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

Percentage Accurate: 96.7% → 99.7%

Time: 13.9s

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: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. sub-neg 96.9%

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

   2. +-commutative 96.9%

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

   3. associate-/r/ 99.9%

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

   4. distribute-lft-neg-in 99.9%

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

   5. fma-define 99.9%

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

   6. distribute-neg-frac2 99.9%

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

   7. distribute-neg-in 99.9%

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

   8. sub-neg 99.9%

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

   9. distribute-neg-in 99.9%

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

   10. remove-double-neg 99.9%

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

   11. +-commutative 99.9%

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

   12. sub-neg 99.9%

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

   13. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot a}{t}\\ \mathbf{if}\;z \leq -9500000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-262}:\\ \;\;\;\;\frac{y \cdot a}{-1 - t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* y a) t))))
   (if (<= z -9500000000000.0)
     (- x a)
     (if (<= z -9e-110)
       (+ x (/ z (/ t a)))
       (if (<= z -1.3e-245)
         t_1
         (if (<= z 8e-262)
           (/ (* y a) (- -1.0 t))
           (if (<= z 7e-10)
             t_1
             (if (<= z 2.3e+51) (+ x (/ (* y a) z)) (- x a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * a) / t);
	double tmp;
	if (z <= -9500000000000.0) {
		tmp = x - a;
	} else if (z <= -9e-110) {
		tmp = x + (z / (t / a));
	} else if (z <= -1.3e-245) {
		tmp = t_1;
	} else if (z <= 8e-262) {
		tmp = (y * a) / (-1.0 - t);
	} else if (z <= 7e-10) {
		tmp = t_1;
	} else if (z <= 2.3e+51) {
		tmp = x + ((y * a) / z);
	} 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) / t)
    if (z <= (-9500000000000.0d0)) then
        tmp = x - a
    else if (z <= (-9d-110)) then
        tmp = x + (z / (t / a))
    else if (z <= (-1.3d-245)) then
        tmp = t_1
    else if (z <= 8d-262) then
        tmp = (y * a) / ((-1.0d0) - t)
    else if (z <= 7d-10) then
        tmp = t_1
    else if (z <= 2.3d+51) then
        tmp = x + ((y * a) / z)
    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) / t);
	double tmp;
	if (z <= -9500000000000.0) {
		tmp = x - a;
	} else if (z <= -9e-110) {
		tmp = x + (z / (t / a));
	} else if (z <= -1.3e-245) {
		tmp = t_1;
	} else if (z <= 8e-262) {
		tmp = (y * a) / (-1.0 - t);
	} else if (z <= 7e-10) {
		tmp = t_1;
	} else if (z <= 2.3e+51) {
		tmp = x + ((y * a) / z);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y * a) / t)
	tmp = 0
	if z <= -9500000000000.0:
		tmp = x - a
	elif z <= -9e-110:
		tmp = x + (z / (t / a))
	elif z <= -1.3e-245:
		tmp = t_1
	elif z <= 8e-262:
		tmp = (y * a) / (-1.0 - t)
	elif z <= 7e-10:
		tmp = t_1
	elif z <= 2.3e+51:
		tmp = x + ((y * a) / z)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y * a) / t))
	tmp = 0.0
	if (z <= -9500000000000.0)
		tmp = Float64(x - a);
	elseif (z <= -9e-110)
		tmp = Float64(x + Float64(z / Float64(t / a)));
	elseif (z <= -1.3e-245)
		tmp = t_1;
	elseif (z <= 8e-262)
		tmp = Float64(Float64(y * a) / Float64(-1.0 - t));
	elseif (z <= 7e-10)
		tmp = t_1;
	elseif (z <= 2.3e+51)
		tmp = Float64(x + Float64(Float64(y * a) / z));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y * a) / t);
	tmp = 0.0;
	if (z <= -9500000000000.0)
		tmp = x - a;
	elseif (z <= -9e-110)
		tmp = x + (z / (t / a));
	elseif (z <= -1.3e-245)
		tmp = t_1;
	elseif (z <= 8e-262)
		tmp = (y * a) / (-1.0 - t);
	elseif (z <= 7e-10)
		tmp = t_1;
	elseif (z <= 2.3e+51)
		tmp = x + ((y * a) / z);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9500000000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, -9e-110], N[(x + N[(z / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-245], t$95$1, If[LessEqual[z, 8e-262], N[(N[(y * a), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-10], t$95$1, If[LessEqual[z, 2.3e+51], N[(x + N[(N[(y * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.5e12 or 2.30000000000000005e51 < 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/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 84.8%

