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

Percentage Accurate: 96.9% → 99.6%

Time: 14.2s

Alternatives: 14

Speedup: 1.0×

• could not determine a ground truth

  1. branch4585 = -1.2500676395587121e-284
  2. x = 6.3254187249544964e+50
  3. y = 6.638120248684861e+70
  4. z = 1.6871358311523156e+112
  5. t = -7.681582019098285e-37
  6. a = 1.796982370557324e-285

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: 96.9% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. sub-neg 96.2%

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

   2. +-commutative 96.2%

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

   3. associate-/r/ 99.7%

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

   4. distribute-lft-neg-in 99.7%

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

   5. fma-define 99.7%

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

   6. distribute-neg-frac2 99.7%

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

   7. distribute-neg-in 99.7%

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

   8. sub-neg 99.7%

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

   9. distribute-neg-in 99.7%

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

   10. remove-double-neg 99.7%

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

   11. +-commutative 99.7%

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

   12. sub-neg 99.7%

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

   13. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Final simplification 99.7%

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

Alternative 2: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ t_2 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;t \leq -14.5:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{-271}:\\ \;\;\;\;a \cdot \frac{y - z}{z + -1}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-6}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))) (t_2 (+ x (* a (/ (- z y) t)))))
   (if (<= t -14.5)
     t_2
     (if (<= t -3.6e-189)
       t_1
       (if (<= t 1e-271)
         (* a (/ (- y z) (+ z -1.0)))
         (if (<= t 1.6e-138) t_1 (if (<= t 9e-6) (- x a) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -14.5) {
		tmp = t_2;
	} else if (t <= -3.6e-189) {
		tmp = t_1;
	} else if (t <= 1e-271) {
		tmp = a * ((y - z) / (z + -1.0));
	} else if (t <= 1.6e-138) {
		tmp = t_1;
	} else if (t <= 9e-6) {
		tmp = x - a;
	} else {
		tmp = t_2;
	}
	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 - (y * a)
    t_2 = x + (a * ((z - y) / t))
    if (t <= (-14.5d0)) then
        tmp = t_2
    else if (t <= (-3.6d-189)) then
        tmp = t_1
    else if (t <= 1d-271) then
        tmp = a * ((y - z) / (z + (-1.0d0)))
    else if (t <= 1.6d-138) then
        tmp = t_1
    else if (t <= 9d-6) then
        tmp = x - a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -14.5) {
		tmp = t_2;
	} else if (t <= -3.6e-189) {
		tmp = t_1;
	} else if (t <= 1e-271) {
		tmp = a * ((y - z) / (z + -1.0));
	} else if (t <= 1.6e-138) {
		tmp = t_1;
	} else if (t <= 9e-6) {
		tmp = x - a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	t_2 = x + (a * ((z - y) / t))
	tmp = 0
	if t <= -14.5:
		tmp = t_2
	elif t <= -3.6e-189:
		tmp = t_1
	elif t <= 1e-271:
		tmp = a * ((y - z) / (z + -1.0))
	elif t <= 1.6e-138:
		tmp = t_1
	elif t <= 9e-6:
		tmp = x - a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	t_2 = Float64(x + Float64(a * Float64(Float64(z - y) / t)))
	tmp = 0.0
	if (t <= -14.5)
		tmp = t_2;
	elseif (t <= -3.6e-189)
		tmp = t_1;
	elseif (t <= 1e-271)
		tmp = Float64(a * Float64(Float64(y - z) / Float64(z + -1.0)));
	elseif (t <= 1.6e-138)
		tmp = t_1;
	elseif (t <= 9e-6)
		tmp = Float64(x - a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	t_2 = x + (a * ((z - y) / t));
	tmp = 0.0;
	if (t <= -14.5)
		tmp = t_2;
	elseif (t <= -3.6e-189)
		tmp = t_1;
	elseif (t <= 1e-271)
		tmp = a * ((y - z) / (z + -1.0));
	elseif (t <= 1.6e-138)
		tmp = t_1;
	elseif (t <= 9e-6)
		tmp = x - a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -14.5], t$95$2, If[LessEqual[t, -3.6e-189], t$95$1, If[LessEqual[t, 1e-271], N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-138], t$95$1, If[LessEqual[t, 9e-6], N[(x - a), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -14.5 or 9.00000000000000023e-6 < t

   1. Initial program 94.7%

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

      1. associate-/r/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around inf 83.4%

