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

Percentage Accurate: 97.1% → 99.7%

Time: 10.0s

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: 97.1% 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, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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. Final simplification 100.0%

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

Alternative 2: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+42} \lor \neg \left(z \leq 8 \cdot 10^{-40}\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e+42) (not (<= z 8e-40)))
   (+ x (/ a (/ (+ (- t z) 1.0) z)))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+42) || !(z <= 8e-40)) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	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+42)) .or. (.not. (z <= 8d-40))) then
        tmp = x + (a / (((t - z) + 1.0d0) / z))
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    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+42) || !(z <= 8e-40)) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e+42) or not (z <= 8e-40):
		tmp = x + (a / (((t - z) + 1.0) / z))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e+42) || !(z <= 8e-40))
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t - z) + 1.0) / z)));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e+42) || ~((z <= 8e-40)))
		tmp = x + (a / (((t - z) + 1.0) / z));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e+42], N[Not[LessEqual[z, 8e-40]], $MachinePrecision]], N[(x + N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000002e42 or 7.9999999999999994e-40 < z

   1. Initial program 95.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in y around 0 73.3%

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

      1. sub-neg 73.3%

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

      2. mul-1-neg 73.3%

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

      3. *-commutative 73.3%

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

      4. associate--l+ 73.3%

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

      5. +-commutative 73.3%

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

      6. associate-*r/ 87.9%

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

      7. remove-double-neg 87.9%

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

      8. associate-*r/ 73.3%

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

      9. *-commutative 73.3%

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

      10. +-commutative 73.3%

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

      11. associate--l+ 73.3%

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

      12. associate-/l* 91.7%

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

      13. associate--l+ 91.7%

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

   6. Simplified 91.7%

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

   if -7.2000000000000002e42 < z < 7.9999999999999994e-40

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around 0 95.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+42} \lor \neg \left(z \leq 8 \cdot 10^{-40}\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 3: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-40}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{\left(z + -1\right) - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.8e+41)
   (+ x (/ a (/ (+ (- t z) 1.0) z)))
   (if (<= z 7.2e-40)
     (- x (* a (/ y (+ t 1.0))))
     (- x (* a (/ z (- (+ z -1.0) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e+41) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else if (z <= 7.2e-40) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x - (a * (z / ((z + -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 <= (-5.8d+41)) then
        tmp = x + (a / (((t - z) + 1.0d0) / z))
    else if (z <= 7.2d-40) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else
        tmp = x - (a * (z / ((z + (-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 <= -5.8e+41) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else if (z <= 7.2e-40) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x - (a * (z / ((z + -1.0) - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.8e+41:
		tmp = x + (a / (((t - z) + 1.0) / z))
	elif z <= 7.2e-40:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = x - (a * (z / ((z + -1.0) - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.8e+41)
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t - z) + 1.0) / z)));
	elseif (z <= 7.2e-40)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = Float64(x - Float64(a * Float64(z / Float64(Float64(z + -1.0) - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.8e+41)
		tmp = x + (a / (((t - z) + 1.0) / z));
	elseif (z <= 7.2e-40)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = x - (a * (z / ((z + -1.0) - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.8e+41], N[(x + N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-40], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(z / N[(N[(z + -1.0), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.79999999999999977e41

   1. Initial program 94.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 77.0%

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

      1. sub-neg 77.0%

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

      2. mul-1-neg 77.0%

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

      3. *-commutative 77.0%

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

      4. associate--l+ 77.0%

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

      5. +-commutative 77.0%

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

      6. associate-*r/ 88.2%

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

      7. remove-double-neg 88.2%

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

      8. associate-*r/ 77.0%

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

      9. *-commutative 77.0%

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

      10. +-commutative 77.0%

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

      11. associate--l+ 77.0%

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

      12. associate-/l* 93.3%

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

      13. associate--l+ 93.3%

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

   6. Simplified 93.3%

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

   if -5.79999999999999977e41 < z < 7.2e-40

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around 0 95.0%

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

   if 7.2e-40 < z

   1. Initial program 96.8%

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

      1. frac-2neg 100.0%

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

      2. div-inv 99.8%

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

      3. +-commutative 99.8%

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

      4. distribute-neg-in 99.8%

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

      5. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around 0 90.2%

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

      1. associate--r+ 90.2%

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

      2. sub-neg 90.2%

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

      3. metadata-eval 90.2%

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

   8. Simplified 90.2%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-40}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{\left(z + -1\right) - t}\\ \end{array} \]