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

   if -9.5e12 < z < -9.0000000000000002e-110

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 71.8%

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

   6. Taylor expanded in y around 0 72.7%

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

      1. cancel-sign-sub-inv 72.7%

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

      2. metadata-eval 72.7%

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

      3. *-lft-identity 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-/l* 72.7%

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

   8. Simplified 72.7%

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

      1. associate-*r/ 72.7%

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

      2. add-cube-cbrt 72.5%

         \[\leadsto \frac{a \cdot z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} + x \]

      3. times-frac 72.5%

         \[\leadsto \color{blue}{\frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}} + x \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}{\sqrt[3]{t}} + x \]

      5. sqrt-unprod 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{z \cdot z}}}{\sqrt[3]{t}} + x \]

      6. sqr-neg 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{\color{blue}{\left(-z\right) \cdot \left(-z\right)}}}{\sqrt[3]{t}} + x \]

      7. sqrt-unprod 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}{\sqrt[3]{t}} + x \]

      8. add-sqr-sqrt 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{-z}}{\sqrt[3]{t}} + x \]

      9. times-frac 56.7%

         \[\leadsto \color{blue}{\frac{a \cdot \left(-z\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} + x \]

      10. *-commutative 56.7%

          \[\leadsto \frac{\color{blue}{\left(-z\right) \cdot a}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}} + x \]

      11. add-cube-cbrt 56.7%

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

      12. associate-/l* 56.7%

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

      13. add-sqr-sqrt 56.7%

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

      14. sqrt-unprod 56.7%

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

      15. sqr-neg 56.7%

          \[\leadsto \sqrt{\color{blue}{z \cdot z}} \cdot \frac{a}{t} + x \]

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 76.5%

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

      18. clear-num 76.6%

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

      19. div-inv 76.6%

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

   10. Applied egg-rr 76.6%

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

   if -9.0000000000000002e-110 < z < -1.30000000000000003e-245 or 8.0000000000000001e-262 < z < 6.99999999999999961e-10

   1. Initial program 98.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 67.4%

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

   6. Taylor expanded in z around 0 64.1%

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

   if -1.30000000000000003e-245 < z < 8.0000000000000001e-262

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-/r/ 100.0%

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

      4. distribute-lft-neg-in 100.0%

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

      5. fma-define 100.0%

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

      6. distribute-neg-frac2 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. sub-neg 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. remove-double-neg 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 59.6%

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

   6. Taylor expanded in z around 0 59.6%

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

      1. associate-*r/ 59.6%

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

      2. neg-mul-1 59.6%

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

      3. distribute-rgt-neg-in 59.6%

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

   8. Simplified 59.6%

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

   if 6.99999999999999961e-10 < z < 2.30000000000000005e51

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 82.1%

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

      1. associate-*r/ 82.1%

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

      2. neg-mul-1 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in y around inf 82.9%