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

   if -14.5 < t < -3.60000000000000017e-189 or 9.99999999999999963e-272 < t < 1.60000000000000005e-138

   1. Initial program 97.2%

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

      1. associate-/r/ 97.2%

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

      2. clear-num 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in t around 0 97.1%

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

   8. Taylor expanded in z around 0 83.2%

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

   if -3.60000000000000017e-189 < t < 9.99999999999999963e-272

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-/r/ 99.9%

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

      2. clear-num 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 99.8%

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

   8. Taylor expanded in x around 0 57.7%

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

      1. mul-1-neg 57.7%

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

      2. associate-/l* 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. distribute-frac-neg2 73.7%

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

      5. neg-sub0 73.7%

         \[\leadsto a \cdot \frac{y - z}{\color{blue}{0 - \left(1 - z\right)}} \]

      6. associate--r- 73.7%

         \[\leadsto a \cdot \frac{y - z}{\color{blue}{\left(0 - 1\right) + z}} \]

      7. metadata-eval 73.7%

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

   10. Simplified 73.7%

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

   if 1.60000000000000005e-138 < t < 9.00000000000000023e-6

   1. Initial program 96.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.3%

      \[\leadsto x - \color{blue}{a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -14.5:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-189}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 10^{-271}:\\ \;\;\;\;a \cdot \frac{y - z}{z + -1}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-138}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-6}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+20}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-133}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+134}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -1.45e+20)
     (- x a)
     (if (<= z 1.1e-196)
       t_1
       (if (<= z 3e-133)
         (- x (* y (/ a t)))
         (if (<= z 1.45e-7)
           t_1
           (if (<= z 1.05e+134) (+ x (/ a (/ z y))) (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -1.45e+20) {
		tmp = x - a;
	} else if (z <= 1.1e-196) {
		tmp = t_1;
	} else if (z <= 3e-133) {
		tmp = x - (y * (a / t));
	} else if (z <= 1.45e-7) {
		tmp = t_1;
	} else if (z <= 1.05e+134) {
		tmp = x + (a / (z / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * a)
    if (z <= (-1.45d+20)) then
        tmp = x - a
    else if (z <= 1.1d-196) then
        tmp = t_1
    else if (z <= 3d-133) then
        tmp = x - (y * (a / t))
    else if (z <= 1.45d-7) then
        tmp = t_1
    else if (z <= 1.05d+134) then
        tmp = x + (a / (z / y))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -1.45e+20) {
		tmp = x - a;
	} else if (z <= 1.1e-196) {
		tmp = t_1;
	} else if (z <= 3e-133) {
		tmp = x - (y * (a / t));
	} else if (z <= 1.45e-7) {
		tmp = t_1;
	} else if (z <= 1.05e+134) {
		tmp = x + (a / (z / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -1.45e+20:
		tmp = x - a
	elif z <= 1.1e-196:
		tmp = t_1
	elif z <= 3e-133:
		tmp = x - (y * (a / t))
	elif z <= 1.45e-7:
		tmp = t_1
	elif z <= 1.05e+134:
		tmp = x + (a / (z / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -1.45e+20)
		tmp = Float64(x - a);
	elseif (z <= 1.1e-196)
		tmp = t_1;
	elseif (z <= 3e-133)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (z <= 1.45e-7)
		tmp = t_1;
	elseif (z <= 1.05e+134)
		tmp = Float64(x + Float64(a / Float64(z / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (z <= -1.45e+20)
		tmp = x - a;
	elseif (z <= 1.1e-196)
		tmp = t_1;
	elseif (z <= 3e-133)
		tmp = x - (y * (a / t));
	elseif (z <= 1.45e-7)
		tmp = t_1;
	elseif (z <= 1.05e+134)
		tmp = x + (a / (z / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+20], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.1e-196], t$95$1, If[LessEqual[z, 3e-133], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-7], t$95$1, If[LessEqual[z, 1.05e+134], N[(x + N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45e20 or 1.05e134 < z

   1. Initial program 92.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.7%

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

   if -1.45e20 < z < 1.10000000000000007e-196 or 3.00000000000000019e-133 < z < 1.4499999999999999e-7

   1. Initial program 97.6%

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

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 97.6%

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

      2. clear-num 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in t around 0 81.1%

