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

Percentage Accurate: 97.3% → 99.6%

Time: 10.0s

Alternatives: 11

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: 97.3% 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

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

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 2: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -1450:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-300}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+36}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ a t) (- z y)))))
   (if (<= t -1450.0)
     t_1
     (if (<= t -7.4e-300) (- x a) (if (<= t 2.5e+36) (- x (* y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a / t) * (z - y));
	double tmp;
	if (t <= -1450.0) {
		tmp = t_1;
	} else if (t <= -7.4e-300) {
		tmp = x - a;
	} else if (t <= 2.5e+36) {
		tmp = x - (y * a);
	} 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 / t) * (z - y))
    if (t <= (-1450.0d0)) then
        tmp = t_1
    else if (t <= (-7.4d-300)) then
        tmp = x - a
    else if (t <= 2.5d+36) then
        tmp = x - (y * a)
    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 / t) * (z - y));
	double tmp;
	if (t <= -1450.0) {
		tmp = t_1;
	} else if (t <= -7.4e-300) {
		tmp = x - a;
	} else if (t <= 2.5e+36) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a / t) * (z - y))
	tmp = 0
	if t <= -1450.0:
		tmp = t_1
	elif t <= -7.4e-300:
		tmp = x - a
	elif t <= 2.5e+36:
		tmp = x - (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a / t) * Float64(z - y)))
	tmp = 0.0
	if (t <= -1450.0)
		tmp = t_1;
	elseif (t <= -7.4e-300)
		tmp = Float64(x - a);
	elseif (t <= 2.5e+36)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((a / t) * (z - y));
	tmp = 0.0;
	if (t <= -1450.0)
		tmp = t_1;
	elseif (t <= -7.4e-300)
		tmp = x - a;
	elseif (t <= 2.5e+36)
		tmp = x - (y * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1450.0], t$95$1, If[LessEqual[t, -7.4e-300], N[(x - a), $MachinePrecision], If[LessEqual[t, 2.5e+36], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1450 or 2.49999999999999988e36 < t

   1. Initial program 99.1%

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

      1. clear-num 99.0%

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

      2. associate-/r/ 98.9%

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

      3. clear-num 99.0%

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

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in t around inf 86.8%

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

   if -1450 < t < -7.4000000000000003e-300

   1. Initial program 92.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 66.4%

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

   if -7.4000000000000003e-300 < t < 2.49999999999999988e36

   1. Initial program 97.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 70.7%

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

   6. Taylor expanded in t around 0 70.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1450:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-300}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+36}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6500000000000 \lor \neg \left(z \leq 3\right):\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y + -1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6500000000000.0) (not (<= z 3.0)))
   (+ x (* a (+ -1.0 (/ (+ y -1.0) z))))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6500000000000.0) || !(z <= 3.0)) {
		tmp = x + (a * (-1.0 + ((y + -1.0) / 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 <= (-6500000000000.0d0)) .or. (.not. (z <= 3.0d0))) then
        tmp = x + (a * ((-1.0d0) + ((y + (-1.0d0)) / 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 <= -6500000000000.0) || !(z <= 3.0)) {
		tmp = x + (a * (-1.0 + ((y + -1.0) / z)));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6500000000000.0) or not (z <= 3.0):
		tmp = x + (a * (-1.0 + ((y + -1.0) / z)))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6500000000000.0) || !(z <= 3.0))
		tmp = Float64(x + Float64(a * Float64(-1.0 + Float64(Float64(y + -1.0) / 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 <= -6500000000000.0) || ~((z <= 3.0)))
		tmp = x + (a * (-1.0 + ((y + -1.0) / 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, -6500000000000.0], N[Not[LessEqual[z, 3.0]], $MachinePrecision]], N[(x + N[(a * N[(-1.0 + N[(N[(y + -1.0), $MachinePrecision] / z), $MachinePrecision]), $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 < -6.5e12 or 3 < z

