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

Percentage Accurate: 97.0% → 99.7%

Time: 14.9s

Alternatives: 10

Speedup: 1.0×

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: 97.0% 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: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. sub-neg 96.9%

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

   2. +-commutative 96.9%

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

   3. associate-/r/ 99.9%

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

   4. distribute-lft-neg-in 99.9%

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

   5. fma-define 99.9%

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

   6. distribute-neg-frac2 99.9%

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

   7. distribute-neg-in 99.9%

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

   8. sub-neg 99.9%

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

   9. distribute-neg-in 99.9%

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

   10. remove-double-neg 99.9%

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

   11. +-commutative 99.9%

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

   12. sub-neg 99.9%

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

   13. metadata-eval 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{\left(z - t\right) + -1}, a, x\right)} \]
4. Add Preprocessing

5. Final simplification 99.9%

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

Alternative 2: 87.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{y - z}{z}\\ \mathbf{if}\;z \leq -0.00031:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-49}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+109}:\\ \;\;\;\;x - \frac{z \cdot a}{\left(z + -1\right) - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ (- y z) z)))))
   (if (<= z -0.00031)
     t_1
     (if (<= z 5e-49)
       (+ x (* a (/ y (- -1.0 t))))
       (if (<= z 6.4e+109) (- x (/ (* z a) (- (+ z -1.0) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((y - z) / z));
	double tmp;
	if (z <= -0.00031) {
		tmp = t_1;
	} else if (z <= 5e-49) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 6.4e+109) {
		tmp = x - ((z * a) / ((z + -1.0) - t));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + (a * ((y - z) / z))
    if (z <= (-0.00031d0)) then
        tmp = t_1
    else if (z <= 5d-49) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 6.4d+109) then
        tmp = x - ((z * a) / ((z + (-1.0d0)) - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((y - z) / z));
	double tmp;
	if (z <= -0.00031) {
		tmp = t_1;
	} else if (z <= 5e-49) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 6.4e+109) {
		tmp = x - ((z * a) / ((z + -1.0) - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * ((y - z) / z))
	tmp = 0
	if z <= -0.00031:
		tmp = t_1
	elif z <= 5e-49:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 6.4e+109:
		tmp = x - ((z * a) / ((z + -1.0) - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(Float64(y - z) / z)))
	tmp = 0.0
	if (z <= -0.00031)
		tmp = t_1;
	elseif (z <= 5e-49)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 6.4e+109)
		tmp = Float64(x - Float64(Float64(z * a) / Float64(Float64(z + -1.0) - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * ((y - z) / z));
	tmp = 0.0;
	if (z <= -0.00031)
		tmp = t_1;
	elseif (z <= 5e-49)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 6.4e+109)
		tmp = x - ((z * a) / ((z + -1.0) - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.00031], t$95$1, If[LessEqual[z, 5e-49], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+109], N[(x - N[(N[(z * a), $MachinePrecision] / N[(N[(z + -1.0), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1e-4 or 6.4000000000000002e109 < z

   1. Initial program 92.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 92.2%

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

      1. neg-mul-1 92.2%

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

   7. Simplified 92.2%

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

   if -3.1e-4 < z < 4.9999999999999999e-49

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 96.4%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]