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

   8. Taylor expanded in z around 0 81.8%

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

   if 1.10000000000000007e-196 < z < 3.00000000000000019e-133

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 y around inf 94.8%

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

      1. *-commutative 94.8%

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

      2. associate--l+ 94.8%

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

      3. +-commutative 94.8%

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

      4. associate-*r/ 99.8%

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

      5. +-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in t around inf 90.2%

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

   if 1.4499999999999999e-7 < z < 1.05e134

   1. Initial program 99.8%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. associate--l+ 78.4%

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

      3. +-commutative 78.4%

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

      4. associate-*r/ 82.4%

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

      5. +-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in z around inf 67.4%

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

      1. +-commutative 67.4%

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

      2. associate-/l* 71.4%

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

   10. Simplified 71.4%

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

       1. clear-num 71.4%

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

       2. un-div-inv 71.5%

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

   12. Applied egg-rr 71.5%

       \[\leadsto \color{blue}{\frac{a}{\frac{z}{y}}} + x \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+20}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-196}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-133}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-7}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+134}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+134}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.8e+18)
   (- x a)
   (if (<= z 5.8e-8)
     (- x (* y a))
     (if (<= z 4.2e+134) (+ x (* a (/ y z))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.8e+18) {
		tmp = x - a;
	} else if (z <= 5.8e-8) {
		tmp = x - (y * a);
	} else if (z <= 4.2e+134) {
		tmp = x + (a * (y / 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 <= (-7.8d+18)) then
        tmp = x - a
    else if (z <= 5.8d-8) then
        tmp = x - (y * a)
    else if (z <= 4.2d+134) then
        tmp = x + (a * (y / 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 <= -7.8e+18) {
		tmp = x - a;
	} else if (z <= 5.8e-8) {
		tmp = x - (y * a);
	} else if (z <= 4.2e+134) {
		tmp = x + (a * (y / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.8e+18:
		tmp = x - a
	elif z <= 5.8e-8:
		tmp = x - (y * a)
	elif z <= 4.2e+134:
		tmp = x + (a * (y / z))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.8e+18)
		tmp = Float64(x - a);
	elseif (z <= 5.8e-8)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 4.2e+134)
		tmp = Float64(x + Float64(a * Float64(y / 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 <= -7.8e+18)
		tmp = x - a;
	elseif (z <= 5.8e-8)
		tmp = x - (y * a);
	elseif (z <= 4.2e+134)
		tmp = x + (a * (y / z));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.8e+18], N[(x - a), $MachinePrecision], If[LessEqual[z, 5.8e-8], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+134], N[(x + N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8e18 or 4.2000000000000002e134 < z

   1. Initial program 92.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.7%

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

   if -7.8e18 < z < 5.8000000000000003e-8

   1. Initial program 97.9%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 97.9%

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

      2. clear-num 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in t around 0 79.4%

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

   8. Taylor expanded in z around 0 80.0%

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

   if 5.8000000000000003e-8 < z < 4.2000000000000002e134

   1. Initial program 99.8%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. associate--l+ 78.4%

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

      3. +-commutative 78.4%

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

      4. associate-*r/ 82.4%

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

      5. +-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in z around inf 67.4%

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

      1. +-commutative 67.4%

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

      2. associate-/l* 71.4%

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

   10. Simplified 71.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+134}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+21}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-7}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+134}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.6e+21)
   (- x a)
   (if (<= z 1.45e-7)
     (- x (* y a))
     (if (<= z 1.4e+134) (+ x (/ a (/ z y))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+21) {
		tmp = x - a;
	} else if (z <= 1.45e-7) {
		tmp = x - (y * a);
	} else if (z <= 1.4e+134) {
		tmp = x + (a / (z / y));
	} 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 <= (-8.6d+21)) then
        tmp = x - a
    else if (z <= 1.45d-7) then
        tmp = x - (y * a)
    else if (z <= 1.4d+134) then
        tmp = x + (a / (z / y))
    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 <= -8.6e+21) {
		tmp = x - a;
	} else if (z <= 1.45e-7) {
		tmp = x - (y * a);
	} else if (z <= 1.4e+134) {
		tmp = x + (a / (z / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.6e+21:
		tmp = x - a
	elif z <= 1.45e-7:
		tmp = x - (y * a)
	elif z <= 1.4e+134:
		tmp = x + (a / (z / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.6e+21)
		tmp = Float64(x - a);
	elseif (z <= 1.45e-7)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 1.4e+134)
		tmp = Float64(x + Float64(a / Float64(z / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.6e+21)
		tmp = x - a;
	elseif (z <= 1.45e-7)
		tmp = x - (y * a);
	elseif (z <= 1.4e+134)
		tmp = x + (a / (z / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.6e+21], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.45e-7], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+134], N[(x + N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6e21 or 1.3999999999999999e134 < z