   1. Initial program 93.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 84.8%

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

   6. Taylor expanded in z around inf 84.3%

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

      1. +-commutative 84.3%

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

      2. mul-1-neg 84.3%

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

      3. sub-neg 84.3%

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

      4. div-sub 84.3%

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

      5. sub-neg 84.3%

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

      6. +-commutative 84.3%

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

      7. neg-mul-1 84.3%

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

      8. metadata-eval 84.3%

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

      9. distribute-lft-in 84.3%

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

      10. metadata-eval 84.3%

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

      11. sub-neg 84.3%

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

      12. associate-*r/ 84.3%

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

      13. mul-1-neg 84.3%

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

      14. unsub-neg 84.3%

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

      15. sub-neg 84.3%

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

      16. metadata-eval 84.3%

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

   8. Simplified 84.3%

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

   if -6.5e12 < z < 3

   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 88.3%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500000000000 \lor \neg \left(z \leq 3\right):\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y + -1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -155000000000:\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y + -1}{z}\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-32}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -155000000000.0)
   (+ x (* a (+ -1.0 (/ (+ y -1.0) z))))
   (if (<= z 1.16e-32)
     (+ x (* a (/ y (- -1.0 t))))
     (+ x (* a (/ z (+ (- t z) 1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -155000000000.0) {
		tmp = x + (a * (-1.0 + ((y + -1.0) / z)));
	} else if (z <= 1.16e-32) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (a * (z / ((t - z) + 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 <= (-155000000000.0d0)) then
        tmp = x + (a * ((-1.0d0) + ((y + (-1.0d0)) / z)))
    else if (z <= 1.16d-32) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + (a * (z / ((t - z) + 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 <= -155000000000.0) {
		tmp = x + (a * (-1.0 + ((y + -1.0) / z)));
	} else if (z <= 1.16e-32) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -155000000000.0:
		tmp = x + (a * (-1.0 + ((y + -1.0) / z)))
	elif z <= 1.16e-32:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + (a * (z / ((t - z) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -155000000000.0)
		tmp = Float64(x + Float64(a * Float64(-1.0 + Float64(Float64(y + -1.0) / z))));
	elseif (z <= 1.16e-32)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -155000000000.0)
		tmp = x + (a * (-1.0 + ((y + -1.0) / z)));
	elseif (z <= 1.16e-32)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + (a * (z / ((t - z) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -155000000000.0], N[(x + N[(a * N[(-1.0 + N[(N[(y + -1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.16e-32], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e11

   1. Initial program 96.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around 0 86.8%

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

   6. Taylor expanded in z around inf 86.8%

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

      1. +-commutative 86.8%

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

      2. mul-1-neg 86.8%

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

      3. sub-neg 86.8%

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

      4. div-sub 86.8%

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

      5. sub-neg 86.8%

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

      6. +-commutative 86.8%

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

      7. neg-mul-1 86.8%

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

      8. metadata-eval 86.8%

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

      9. distribute-lft-in 86.8%

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

      10. metadata-eval 86.8%

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

      11. sub-neg 86.8%

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

      12. associate-*r/ 86.8%

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

      13. mul-1-neg 86.8%

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

      14. unsub-neg 86.8%

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

      15. sub-neg 86.8%

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

      16. metadata-eval 86.8%

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

   8. Simplified 86.8%

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

   if -1.55e11 < z < 1.16000000000000001e-32

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   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 89.5%

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

   if 1.16000000000000001e-32 < z

   1. Initial program 93.0%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. associate--l+ 83.6%

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

      3. +-commutative 83.6%

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

      4. distribute-neg-frac2 83.6%

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

      5. +-commutative 83.6%

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

      6. distribute-neg-in 83.6%

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

      7. metadata-eval 83.6%

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

      8. unsub-neg 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -155000000000:\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y + -1}{z}\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-32}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2400:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+56}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2400.0)
   (+ x (* (/ a t) (- z y)))
   (if (<= t 8e+56)
     (+ x (* a (/ (- y z) (+ z -1.0))))
     (+ x (/ (- z y) (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2400.0) {
		tmp = x + ((a / t) * (z - y));
	} else if (t <= 8e+56) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x + ((z - y) / (t / 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 <= (-2400.0d0)) then
        tmp = x + ((a / t) * (z - y))
    else if (t <= 8d+56) then
        tmp = x + (a * ((y - z) / (z + (-1.0d0))))
    else
        tmp = x + ((z - y) / (t / 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 <= -2400.0) {
		tmp = x + ((a / t) * (z - y));
	} else if (t <= 8e+56) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x + ((z - y) / (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2400.0:
		tmp = x + ((a / t) * (z - y))
	elif t <= 8e+56:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	else:
		tmp = x + ((z - y) / (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2400.0)
		tmp = Float64(x + Float64(Float64(a / t) * Float64(z - y)));
	elseif (t <= 8e+56)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2400.0)
		tmp = x + ((a / t) * (z - y));
	elseif (t <= 8e+56)
		tmp = x + (a * ((y - z) / (z + -1.0)));
	else
		tmp = x + ((z - y) / (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2400.0], N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+56], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2400