Alternative 4: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+50}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-20}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{\left(z + -1\right) - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.2e+50)
   (+ x (* a (/ (- z y) t)))
   (if (<= t 2.8e-20)
     (- x (/ a (/ (- 1.0 z) (- y z))))
     (- x (* a (/ z (- (+ z -1.0) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e+50) {
		tmp = x + (a * ((z - y) / t));
	} else if (t <= 2.8e-20) {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	} else {
		tmp = x - (a * (z / ((z + -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 (t <= (-2.2d+50)) then
        tmp = x + (a * ((z - y) / t))
    else if (t <= 2.8d-20) then
        tmp = x - (a / ((1.0d0 - z) / (y - z)))
    else
        tmp = x - (a * (z / ((z + (-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 (t <= -2.2e+50) {
		tmp = x + (a * ((z - y) / t));
	} else if (t <= 2.8e-20) {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	} else {
		tmp = x - (a * (z / ((z + -1.0) - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.2e+50:
		tmp = x + (a * ((z - y) / t))
	elif t <= 2.8e-20:
		tmp = x - (a / ((1.0 - z) / (y - z)))
	else:
		tmp = x - (a * (z / ((z + -1.0) - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.2e+50)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	elseif (t <= 2.8e-20)
		tmp = Float64(x - Float64(a / Float64(Float64(1.0 - z) / Float64(y - z))));
	else
		tmp = Float64(x - Float64(a * Float64(z / Float64(Float64(z + -1.0) - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.2e+50)
		tmp = x + (a * ((z - y) / t));
	elseif (t <= 2.8e-20)
		tmp = x - (a / ((1.0 - z) / (y - z)));
	else
		tmp = x - (a * (z / ((z + -1.0) - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.2e+50], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-20], N[(x - N[(a / N[(N[(1.0 - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(z / N[(N[(z + -1.0), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.20000000000000017e50

   1. Initial program 94.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 92.9%

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

   if -2.20000000000000017e50 < t < 2.8000000000000003e-20

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 87.7%

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

      1. associate-/l* 96.5%

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

   6. Simplified 96.5%

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

   if 2.8000000000000003e-20 < t

   1. Initial program 96.7%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.8%

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

      3. +-commutative 99.8%

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

      4. distribute-neg-in 99.8%

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

      5. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around 0 90.7%

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

      1. associate--r+ 90.7%

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

      2. sub-neg 90.7%

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

      3. metadata-eval 90.7%

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

   8. Simplified 90.7%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+50}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-20}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{\left(z + -1\right) - t}\\ \end{array} \]

Alternative 5: 86.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+55}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+33}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{-\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+55)
   (- x a)
   (if (<= z 4.5e+33)
     (- x (* a (/ y (+ t 1.0))))
     (+ x (/ (- z y) (- (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+55) {
		tmp = x - a;
	} else if (z <= 4.5e+33) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x + ((z - y) / -(z / 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 <= (-5.2d+55)) then
        tmp = x - a
    else if (z <= 4.5d+33) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else
        tmp = x + ((z - y) / -(z / 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 <= -5.2e+55) {
		tmp = x - a;
	} else if (z <= 4.5e+33) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x + ((z - y) / -(z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+55:
		tmp = x - a
	elif z <= 4.5e+33:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = x + ((z - y) / -(z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+55)
		tmp = Float64(x - a);
	elseif (z <= 4.5e+33)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(-Float64(z / a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+55)
		tmp = x - a;
	elseif (z <= 4.5e+33)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = x + ((z - y) / -(z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+55], N[(x - a), $MachinePrecision], If[LessEqual[z, 4.5e+33], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / (-N[(z / a), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e55

   1. Initial program 93.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 82.4%

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

   if -5.2e55 < z < 4.5e33

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around 0 93.0%

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

   if 4.5e33 < z

   1. Initial program 96.0%

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

   2. Taylor expanded in z around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. distribute-neg-frac 90.2%

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

   4. Simplified 90.2%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+55}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+33}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{-\frac{z}{a}}\\ \end{array} \]