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

      1. associate-*r/ 82.9%

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

      2. neg-mul-1 82.9%

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

      3. distribute-rgt-neg-in 82.9%

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

   8. Simplified 82.9%

      \[\leadsto x - \color{blue}{\frac{a \cdot \left(-y\right)}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9500000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-262}:\\ \;\;\;\;\frac{y \cdot a}{-1 - t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x - \frac{y \cdot a}{t}\\ \mathbf{if}\;z \leq -78000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-245}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;\frac{y \cdot a}{-1 - t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (- 1.0 (/ y z))))) (t_2 (- x (/ (* y a) t))))
   (if (<= z -78000000000.0)
     t_1
     (if (<= z -8e-110)
       (+ x (/ z (/ t a)))
       (if (<= z -1.2e-245)
         t_2
         (if (<= z 4.6e-262)
           (/ (* y a) (- -1.0 t))
           (if (<= z 1.05e-10) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (1.0 - (y / z)));
	double t_2 = x - ((y * a) / t);
	double tmp;
	if (z <= -78000000000.0) {
		tmp = t_1;
	} else if (z <= -8e-110) {
		tmp = x + (z / (t / a));
	} else if (z <= -1.2e-245) {
		tmp = t_2;
	} else if (z <= 4.6e-262) {
		tmp = (y * a) / (-1.0 - t);
	} else if (z <= 1.05e-10) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x - (a * (1.0d0 - (y / z)))
    t_2 = x - ((y * a) / t)
    if (z <= (-78000000000.0d0)) then
        tmp = t_1
    else if (z <= (-8d-110)) then
        tmp = x + (z / (t / a))
    else if (z <= (-1.2d-245)) then
        tmp = t_2
    else if (z <= 4.6d-262) then
        tmp = (y * a) / ((-1.0d0) - t)
    else if (z <= 1.05d-10) then
        tmp = t_2
    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 * (1.0 - (y / z)));
	double t_2 = x - ((y * a) / t);
	double tmp;
	if (z <= -78000000000.0) {
		tmp = t_1;
	} else if (z <= -8e-110) {
		tmp = x + (z / (t / a));
	} else if (z <= -1.2e-245) {
		tmp = t_2;
	} else if (z <= 4.6e-262) {
		tmp = (y * a) / (-1.0 - t);
	} else if (z <= 1.05e-10) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (1.0 - (y / z)))
	t_2 = x - ((y * a) / t)
	tmp = 0
	if z <= -78000000000.0:
		tmp = t_1
	elif z <= -8e-110:
		tmp = x + (z / (t / a))
	elif z <= -1.2e-245:
		tmp = t_2
	elif z <= 4.6e-262:
		tmp = (y * a) / (-1.0 - t)
	elif z <= 1.05e-10:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(1.0 - Float64(y / z))))
	t_2 = Float64(x - Float64(Float64(y * a) / t))
	tmp = 0.0
	if (z <= -78000000000.0)
		tmp = t_1;
	elseif (z <= -8e-110)
		tmp = Float64(x + Float64(z / Float64(t / a)));
	elseif (z <= -1.2e-245)
		tmp = t_2;
	elseif (z <= 4.6e-262)
		tmp = Float64(Float64(y * a) / Float64(-1.0 - t));
	elseif (z <= 1.05e-10)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (1.0 - (y / z)));
	t_2 = x - ((y * a) / t);
	tmp = 0.0;
	if (z <= -78000000000.0)
		tmp = t_1;
	elseif (z <= -8e-110)
		tmp = x + (z / (t / a));
	elseif (z <= -1.2e-245)
		tmp = t_2;
	elseif (z <= 4.6e-262)
		tmp = (y * a) / (-1.0 - t);
	elseif (z <= 1.05e-10)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -78000000000.0], t$95$1, If[LessEqual[z, -8e-110], N[(x + N[(z / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-245], t$95$2, If[LessEqual[z, 4.6e-262], N[(N[(y * a), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-10], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.8e10 or 1.05e-10 < z

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. associate-*r/ 85.6%

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

      2. neg-mul-1 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in y around 0 78.8%

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

      1. *-rgt-identity 78.8%

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

      2. mul-1-neg 78.8%

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

      3. associate-/l* 90.1%

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

      4. distribute-rgt-neg-in 90.1%

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

      5. distribute-lft-in 90.1%

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

      6. sub-neg 90.1%

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

   8. Simplified 90.1%

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

   if -7.8e10 < z < -8.0000000000000004e-110

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 71.8%

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

   6. Taylor expanded in y around 0 72.7%

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

      1. cancel-sign-sub-inv 72.7%

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

      2. metadata-eval 72.7%

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

      3. *-lft-identity 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-/l* 72.7%

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

   8. Simplified 72.7%

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

      1. associate-*r/ 72.7%

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

      2. add-cube-cbrt 72.5%

         \[\leadsto \frac{a \cdot z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} + x \]

      3. times-frac 72.5%

         \[\leadsto \color{blue}{\frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}} + x \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}{\sqrt[3]{t}} + x \]