   if 4.9999999999999999e-49 < z < 6.4000000000000002e109

   1. Initial program 99.8%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 81.6%

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

      1. sub-neg 81.6%

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

      2. mul-1-neg 81.6%

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

      3. *-commutative 81.6%

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

      4. associate--l+ 81.6%

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

      5. +-commutative 81.6%

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

      6. associate-*r/ 85.9%

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

      7. remove-double-neg 85.9%

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

      8. associate-*r/ 81.6%

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

      9. *-commutative 81.6%

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

      10. metadata-eval 81.6%

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

      11. sub-neg 81.6%

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

      12. associate--r+ 81.6%

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

      13. +-commutative 81.6%

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

   7. Simplified 81.6%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00031:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-49}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+109}:\\ \;\;\;\;x - \frac{z \cdot a}{\left(z + -1\right) - t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+52}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-63}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+22}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+52)
   (- x a)
   (if (<= z 1.4e-63)
     (- x (* y a))
     (if (<= z 6.8e+22) (- x (* a (/ y t))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+52) {
		tmp = x - a;
	} else if (z <= 1.4e-63) {
		tmp = x - (y * a);
	} else if (z <= 6.8e+22) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	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 <= (-1.05d+52)) then
        tmp = x - a
    else if (z <= 1.4d-63) then
        tmp = x - (y * a)
    else if (z <= 6.8d+22) then
        tmp = x - (a * (y / t))
    else
        tmp = x - a
    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 <= -1.05e+52) {
		tmp = x - a;
	} else if (z <= 1.4e-63) {
		tmp = x - (y * a);
	} else if (z <= 6.8e+22) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+52:
		tmp = x - a
	elif z <= 1.4e-63:
		tmp = x - (y * a)
	elif z <= 6.8e+22:
		tmp = x - (a * (y / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+52)
		tmp = Float64(x - a);
	elseif (z <= 1.4e-63)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 6.8e+22)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+52)
		tmp = x - a;
	elseif (z <= 1.4e-63)
		tmp = x - (y * a);
	elseif (z <= 6.8e+22)
		tmp = x - (a * (y / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+52], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.4e-63], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+22], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e52 or 6.8e22 < z

   1. Initial program 93.4%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 80.7%

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

   if -1.05e52 < z < 1.4000000000000001e-63

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 80.6%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{1 - z}}{a}} \]

   4. Taylor expanded in z around 0 75.2%

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

   if 1.4000000000000001e-63 < z < 6.8e22

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 72.1%

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

   6. Taylor expanded in y around inf 70.0%

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

      1. associate-/l* 73.6%

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

   8. Simplified 73.6%

      \[\leadsto x - \color{blue}{a \cdot \frac{y}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+52}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-63}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+22}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+50} \lor \neg \left(t \leq 3 \cdot 10^{+99}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z + -1}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e+50) (not (<= t 3e+99)))
   (+ x (/ (- z y) (/ t a)))
   (+ x (/ (- y z) (/ (+ z -1.0) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+50) || !(t <= 3e+99)) {
		tmp = x + ((z - y) / (t / a));
	} else {
		tmp = x + ((y - z) / ((z + -1.0) / a));
	}
	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 ((t <= (-8.5d+50)) .or. (.not. (t <= 3d+99))) then
        tmp = x + ((z - y) / (t / a))
    else
        tmp = x + ((y - z) / ((z + (-1.0d0)) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+50) || !(t <= 3e+99)) {
		tmp = x + ((z - y) / (t / a));
	} else {
		tmp = x + ((y - z) / ((z + -1.0) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e+50) or not (t <= 3e+99):
		tmp = x + ((z - y) / (t / a))
	else:
		tmp = x + ((y - z) / ((z + -1.0) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e+50) || !(t <= 3e+99))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(z + -1.0) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.5e+50) || ~((t <= 3e+99)))
		tmp = x + ((z - y) / (t / a));
	else
		tmp = x + ((y - z) / ((z + -1.0) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.5e+50], N[Not[LessEqual[t, 3e+99]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(z + -1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.49999999999999961e50 or 3.00000000000000014e99 < t

