Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F

Percentage Accurate: 93.3% → 96.2%

Time: 11.4s

Alternatives: 13

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y * (z - t)) / 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)) / a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y * (z - t)) / 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)) / a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+285}:\\ \;\;\;\;x - t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 2e+285) (- x t_1) (- x (/ y (/ a (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= 2e+285) {
		tmp = x - t_1;
	} else {
		tmp = x - (y / (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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if (t_1 <= 2d+285) then
        tmp = x - t_1
    else
        tmp = x - (y / (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 t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= 2e+285) {
		tmp = x - t_1;
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= 2e+285:
		tmp = x - t_1
	else:
		tmp = x - (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= 2e+285)
		tmp = Float64(x - t_1);
	else
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= 2e+285)
		tmp = x - t_1;
	else
		tmp = x - (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+285], N[(x - t$95$1), $MachinePrecision], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < 2e285

   1. Initial program 98.2%

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

   if 2e285 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 72.7%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq 2 \cdot 10^{+285}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 2: 50.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.7 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-182}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+188}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+197}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.7e+42)
   (* y (/ t a))
   (if (<= t -4.4e-298)
     x
     (if (<= t 5.6e-182)
       (* z (/ (- y) a))
       (if (<= t 1.55e+46)
         x
         (if (<= t 3.4e+188)
           (* t (/ y a))
           (if (<= t 1.85e+197) x (/ t (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.7e+42) {
		tmp = y * (t / a);
	} else if (t <= -4.4e-298) {
		tmp = x;
	} else if (t <= 5.6e-182) {
		tmp = z * (-y / a);
	} else if (t <= 1.55e+46) {
		tmp = x;
	} else if (t <= 3.4e+188) {
		tmp = t * (y / a);
	} else if (t <= 1.85e+197) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	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 <= (-7.7d+42)) then
        tmp = y * (t / a)
    else if (t <= (-4.4d-298)) then
        tmp = x
    else if (t <= 5.6d-182) then
        tmp = z * (-y / a)
    else if (t <= 1.55d+46) then
        tmp = x
    else if (t <= 3.4d+188) then
        tmp = t * (y / a)
    else if (t <= 1.85d+197) then
        tmp = x
    else
        tmp = t / (a / y)
    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 <= -7.7e+42) {
		tmp = y * (t / a);
	} else if (t <= -4.4e-298) {
		tmp = x;
	} else if (t <= 5.6e-182) {
		tmp = z * (-y / a);
	} else if (t <= 1.55e+46) {
		tmp = x;
	} else if (t <= 3.4e+188) {
		tmp = t * (y / a);
	} else if (t <= 1.85e+197) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.7e+42:
		tmp = y * (t / a)
	elif t <= -4.4e-298:
		tmp = x
	elif t <= 5.6e-182:
		tmp = z * (-y / a)
	elif t <= 1.55e+46:
		tmp = x
	elif t <= 3.4e+188:
		tmp = t * (y / a)
	elif t <= 1.85e+197:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.7e+42)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= -4.4e-298)
		tmp = x;
	elseif (t <= 5.6e-182)
		tmp = Float64(z * Float64(Float64(-y) / a));
	elseif (t <= 1.55e+46)
		tmp = x;
	elseif (t <= 3.4e+188)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 1.85e+197)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.7e+42)
		tmp = y * (t / a);
	elseif (t <= -4.4e-298)
		tmp = x;
	elseif (t <= 5.6e-182)
		tmp = z * (-y / a);
	elseif (t <= 1.55e+46)
		tmp = x;
	elseif (t <= 3.4e+188)
		tmp = t * (y / a);
	elseif (t <= 1.85e+197)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.7e+42], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e-298], x, If[LessEqual[t, 5.6e-182], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+46], x, If[LessEqual[t, 3.4e+188], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+197], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.7000000000000001e42

   1. Initial program 90.7%

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

      1. associate-*r/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in x around 0 68.9%