Alternative 6: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+55}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-150}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -1.65e+55)
     (- x a)
     (if (<= z -5.6e-248)
       t_1
       (if (<= z 1.66e-150)
         (- x (/ a (/ t y)))
         (if (<= z 2.05e+33) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -1.65e+55) {
		tmp = x - a;
	} else if (z <= -5.6e-248) {
		tmp = t_1;
	} else if (z <= 1.66e-150) {
		tmp = x - (a / (t / y));
	} else if (z <= 2.05e+33) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y * a)
    if (z <= (-1.65d+55)) then
        tmp = x - a
    else if (z <= (-5.6d-248)) then
        tmp = t_1
    else if (z <= 1.66d-150) then
        tmp = x - (a / (t / y))
    else if (z <= 2.05d+33) then
        tmp = t_1
    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 t_1 = x - (y * a);
	double tmp;
	if (z <= -1.65e+55) {
		tmp = x - a;
	} else if (z <= -5.6e-248) {
		tmp = t_1;
	} else if (z <= 1.66e-150) {
		tmp = x - (a / (t / y));
	} else if (z <= 2.05e+33) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -1.65e+55:
		tmp = x - a
	elif z <= -5.6e-248:
		tmp = t_1
	elif z <= 1.66e-150:
		tmp = x - (a / (t / y))
	elif z <= 2.05e+33:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -1.65e+55)
		tmp = Float64(x - a);
	elseif (z <= -5.6e-248)
		tmp = t_1;
	elseif (z <= 1.66e-150)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 2.05e+33)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (z <= -1.65e+55)
		tmp = x - a;
	elseif (z <= -5.6e-248)
		tmp = t_1;
	elseif (z <= 1.66e-150)
		tmp = x - (a / (t / y));
	elseif (z <= 2.05e+33)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+55], N[(x - a), $MachinePrecision], If[LessEqual[z, -5.6e-248], t$95$1, If[LessEqual[z, 1.66e-150], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+33], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e55 or 2.04999999999999997e33 < z

   1. Initial program 94.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 85.0%

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

   if -1.65e55 < z < -5.6000000000000002e-248 or 1.6600000000000001e-150 < z < 2.04999999999999997e33

   1. Initial program 98.9%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.9%

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

      3. +-commutative 99.9%

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

      4. distribute-neg-in 99.9%

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

      5. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 88.1%

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

   7. Taylor expanded in t around 0 75.7%

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

   if -5.6000000000000002e-248 < z < 1.6600000000000001e-150

   1. Initial program 97.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around inf 84.5%

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

   5. Taylor expanded in y around inf 76.1%

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

      1. associate-/l* 80.3%

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

   7. Simplified 80.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+55}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-248}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-150}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+33}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+56} \lor \neg \left(z \leq 4 \cdot 10^{+33}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+56) (not (<= z 4e+33)))
   (- x a)
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+56) || !(z <= 4e+33)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	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 <= (-6.5d+56)) .or. (.not. (z <= 4d+33))) then
        tmp = x - a
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    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 <= -6.5e+56) || !(z <= 4e+33)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+56) or not (z <= 4e+33):
		tmp = x - a
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+56) || !(z <= 4e+33))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e+56) || ~((z <= 4e+33)))
		tmp = x - a;
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+56], N[Not[LessEqual[z, 4e+33]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000001e56 or 3.9999999999999998e33 < z

   1. Initial program 94.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 85.0%

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

   if -6.5000000000000001e56 < z < 3.9999999999999998e33

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around 0 93.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+56} \lor \neg \left(z \leq 4 \cdot 10^{+33}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 8: 73.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+55} \lor \neg \left(z \leq 2.9 \cdot 10^{+33}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e+55) (not (<= z 2.9e+33))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+55) || !(z <= 2.9e+33)) {
		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 <= (-1.65d+55)) .or. (.not. (z <= 2.9d+33))) 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 <= -1.65e+55) || !(z <= 2.9e+33)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e+55) or not (z <= 2.9e+33):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e+55) || !(z <= 2.9e+33))
		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 <= -1.65e+55) || ~((z <= 2.9e+33)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e+55], N[Not[LessEqual[z, 2.9e+33]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e55 or 2.90000000000000025e33 < z

   1. Initial program 94.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 85.0%

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

   if -1.65e55 < z < 2.90000000000000025e33

   1. Initial program 98.6%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.9%

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

      3. +-commutative 99.9%

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

      4. distribute-neg-in 99.9%

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

      5. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 89.2%

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

   7. Taylor expanded in t around 0 73.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+55} \lor \neg \left(z \leq 2.9 \cdot 10^{+33}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]

Alternative 9: 65.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-11} \lor \neg \left(z \leq 2.05 \cdot 10^{+33}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.6e-11) (not (<= z 2.05e+33))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e-11) || !(z <= 2.05e+33)) {
		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 <= (-8.6d-11)) .or. (.not. (z <= 2.05d+33))) 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 <= -8.6e-11) || !(z <= 2.05e+33)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.6e-11) or not (z <= 2.05e+33):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.6e-11) || !(z <= 2.05e+33))
		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 <= -8.6e-11) || ~((z <= 2.05e+33)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.6e-11], N[Not[LessEqual[z, 2.05e+33]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.60000000000000003e-11 or 2.04999999999999997e33 < z

   1. Initial program 95.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 82.3%

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

   if -8.60000000000000003e-11 < z < 2.04999999999999997e33

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in x around inf 59.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-11} \lor \neg \left(z \leq 2.05 \cdot 10^{+33}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 53.3% 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 97.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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. Taylor expanded in x around inf 55.8%

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

5. Final simplification 55.8%

   \[\leadsto x \]

Developer target: 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 2023308 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

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