   1. Initial program 92.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.7%

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

   if -8.6e21 < z < 1.4499999999999999e-7

   1. Initial program 97.9%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 97.9%

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

      2. clear-num 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in t around 0 79.4%

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

   8. Taylor expanded in z around 0 80.0%

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

   if 1.4499999999999999e-7 < z < 1.3999999999999999e134

   1. Initial program 99.8%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. associate--l+ 78.4%

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

      3. +-commutative 78.4%

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

      4. associate-*r/ 82.4%

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

      5. +-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in z around inf 67.4%

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

      1. +-commutative 67.4%

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

      2. associate-/l* 71.4%

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

   10. Simplified 71.4%

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

       1. clear-num 71.4%

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

       2. un-div-inv 71.5%

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

   12. Applied egg-rr 71.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+21}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-7}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+134}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+116}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \frac{a}{\left(z - t\right) + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+116)
   (- x a)
   (if (<= z 1.22e+26)
     (+ x (* y (/ a (+ (- z t) -1.0))))
     (- x (/ (- z y) (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+116) {
		tmp = x - a;
	} else if (z <= 1.22e+26) {
		tmp = x + (y * (a / ((z - t) + -1.0)));
	} else {
		tmp = x - ((z - y) / (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.5d+116)) then
        tmp = x - a
    else if (z <= 1.22d+26) then
        tmp = x + (y * (a / ((z - t) + (-1.0d0))))
    else
        tmp = x - ((z - y) / (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+116) {
		tmp = x - a;
	} else if (z <= 1.22e+26) {
		tmp = x + (y * (a / ((z - t) + -1.0)));
	} else {
		tmp = x - ((z - y) / (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+116:
		tmp = x - a
	elif z <= 1.22e+26:
		tmp = x + (y * (a / ((z - t) + -1.0)))
	else:
		tmp = x - ((z - y) / (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+116)
		tmp = Float64(x - a);
	elseif (z <= 1.22e+26)
		tmp = Float64(x + Float64(y * Float64(a / Float64(Float64(z - t) + -1.0))));
	else
		tmp = Float64(x - Float64(Float64(z - y) / Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+116)
		tmp = x - a;
	elseif (z <= 1.22e+26)
		tmp = x + (y * (a / ((z - t) + -1.0)));
	else
		tmp = x - ((z - y) / (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+116], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.22e+26], N[(x + N[(y * N[(a / N[(N[(z - t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z - y), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000004e116

   1. Initial program 88.6%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.9%

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

   if -9.5000000000000004e116 < z < 1.2200000000000001e26

   1. Initial program 98.1%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 90.0%

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

      1. *-commutative 90.0%

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

      2. associate--l+ 90.0%

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

      3. +-commutative 90.0%

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

      4. associate-*r/ 91.7%

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

      5. +-commutative 91.7%

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

   7. Simplified 91.7%

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

   if 1.2200000000000001e26 < z

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 86.7%

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

      1. mul-1-neg 86.7%

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

      2. distribute-neg-frac2 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+116}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \frac{a}{\left(z - t\right) + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+20}:\\ \;\;\;\;x + z \cdot \frac{a}{1 - \left(z - t\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \frac{a}{\left(z - t\right) + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+20)
   (+ x (* z (/ a (- 1.0 (- z t)))))
   (if (<= z 1.3e+26)
     (+ x (* y (/ a (+ (- z t) -1.0))))
     (- x (/ (- z y) (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+20) {
		tmp = x + (z * (a / (1.0 - (z - t))));
	} else if (z <= 1.3e+26) {
		tmp = x + (y * (a / ((z - t) + -1.0)));
	} else {
		tmp = x - ((z - y) / (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.2d+20)) then
        tmp = x + (z * (a / (1.0d0 - (z - t))))
    else if (z <= 1.3d+26) then
        tmp = x + (y * (a / ((z - t) + (-1.0d0))))
    else
        tmp = x - ((z - y) / (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+20) {
		tmp = x + (z * (a / (1.0 - (z - t))));
	} else if (z <= 1.3e+26) {
		tmp = x + (y * (a / ((z - t) + -1.0)));
	} else {
		tmp = x - ((z - y) / (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+20:
		tmp = x + (z * (a / (1.0 - (z - t))))
	elif z <= 1.3e+26:
		tmp = x + (y * (a / ((z - t) + -1.0)))
	else:
		tmp = x - ((z - y) / (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+20)
		tmp = Float64(x + Float64(z * Float64(a / Float64(1.0 - Float64(z - t)))));
	elseif (z <= 1.3e+26)
		tmp = Float64(x + Float64(y * Float64(a / Float64(Float64(z - t) + -1.0))));
	else
		tmp = Float64(x - Float64(Float64(z - y) / Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+20)
		tmp = x + (z * (a / (1.0 - (z - t))));
	elseif (z <= 1.3e+26)
		tmp = x + (y * (a / ((z - t) + -1.0)));
	else
		tmp = x - ((z - y) / (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+20], N[(x + N[(z * N[(a / N[(1.0 - N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+26], N[(x + N[(y * N[(a / N[(N[(z - t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z - y), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e20