      5. sqrt-unprod 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{z \cdot z}}}{\sqrt[3]{t}} + x \]

      6. sqr-neg 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{\color{blue}{\left(-z\right) \cdot \left(-z\right)}}}{\sqrt[3]{t}} + x \]

      7. sqrt-unprod 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}{\sqrt[3]{t}} + x \]

      8. add-sqr-sqrt 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{-z}}{\sqrt[3]{t}} + x \]

      9. times-frac 56.7%

         \[\leadsto \color{blue}{\frac{a \cdot \left(-z\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} + x \]

      10. *-commutative 56.7%

          \[\leadsto \frac{\color{blue}{\left(-z\right) \cdot a}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}} + x \]

      11. add-cube-cbrt 56.7%

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

      12. associate-/l* 56.7%

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

      13. add-sqr-sqrt 56.7%

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

      14. sqrt-unprod 56.7%

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

      15. sqr-neg 56.7%

          \[\leadsto \sqrt{\color{blue}{z \cdot z}} \cdot \frac{a}{t} + x \]

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 76.5%

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

      18. clear-num 76.6%

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

      19. div-inv 76.6%

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

   10. Applied egg-rr 76.6%

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

   if -8.0000000000000004e-110 < z < -1.2e-245 or 4.6000000000000002e-262 < z < 1.05e-10

   1. Initial program 98.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 67.0%

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

   6. Taylor expanded in z around 0 64.8%

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

   if -1.2e-245 < z < 4.6000000000000002e-262

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-/r/ 100.0%

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

      4. distribute-lft-neg-in 100.0%

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

      5. fma-define 100.0%

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

      6. distribute-neg-frac2 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. sub-neg 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. remove-double-neg 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 59.6%

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

   6. Taylor expanded in z around 0 59.6%

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

      1. associate-*r/ 59.6%

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

      2. neg-mul-1 59.6%

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

      3. distribute-rgt-neg-in 59.6%

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

   8. Simplified 59.6%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-y\right)}{1 + t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -78000000000:\\ \;\;\;\;x - a \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-245}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;\frac{y \cdot a}{-1 - t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6900000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6900000.0)
   (- x a)
   (if (<= z -2.9e-108)
     (+ x (/ z (/ t a)))
     (if (<= z 3.3e-10)
       (- x (/ (* y a) t))
       (if (<= z 7.5e+50) (+ x (/ (* y a) z)) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6900000.0) {
		tmp = x - a;
	} else if (z <= -2.9e-108) {
		tmp = x + (z / (t / a));
	} else if (z <= 3.3e-10) {
		tmp = x - ((y * a) / t);
	} else if (z <= 7.5e+50) {
		tmp = x + ((y * a) / z);
	} 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 <= (-6900000.0d0)) then
        tmp = x - a
    else if (z <= (-2.9d-108)) then
        tmp = x + (z / (t / a))
    else if (z <= 3.3d-10) then
        tmp = x - ((y * a) / t)
    else if (z <= 7.5d+50) then
        tmp = x + ((y * a) / z)
    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 <= -6900000.0) {
		tmp = x - a;
	} else if (z <= -2.9e-108) {
		tmp = x + (z / (t / a));
	} else if (z <= 3.3e-10) {
		tmp = x - ((y * a) / t);
	} else if (z <= 7.5e+50) {
		tmp = x + ((y * a) / z);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6900000.0:
		tmp = x - a
	elif z <= -2.9e-108:
		tmp = x + (z / (t / a))
	elif z <= 3.3e-10:
		tmp = x - ((y * a) / t)
	elif z <= 7.5e+50:
		tmp = x + ((y * a) / z)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6900000.0)
		tmp = Float64(x - a);
	elseif (z <= -2.9e-108)
		tmp = Float64(x + Float64(z / Float64(t / a)));
	elseif (z <= 3.3e-10)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	elseif (z <= 7.5e+50)
		tmp = Float64(x + Float64(Float64(y * a) / z));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6900000.0)
		tmp = x - a;
	elseif (z <= -2.9e-108)
		tmp = x + (z / (t / a));
	elseif (z <= 3.3e-10)
		tmp = x - ((y * a) / t);
	elseif (z <= 7.5e+50)
		tmp = x + ((y * a) / z);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6900000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.9e-108], N[(x + N[(z / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e-10], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+50], N[(x + N[(N[(y * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.9e6 or 7.4999999999999999e50 < 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/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 84.8%