   1. Initial program 98.4%

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

      1. clear-num 98.3%

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

      2. associate-/r/ 98.3%

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

      3. clear-num 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in t around inf 83.2%

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

   if -2400 < t < 8.00000000000000074e56

   1. Initial program 95.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 99.2%

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

   if 8.00000000000000074e56 < t

   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 inf 92.8%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2400:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+56}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+126} \lor \neg \left(z \leq 3.3 \cdot 10^{+115}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+126) (not (<= z 3.3e+115)))
   (- 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 <= -1.4e+126) || !(z <= 3.3e+115)) {
		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 <= (-1.4d+126)) .or. (.not. (z <= 3.3d+115))) 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 <= -1.4e+126) || !(z <= 3.3e+115)) {
		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 <= -1.4e+126) or not (z <= 3.3e+115):
		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 <= -1.4e+126) || !(z <= 3.3e+115))
		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 <= -1.4e+126) || ~((z <= 3.3e+115)))
		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, -1.4e+126], N[Not[LessEqual[z, 3.3e+115]], $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 < -1.40000000000000005e126 or 3.30000000000000005e115 < z

   1. Initial program 89.7%

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

   5. Taylor expanded in z around inf 86.1%

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

   if -1.40000000000000005e126 < z < 3.30000000000000005e115

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   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 79.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+126} \lor \neg \left(z \leq 3.3 \cdot 10^{+115}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{a}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+118}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e+21)
   (- x (* (/ a z) (- z y)))
   (if (<= z 2.4e+118) (+ x (* a (/ y (- -1.0 t)))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+21) {
		tmp = x - ((a / z) * (z - y));
	} else if (z <= 2.4e+118) {
		tmp = x + (a * (y / (-1.0 - 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 <= (-2.1d+21)) then
        tmp = x - ((a / z) * (z - y))
    else if (z <= 2.4d+118) then
        tmp = x + (a * (y / ((-1.0d0) - 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 <= -2.1e+21) {
		tmp = x - ((a / z) * (z - y));
	} else if (z <= 2.4e+118) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e+21:
		tmp = x - ((a / z) * (z - y))
	elif z <= 2.4e+118:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e+21)
		tmp = Float64(x - Float64(Float64(a / z) * Float64(z - y)));
	elseif (z <= 2.4e+118)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - 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 <= -2.1e+21)
		tmp = x - ((a / z) * (z - y));
	elseif (z <= 2.4e+118)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e+21], N[(x - N[(N[(a / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+118], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e21

   1. Initial program 96.3%

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

      1. clear-num 96.2%

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

      2. associate-/r/ 96.3%

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

      3. clear-num 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around inf 84.7%

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

      1. mul-1-neg 84.7%

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

      2. distribute-neg-frac2 84.7%

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

   7. Simplified 84.7%

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

   if -2.1e21 < z < 2.4e118

   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 82.1%

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

   if 2.4e118 < z

   1. Initial program 81.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 89.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{a}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+118}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{+121}:\\ \;\;\;\;x + \frac{a}{\left(t - z\right) + 1} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y + -1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 1.7e+121)
   (+ x (* (/ a (+ (- t z) 1.0)) (- z y)))
   (+ x (* a (+ -1.0 (/ (+ y -1.0) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.7e+121) {
		tmp = x + ((a / ((t - z) + 1.0)) * (z - y));
	} else {
		tmp = x + (a * (-1.0 + ((y + -1.0) / z)));
	}
	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 <= 1.7d+121) then
        tmp = x + ((a / ((t - z) + 1.0d0)) * (z - y))
    else
        tmp = x + (a * ((-1.0d0) + ((y + (-1.0d0)) / z)))
    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 <= 1.7e+121) {
		tmp = x + ((a / ((t - z) + 1.0)) * (z - y));
	} else {
		tmp = x + (a * (-1.0 + ((y + -1.0) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.7e+121:
		tmp = x + ((a / ((t - z) + 1.0)) * (z - y))
	else:
		tmp = x + (a * (-1.0 + ((y + -1.0) / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.7e+121)
		tmp = Float64(x + Float64(Float64(a / Float64(Float64(t - z) + 1.0)) * Float64(z - y)));
	else
		tmp = Float64(x + Float64(a * Float64(-1.0 + Float64(Float64(y + -1.0) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.7e+121)
		tmp = x + ((a / ((t - z) + 1.0)) * (z - y));
	else
		tmp = x + (a * (-1.0 + ((y + -1.0) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 1.7e+121], N[(x + N[(N[(a / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(-1.0 + N[(N[(y + -1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.70000000000000005e121