   1. Initial program 98.0%

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

   3. Taylor expanded in t around inf 93.6%

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

   if -8.49999999999999961e50 < t < 3.00000000000000014e99

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 93.6%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{1 - z}}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+50} \lor \neg \left(t \leq 3 \cdot 10^{+99}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z + -1}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00031 \lor \neg \left(z \leq 220000000000\right):\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.00031) (not (<= z 220000000000.0)))
   (+ x (* a (/ (- y z) z)))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.00031) || !(z <= 220000000000.0)) {
		tmp = x + (a * ((y - z) / z));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	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 <= (-0.00031d0)) .or. (.not. (z <= 220000000000.0d0))) then
        tmp = x + (a * ((y - z) / z))
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    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 <= -0.00031) || !(z <= 220000000000.0)) {
		tmp = x + (a * ((y - z) / z));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.00031) or not (z <= 220000000000.0):
		tmp = x + (a * ((y - z) / z))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.00031) || !(z <= 220000000000.0))
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / z)));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -0.00031) || ~((z <= 220000000000.0)))
		tmp = x + (a * ((y - z) / z));
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.00031], N[Not[LessEqual[z, 220000000000.0]], $MachinePrecision]], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e-4 or 2.2e11 < z

   1. Initial program 94.0%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 88.6%

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

      1. neg-mul-1 88.6%

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

   7. Simplified 88.6%

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

   if -3.1e-4 < z < 2.2e11

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 92.4%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00031 \lor \neg \left(z \leq 220000000000\right):\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+76} \lor \neg \left(z \leq 1.76 \cdot 10^{+21}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e+76) (not (<= z 1.76e+21)))
   (- x a)
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+76) || !(z <= 1.76e+21)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	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 <= (-2.4d+76)) .or. (.not. (z <= 1.76d+21))) then
        tmp = x - a
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    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 <= -2.4e+76) || !(z <= 1.76e+21)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e+76) or not (z <= 1.76e+21):
		tmp = x - a
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e+76) || !(z <= 1.76e+21))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.4e+76) || ~((z <= 1.76e+21)))
		tmp = x - a;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e+76], N[Not[LessEqual[z, 1.76e+21]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e76 or 1.76e21 < z

   1. Initial program 93.2%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 81.2%

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

   if -2.4e76 < z < 1.76e21

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 88.8%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+76} \lor \neg \left(z \leq 1.76 \cdot 10^{+21}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+52} \lor \neg \left(z \leq 1.8 \cdot 10^{+20}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e+52) (not (<= z 1.8e+20))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+52) || !(z <= 1.8e+20)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	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 <= (-7.2d+52)) .or. (.not. (z <= 1.8d+20))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    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 <= -7.2e+52) || !(z <= 1.8e+20)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e+52) or not (z <= 1.8e+20):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e+52) || !(z <= 1.8e+20))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e+52) || ~((z <= 1.8e+20)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e+52], N[Not[LessEqual[z, 1.8e+20]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e52 or 1.8e20 < z

   1. Initial program 93.4%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 80.7%

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

   if -7.2e52 < z < 1.8e20

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 77.8%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{1 - z}}{a}} \]

   4. Taylor expanded in z around 0 70.8%

      \[\leadsto \color{blue}{x - a \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+52} \lor \neg \left(z \leq 1.8 \cdot 10^{+20}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-46} \lor \neg \left(z \leq 8 \cdot 10^{+20}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.12e-46) (not (<= z 8e+20))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.12e-46) || !(z <= 8e+20)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	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 <= (-1.12d-46)) .or. (.not. (z <= 8d+20))) then
        tmp = x - a
    else
        tmp = x
    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 <= -1.12e-46) || !(z <= 8e+20)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.12e-46) or not (z <= 8e+20):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.12e-46) || !(z <= 8e+20))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.12e-46) || ~((z <= 8e+20)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.12e-46], N[Not[LessEqual[z, 8e+20]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.11999999999999997e-46 or 8e20 < z

   1. Initial program 94.2%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 75.7%

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

   if -1.11999999999999997e-46 < z < 8e20

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 55.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-46} \lor \neg \left(z \leq 8 \cdot 10^{+20}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * ((y - z) / ((-1.0d0) + (z - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 10: 53.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 53.6%

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

Developer Target 1: 99.7% accurate, 1.0× 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 2024116 
(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))))