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

   if -6.9e6 < z < -2.9000000000000001e-108

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 71.8%

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

   6. Taylor expanded in y around 0 72.7%

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

      1. cancel-sign-sub-inv 72.7%

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

      2. metadata-eval 72.7%

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

      3. *-lft-identity 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-/l* 72.7%

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

   8. Simplified 72.7%

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

      1. associate-*r/ 72.7%

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

      2. add-cube-cbrt 72.5%

         \[\leadsto \frac{a \cdot z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} + x \]

      3. times-frac 72.5%

         \[\leadsto \color{blue}{\frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}} + x \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}{\sqrt[3]{t}} + x \]

      5. sqrt-unprod 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{z \cdot z}}}{\sqrt[3]{t}} + x \]

      6. sqr-neg 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{\color{blue}{\left(-z\right) \cdot \left(-z\right)}}}{\sqrt[3]{t}} + x \]

      7. sqrt-unprod 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}{\sqrt[3]{t}} + x \]

      8. add-sqr-sqrt 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{-z}}{\sqrt[3]{t}} + x \]

      9. times-frac 56.7%

         \[\leadsto \color{blue}{\frac{a \cdot \left(-z\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} + x \]

      10. *-commutative 56.7%

          \[\leadsto \frac{\color{blue}{\left(-z\right) \cdot a}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}} + x \]

      11. add-cube-cbrt 56.7%

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

      12. associate-/l* 56.7%

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

      13. add-sqr-sqrt 56.7%

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

      14. sqrt-unprod 56.7%

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

      15. sqr-neg 56.7%

          \[\leadsto \sqrt{\color{blue}{z \cdot z}} \cdot \frac{a}{t} + x \]

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 76.5%

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

      18. clear-num 76.6%

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

      19. div-inv 76.6%

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

   10. Applied egg-rr 76.6%

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

   if -2.9000000000000001e-108 < z < 3.3e-10

   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. Add Preprocessing

   5. Taylor expanded in t around inf 63.3%

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

   6. Taylor expanded in z around 0 59.0%

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

   if 3.3e-10 < z < 7.4999999999999999e50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 82.1%

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

      1. associate-*r/ 82.1%

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

      2. neg-mul-1 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in y around inf 82.9%

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

      1. associate-*r/ 82.9%

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

      2. neg-mul-1 82.9%

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

      3. distribute-rgt-neg-in 82.9%

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

   8. Simplified 82.9%

      \[\leadsto x - \color{blue}{\frac{a \cdot \left(-y\right)}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6900000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1960000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1960000000000.0)
   (- x a)
   (if (<= z -5.1e-108)
     (+ x (/ z (/ t a)))
     (if (<= z 1.05e-10) (- x (/ (* y a) t)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1960000000000.0) {
		tmp = x - a;
	} else if (z <= -5.1e-108) {
		tmp = x + (z / (t / a));
	} else if (z <= 1.05e-10) {
		tmp = x - ((y * a) / 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 <= (-1960000000000.0d0)) then
        tmp = x - a
    else if (z <= (-5.1d-108)) then
        tmp = x + (z / (t / a))
    else if (z <= 1.05d-10) then
        tmp = x - ((y * a) / 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 <= -1960000000000.0) {
		tmp = x - a;
	} else if (z <= -5.1e-108) {
		tmp = x + (z / (t / a));
	} else if (z <= 1.05e-10) {
		tmp = x - ((y * a) / t);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1960000000000.0:
		tmp = x - a
	elif z <= -5.1e-108:
		tmp = x + (z / (t / a))
	elif z <= 1.05e-10:
		tmp = x - ((y * a) / t)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1960000000000.0)
		tmp = Float64(x - a);
	elseif (z <= -5.1e-108)
		tmp = Float64(x + Float64(z / Float64(t / a)));
	elseif (z <= 1.05e-10)
		tmp = Float64(x - Float64(Float64(y * a) / 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 <= -1960000000000.0)
		tmp = x - a;
	elseif (z <= -5.1e-108)
		tmp = x + (z / (t / a));
	elseif (z <= 1.05e-10)
		tmp = x - ((y * a) / t);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1960000000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, -5.1e-108], N[(x + N[(z / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-10], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.96e12 or 1.05e-10 < 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. Add Preprocessing