   1. Initial program 99.0%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 98.9%

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

      3. clear-num 99.0%

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

   4. Applied egg-rr 99.0%

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

   if 1.70000000000000005e121 < z

   1. Initial program 81.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around 0 98.9%

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

   6. Taylor expanded in z around inf 98.9%

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

      1. +-commutative 98.9%

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

      2. mul-1-neg 98.9%

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

      3. sub-neg 98.9%

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

      4. div-sub 98.9%

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

      5. sub-neg 98.9%

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

      6. +-commutative 98.9%

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

      7. neg-mul-1 98.9%

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

      8. metadata-eval 98.9%

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

      9. distribute-lft-in 98.9%

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

      10. metadata-eval 98.9%

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

      11. sub-neg 98.9%

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

      12. associate-*r/ 98.9%

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

      13. mul-1-neg 98.9%

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

      14. unsub-neg 98.9%

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

      15. sub-neg 98.9%

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

      16. metadata-eval 98.9%

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

   8. Simplified 98.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{+121}:\\ \;\;\;\;x + \frac{a}{\left(t - z\right) + 1} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y + -1}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-6} \lor \neg \left(z \leq 1.6\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e-6) (not (<= z 1.6))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e-6) || !(z <= 1.6)) {
		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 <= (-2.4d-6)) .or. (.not. (z <= 1.6d0))) 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 <= -2.4e-6) || !(z <= 1.6)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e-6) or not (z <= 1.6):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e-6) || !(z <= 1.6))
		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 <= -2.4e-6) || ~((z <= 1.6)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e-6], N[Not[LessEqual[z, 1.6]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3999999999999999e-6 or 1.6000000000000001 < z

   1. Initial program 94.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 71.4%

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

   if -2.3999999999999999e-6 < z < 1.6000000000000001

   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 89.2%

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

   6. Taylor expanded in t around 0 71.3%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-6} \lor \neg \left(z \leq 1.6\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+21} \lor \neg \left(z \leq 7.2 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+21) (not (<= z 7.2e-7))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+21) || !(z <= 7.2e-7)) {
		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 <= (-1.3d+21)) .or. (.not. (z <= 7.2d-7))) 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 <= -1.3e+21) || !(z <= 7.2e-7)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e+21) or not (z <= 7.2e-7):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+21) || !(z <= 7.2e-7))
		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 <= -1.3e+21) || ~((z <= 7.2e-7)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+21], N[Not[LessEqual[z, 7.2e-7]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e21 or 7.19999999999999989e-7 < 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/ 99.9%

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

   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 73.5%

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

   if -1.3e21 < z < 7.19999999999999989e-7

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-/r/ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. associate-*l/ 97.7%

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

      6. associate-/l* 99.9%

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

      7. fma-define 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. sub-neg 99.9%

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

      12. distribute-neg-in 99.9%

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

      13. remove-double-neg 99.9%

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

      14. +-commutative 99.9%

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

      15. sub-neg 99.9%

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

      16. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 52.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+21} \lor \neg \left(z \leq 7.2 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.0% 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. 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-rgt-neg-in 99.9%

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

   5. associate-*l/ 87.5%

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

   6. associate-/l* 96.9%

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

   7. fma-define 96.9%

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

   8. distribute-frac-neg 96.9%

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

   9. distribute-neg-frac2 96.9%

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

   10. distribute-neg-in 96.9%

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

   11. sub-neg 96.9%

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

   12. distribute-neg-in 96.9%

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

   13. remove-double-neg 96.9%

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

   14. +-commutative 96.9%

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

   15. sub-neg 96.9%

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

   16. metadata-eval 96.9%

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

3. Simplified 96.9%

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

5. Taylor expanded in a around 0 50.0%

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

6. Final simplification 50.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.6% 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 2024115 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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