - y)));
}

Python

def code(x, y, z, t, a):
	return x - (a / ((-1.0 - (t - z)) / (z - y)))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(a / Float64(Float64(-1.0 - Float64(t - z)) / Float64(z - y))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (a / ((-1.0 - (t - z)) / (z - y)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(a / N[(N[(-1.0 - N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.2%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-/r/ N/A

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

   4. *-commutative N/A

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

   5. clear-num N/A

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

   6. un-div-inv N/A

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

   7. lower-/.f64 N/A

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

   8. lower-/.f64 99.5

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

   9. lift-+.f64 N/A

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

   10. +-commutative N/A

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

   11. lower-+.f64 99.5

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

4. Applied rewrites 99.5%

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

5. Final simplification 99.5%

   \[\leadsto x - \frac{a}{\frac{-1 - \left(t - z\right)}{z - y}} \]
6. Add Preprocessing

Alternative 2: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z - y}{\frac{-1 - \left(t - z\right)}{a}} \leq 10^{+308}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (- z y) (/ (- -1.0 (- t z)) a)) 1e+308) (- x a) (* (- a) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - y) / ((-1.0 - (t - z)) / a)) <= 1e+308) {
		tmp = x - a;
	} else {
		tmp = -a * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z - y) / (((-1.0d0) - (t - z)) / a)) <= 1d+308) then
        tmp = x - a
    else
        tmp = -a * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - y) / ((-1.0 - (t - z)) / a)) <= 1e+308) {
		tmp = x - a;
	} else {
		tmp = -a * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - y) / ((-1.0 - (t - z)) / a)) <= 1e+308:
		tmp = x - a
	else:
		tmp = -a * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z - y) / Float64(Float64(-1.0 - Float64(t - z)) / a)) <= 1e+308)
		tmp = Float64(x - a);
	else
		tmp = Float64(Float64(-a) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - y) / ((-1.0 - (t - z)) / a)) <= 1e+308)
		tmp = x - a;
	else
		tmp = -a * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z - y), $MachinePrecision] / N[(N[(-1.0 - N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], 1e+308], N[(x - a), $MachinePrecision], N[((-a) * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a)) < 1e308

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x - a} \]
   4. Step-by-step derivation

      1. lower--.f64 62.5

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

   5. Applied rewrites 62.5%

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

   if 1e308 < (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a))

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(a \cdot y\right)}}{\left(1 + t\right) - z} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(a \cdot y\right)}{\left(1 + t\right) - z}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{y \cdot a}\right)}{\left(1 + t\right) - z} \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot a}}{\left(1 + t\right) - z} \]

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot a}{\left(1 + t\right) - z} \]

      9. lower-neg.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot a}{\left(1 + t\right) - z} \]

      10. sub-neg N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(y\right)\right) \cdot a}{\color{blue}{\left(1 + t\right) + \left(\mathsf{neg}\left(z\right)\right)}} \]

      11. associate-+r+ N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(y\right)\right) \cdot a}{\color{blue}{1 + \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)}} \]

      12. +-commutative N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(y\right)\right) \cdot a}{1 + \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + t\right)}} \]

      13. associate-+r+ N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(y\right)\right) \cdot a}{\color{blue}{\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right) + t}} \]

      14. sub-neg N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(y\right)\right) \cdot a}{\color{blue}{\left(1 - z\right)} + t} \]

      15. lower-+.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(y\right)\right) \cdot a}{\color{blue}{\left(1 - z\right) + t}} \]

      16. lower--.f64 99.6

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

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in t around 0

      \[\leadsto -1 \cdot \color{blue}{\frac{a \cdot y}{1 - z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 87.8%

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

   9. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \left(a \cdot \color{blue}{y}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 79.1%

       \[\leadsto \left(-y\right) \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - y}{\frac{-1 - \left(t - z\right)}{a}} \leq 10^{+308}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Developer Target 1: 99.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (* (/ (- y z) (+ (- t z) 1.0)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - (((y - z) / ((t - z) + 1.0d0)) * a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

Python

def code(x, y, z, t, a):
	return x - (((y - z) / ((t - z) + 1.0)) * a)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(Float64(y - z) / Float64(Float64(t - z) + 1.0)) * a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (((y - z) / ((t - z) + 1.0)) * a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024230 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))