   5. Taylor expanded in z around inf 80.5%

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

   if -1.96e12 < z < -5.1000000000000002e-108

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 71.8%

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

   6. Taylor expanded in y around 0 72.7%

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

      1. cancel-sign-sub-inv 72.7%

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

      2. metadata-eval 72.7%

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

      3. *-lft-identity 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-/l* 72.7%

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

   8. Simplified 72.7%

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

      1. associate-*r/ 72.7%

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

      2. add-cube-cbrt 72.5%

         \[\leadsto \frac{a \cdot z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} + x \]

      3. times-frac 72.5%

         \[\leadsto \color{blue}{\frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}} + x \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}{\sqrt[3]{t}} + x \]

      5. sqrt-unprod 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{z \cdot z}}}{\sqrt[3]{t}} + x \]

      6. sqr-neg 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{\color{blue}{\left(-z\right) \cdot \left(-z\right)}}}{\sqrt[3]{t}} + x \]

      7. sqrt-unprod 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}{\sqrt[3]{t}} + x \]

      8. add-sqr-sqrt 56.7%

         \[\leadsto \frac{a}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\color{blue}{-z}}{\sqrt[3]{t}} + x \]

      9. times-frac 56.7%

         \[\leadsto \color{blue}{\frac{a \cdot \left(-z\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} + x \]

      10. *-commutative 56.7%

          \[\leadsto \frac{\color{blue}{\left(-z\right) \cdot a}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}} + x \]

      11. add-cube-cbrt 56.7%

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

      12. associate-/l* 56.7%

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

      13. add-sqr-sqrt 56.7%

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

      14. sqrt-unprod 56.7%

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

      15. sqr-neg 56.7%

          \[\leadsto \sqrt{\color{blue}{z \cdot z}} \cdot \frac{a}{t} + x \]

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 76.5%

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

      18. clear-num 76.6%

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

      19. div-inv 76.6%

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

   10. Applied egg-rr 76.6%

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

   if -5.1000000000000002e-108 < z < 1.05e-10

   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. Add Preprocessing

   5. Taylor expanded in t around inf 63.0%

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

   6. Taylor expanded in z around 0 59.5%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1960000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+45}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.7e+37)
   (+ x (/ (- z y) (/ t a)))
   (if (<= t 8.5e+45)
     (- x (* a (/ (- y z) (- 1.0 z))))
     (+ x (* a (/ (- z y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.7e+37) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 8.5e+45) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else {
		tmp = x + (a * ((z - y) / 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 <= (-3.7d+37)) then
        tmp = x + ((z - y) / (t / a))
    else if (t <= 8.5d+45) then
        tmp = x - (a * ((y - z) / (1.0d0 - z)))
    else
        tmp = x + (a * ((z - y) / 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 <= -3.7e+37) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 8.5e+45) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.7e+37:
		tmp = x + ((z - y) / (t / a))
	elif t <= 8.5e+45:
		tmp = x - (a * ((y - z) / (1.0 - z)))
	else:
		tmp = x + (a * ((z - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.7e+37)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	elseif (t <= 8.5e+45)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.7e+37)
		tmp = x + ((z - y) / (t / a));
	elseif (t <= 8.5e+45)
		tmp = x - (a * ((y - z) / (1.0 - z)));
	else
		tmp = x + (a * ((z - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.7e+37], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+45], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6999999999999999e37