   1. Initial program 92.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 y around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. *-commutative 64.3%

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

      3. associate--l+ 64.3%

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

      4. +-commutative 64.3%

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

      5. associate-*r/ 81.8%

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

      6. distribute-lft-neg-in 81.8%

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

      7. +-commutative 81.8%

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

   7. Simplified 81.8%

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

   if -1.2e20 < z < 1.30000000000000001e26

   1. Initial program 97.9%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 92.8%

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

      1. *-commutative 92.8%

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

      2. associate--l+ 92.8%

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

      3. +-commutative 92.8%

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

      4. associate-*r/ 94.1%

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

      5. +-commutative 94.1%

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

   7. Simplified 94.1%

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

   if 1.30000000000000001e26 < z

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 86.7%

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

      1. mul-1-neg 86.7%

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

      2. distribute-neg-frac2 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+20}:\\ \;\;\;\;x + z \cdot \frac{a}{1 - \left(z - t\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \frac{a}{\left(z - t\right) + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-60} \lor \neg \left(z \leq 2.8 \cdot 10^{+26}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-60) (not (<= z 2.8e+26)))
   (- x a)
   (+ x (/ (* y a) (- -1.0 t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-60) || !(z <= 2.8e+26)) {
		tmp = x - a;
	} else {
		tmp = x + ((y * a) / (-1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d-60)) .or. (.not. (z <= 2.8d+26))) then
        tmp = x - a
    else
        tmp = x + ((y * a) / ((-1.0d0) - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-60) || !(z <= 2.8e+26)) {
		tmp = x - a;
	} else {
		tmp = x + ((y * a) / (-1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-60) or not (z <= 2.8e+26):
		tmp = x - a
	else:
		tmp = x + ((y * a) / (-1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-60) || !(z <= 2.8e+26))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(Float64(y * a) / Float64(-1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-60) || ~((z <= 2.8e+26)))
		tmp = x - a;
	else
		tmp = x + ((y * a) / (-1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-60], N[Not[LessEqual[z, 2.8e+26]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(N[(y * a), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e-60 or 2.8e26 < z

   1. Initial program 94.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 75.7%

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

   if -2.7e-60 < z < 2.8e26

   1. Initial program 97.8%

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

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 93.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-60} \lor \neg \left(z \leq 2.8 \cdot 10^{+26}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-60} \lor \neg \left(z \leq 3.3 \cdot 10^{+26}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-60) (not (<= z 3.3e+26)))
   (- x (/ (- z y) (/ z a)))
   (+ x (/ (* y a) (- -1.0 t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-60) || !(z <= 3.3e+26)) {
		tmp = x - ((z - y) / (z / a));
	} else {
		tmp = x + ((y * a) / (-1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d-60)) .or. (.not. (z <= 3.3d+26))) then
        tmp = x - ((z - y) / (z / a))
    else
        tmp = x + ((y * a) / ((-1.0d0) - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-60) || !(z <= 3.3e+26)) {
		tmp = x - ((z - y) / (z / a));
	} else {
		tmp = x + ((y * a) / (-1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-60) or not (z <= 3.3e+26):
		tmp = x - ((z - y) / (z / a))
	else:
		tmp = x + ((y * a) / (-1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-60) || !(z <= 3.3e+26))
		tmp = Float64(x - Float64(Float64(z - y) / Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(y * a) / Float64(-1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-60) || ~((z <= 3.3e+26)))
		tmp = x - ((z - y) / (z / a));
	else
		tmp = x + ((y * a) / (-1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-60], N[Not[LessEqual[z, 3.3e+26]], $MachinePrecision]], N[(x - N[(N[(z - y), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * a), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e-60 or 3.29999999999999993e26 < z

   1. Initial program 94.3%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. mul-1-neg 82.3%

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

      2. distribute-neg-frac2 82.3%

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

   5. Simplified 82.3%

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

   if -2.7e-60 < z < 3.29999999999999993e26

   1. Initial program 97.8%

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

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 93.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-60} \lor \neg \left(z \leq 3.3 \cdot 10^{+26}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+21} \lor \neg \left(z \leq 1.45 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.8e+21) (not (<= z 1.45e-7))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+21) || !(z <= 1.45e-7)) {
		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 <= (-3.8d+21)) .or. (.not. (z <= 1.45d-7))) 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 <= -3.8e+21) || !(z <= 1.45e-7)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.8e+21) or not (z <= 1.45e-7):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.8e+21) || !(z <= 1.45e-7))
		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 <= -3.8e+21) || ~((z <= 1.45e-7)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.8e+21], N[Not[LessEqual[z, 1.45e-7]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e21 or 1.4499999999999999e-7 < 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 z around inf 74.3%

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

   if -3.8e21 < z < 1.4499999999999999e-7

   1. Initial program 97.9%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 97.9%

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

      2. clear-num 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in t around 0 79.4%

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

   8. Taylor expanded in z around 0 80.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+21} \lor \neg \left(z \leq 1.45 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-84} \lor \neg \left(z \leq 2.75 \cdot 10^{+31}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e-84) (not (<= z 2.75e+31))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e-84) || !(z <= 2.75e+31)) {
		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 <= (-1.15d-84)) .or. (.not. (z <= 2.75d+31))) 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 <= -1.15e-84) || !(z <= 2.75e+31)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e-84) or not (z <= 2.75e+31):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e-84) || !(z <= 2.75e+31))
		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 <= -1.15e-84) || ~((z <= 2.75e+31)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e-84], N[Not[LessEqual[z, 2.75e+31]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.1499999999999999e-84 or 2.75000000000000001e31 < z

   1. Initial program 94.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 75.2%

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

   if -1.1499999999999999e-84 < z < 2.75000000000000001e31

   1. Initial program 97.7%

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

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 61.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-84} \lor \neg \left(z \leq 2.75 \cdot 10^{+31}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. associate-/r/ 99.7%

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

3. Simplified 99.7%

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

5. Final simplification 99.7%

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

Alternative 13: 55.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-282}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-152}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.3e-282) x (if (<= x 2.8e-152) (- a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.3e-282) {
		tmp = x;
	} else if (x <= 2.8e-152) {
		tmp = -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 (x <= (-2.3d-282)) then
        tmp = x
    else if (x <= 2.8d-152) then
        tmp = -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 (x <= -2.3e-282) {
		tmp = x;
	} else if (x <= 2.8e-152) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.3e-282:
		tmp = x
	elif x <= 2.8e-152:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.3e-282)
		tmp = x;
	elseif (x <= 2.8e-152)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.3e-282)
		tmp = x;
	elseif (x <= 2.8e-152)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.3e-282], x, If[LessEqual[x, 2.8e-152], (-a), x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999999e-282 or 2.79999999999999984e-152 < x

   1. Initial program 97.4%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 64.4%

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

   if -2.2999999999999999e-282 < x < 2.79999999999999984e-152

   1. Initial program 90.9%

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

      1. associate-/r/ 90.9%

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

      2. clear-num 90.8%

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

   6. Applied egg-rr 90.8%

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

   7. Taylor expanded in t around 0 64.8%

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

   8. Taylor expanded in x around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. associate-/l* 63.5%

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

      3. distribute-rgt-neg-in 63.5%

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

      4. distribute-frac-neg2 63.5%

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

      5. neg-sub0 63.5%

         \[\leadsto a \cdot \frac{y - z}{\color{blue}{0 - \left(1 - z\right)}} \]

      6. associate--r- 63.5%

         \[\leadsto a \cdot \frac{y - z}{\color{blue}{\left(0 - 1\right) + z}} \]

      7. metadata-eval 63.5%

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

   10. Simplified 63.5%

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

   11. Taylor expanded in z around inf 41.2%

       \[\leadsto \color{blue}{-1 \cdot a} \]
   12. Step-by-step derivation

       1. neg-mul-1 41.2%

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

   13. Simplified 41.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-282}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-152}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.9% 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 96.2%

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

   1. associate-/r/ 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in x around inf 55.4%

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

6. Final simplification 55.4%

   \[\leadsto x \]
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 2024067 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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