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 91.3%

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

   if -3.6999999999999999e37 < t < 8.4999999999999996e45

   1. Initial program 95.6%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 99.0%

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

   if 8.4999999999999996e45 < t

   1. Initial program 97.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 89.5%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+45}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3800000000 \lor \neg \left(z \leq 1.05 \cdot 10^{-10}\right):\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3800000000.0) (not (<= z 1.05e-10)))
   (+ x (* a (+ -1.0 (/ y z))))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3800000000.0) || !(z <= 1.05e-10)) {
		tmp = x + (a * (-1.0 + (y / 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 <= (-3800000000.0d0)) .or. (.not. (z <= 1.05d-10))) then
        tmp = x + (a * ((-1.0d0) + (y / 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 <= -3800000000.0) || !(z <= 1.05e-10)) {
		tmp = x + (a * (-1.0 + (y / z)));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3800000000.0) or not (z <= 1.05e-10):
		tmp = x + (a * (-1.0 + (y / z)))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3800000000.0) || !(z <= 1.05e-10))
		tmp = Float64(x + Float64(a * Float64(-1.0 + Float64(y / 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 <= -3800000000.0) || ~((z <= 1.05e-10)))
		tmp = x + (a * (-1.0 + (y / 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, -3800000000.0], N[Not[LessEqual[z, 1.05e-10]], $MachinePrecision]], N[(x + N[(a * N[(-1.0 + N[(y / z), $MachinePrecision]), $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 < -3.8e9 or 1.05e-10 < z

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. associate-*r/ 85.6%

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

      2. neg-mul-1 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in y around 0 78.8%

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

      1. *-rgt-identity 78.8%

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

      2. mul-1-neg 78.8%

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

      3. associate-/l* 90.1%

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

      4. distribute-rgt-neg-in 90.1%

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

      5. distribute-lft-in 90.1%

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

      6. sub-neg 90.1%

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

   8. Simplified 90.1%

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

   if -3.8e9 < z < 1.05e-10

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 93.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3800000000 \lor \neg \left(z \leq 1.05 \cdot 10^{-10}\right):\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -880000000000 \lor \neg \left(z \leq 3.8 \cdot 10^{-10}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -880000000000.0) (not (<= z 3.8e-10)))
   (- x a)
   (+ x (* a (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -880000000000.0) || !(z <= 3.8e-10)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (z / 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 <= (-880000000000.0d0)) .or. (.not. (z <= 3.8d-10))) then
        tmp = x - a
    else
        tmp = x + (a * (z / 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 <= -880000000000.0) || !(z <= 3.8e-10)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -880000000000.0) or not (z <= 3.8e-10):
		tmp = x - a
	else:
		tmp = x + (a * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -880000000000.0) || !(z <= 3.8e-10))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -880000000000.0) || ~((z <= 3.8e-10)))
		tmp = x - a;
	else
		tmp = x + (a * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -880000000000.0], N[Not[LessEqual[z, 3.8e-10]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8e11 or 3.7999999999999998e-10 < z

   1. Initial program 94.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 81.1%

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

   if -8.8e11 < z < 3.7999999999999998e-10

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 64.9%

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

   6. Taylor expanded in y around 0 55.0%

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

      1. cancel-sign-sub-inv 55.0%

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

      2. metadata-eval 55.0%

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

      3. *-lft-identity 55.0%

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

      4. +-commutative 55.0%

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

      5. associate-/l* 55.0%

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

   8. Simplified 55.0%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -880000000000 \lor \neg \left(z \leq 3.8 \cdot 10^{-10}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13200000 \lor \neg \left(z \leq 2.75 \cdot 10^{+29}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -13200000.0) (not (<= z 2.75e+29))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -13200000.0) || !(z <= 2.75e+29)) {
		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 <= (-13200000.0d0)) .or. (.not. (z <= 2.75d+29))) 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 <= -13200000.0) || !(z <= 2.75e+29)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -13200000.0) or not (z <= 2.75e+29):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -13200000.0) || !(z <= 2.75e+29))
		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 <= -13200000.0) || ~((z <= 2.75e+29)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -13200000.0], N[Not[LessEqual[z, 2.75e+29]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.32e7 or 2.75e29 < z

   1. Initial program 94.2%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 83.4%

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

   if -1.32e7 < z < 2.75e29

   1. Initial program 99.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 53.2%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13200000 \lor \neg \left(z \leq 2.75 \cdot 10^{+29}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 11: 54.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 51.7%

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

6. Final simplification 51.7%

   \[\leadsto x \]
7. Add Preprocessing

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 2024079 
(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))))