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

      1. associate-/l* 73.3%

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

      2. associate-*r/ 73.3%

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

      3. neg-mul-1 73.3%

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

      4. *-rgt-identity 73.3%

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

      5. *-commutative 73.3%

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

      6. remove-double-neg 73.3%

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

      7. distribute-frac-neg 73.3%

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

      8. neg-mul-1 73.3%

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

      9. times-frac 73.3%

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

      10. metadata-eval 73.3%

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

      11. *-rgt-identity 73.3%

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

      12. associate-*r/ 73.4%

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

      13. associate-*l* 73.4%

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

      14. neg-mul-1 73.4%

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

      15. remove-double-neg 73.4%

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

      16. associate-/r/ 73.3%

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

      17. associate-*l/ 73.5%

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

      18. *-lft-identity 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in z around 0 62.1%

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

   if -7.7000000000000001e42 < t < -4.4e-298 or 5.59999999999999986e-182 < t < 1.54999999999999988e46 or 3.39999999999999995e188 < t < 1.8500000000000002e197

   1. Initial program 97.7%

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

      1. associate-*r/ 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around inf 57.9%

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

   if -4.4e-298 < t < 5.59999999999999986e-182

   1. Initial program 89.4%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. associate-*l/ 65.0%

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

      3. *-commutative 65.0%

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

   6. Simplified 65.0%

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

   if 1.54999999999999988e46 < t < 3.39999999999999995e188

   1. Initial program 93.6%

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

      1. associate-*r/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around inf 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*r/ 68.3%

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

   6. Simplified 68.3%

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

   if 1.8500000000000002e197 < t

   1. Initial program 86.6%

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

      1. associate-*r/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in t around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*r/ 78.6%

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

   6. Simplified 78.6%

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

      1. clear-num 78.6%

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

      2. div-inv 78.8%

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

   8. Applied egg-rr 78.8%

      \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.7 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-182}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+188}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+197}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 3: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;t \leq 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+187}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+197}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e+41)
   (* y (/ t a))
   (if (<= t -1.6e-298)
     x
     (if (<= t 7.8e-166)
       (* y (/ (- z) a))
       (if (<= t 1e+51)
         x
         (if (<= t 2.05e+187)
           (* t (/ y a))
           (if (<= t 2.3e+197) x (/ t (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+41) {
		tmp = y * (t / a);
	} else if (t <= -1.6e-298) {
		tmp = x;
	} else if (t <= 7.8e-166) {
		tmp = y * (-z / a);
	} else if (t <= 1e+51) {
		tmp = x;
	} else if (t <= 2.05e+187) {
		tmp = t * (y / a);
	} else if (t <= 2.3e+197) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	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 <= (-1.8d+41)) then
        tmp = y * (t / a)
    else if (t <= (-1.6d-298)) then
        tmp = x
    else if (t <= 7.8d-166) then
        tmp = y * (-z / a)
    else if (t <= 1d+51) then
        tmp = x
    else if (t <= 2.05d+187) then
        tmp = t * (y / a)
    else if (t <= 2.3d+197) then
        tmp = x
    else
        tmp = t / (a / y)
    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 <= -1.8e+41) {
		tmp = y * (t / a);
	} else if (t <= -1.6e-298) {
		tmp = x;
	} else if (t <= 7.8e-166) {
		tmp = y * (-z / a);
	} else if (t <= 1e+51) {
		tmp = x;
	} else if (t <= 2.05e+187) {
		tmp = t * (y / a);
	} else if (t <= 2.3e+197) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e+41:
		tmp = y * (t / a)
	elif t <= -1.6e-298:
		tmp = x
	elif t <= 7.8e-166:
		tmp = y * (-z / a)
	elif t <= 1e+51:
		tmp = x
	elif t <= 2.05e+187:
		tmp = t * (y / a)
	elif t <= 2.3e+197:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e+41)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= -1.6e-298)
		tmp = x;
	elseif (t <= 7.8e-166)
		tmp = Float64(y * Float64(Float64(-z) / a));
	elseif (t <= 1e+51)
		tmp = x;
	elseif (t <= 2.05e+187)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 2.3e+197)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.8e+41)
		tmp = y * (t / a);
	elseif (t <= -1.6e-298)
		tmp = x;
	elseif (t <= 7.8e-166)
		tmp = y * (-z / a);
	elseif (t <= 1e+51)
		tmp = x;
	elseif (t <= 2.05e+187)
		tmp = t * (y / a);
	elseif (t <= 2.3e+197)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e+41], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.6e-298], x, If[LessEqual[t, 7.8e-166], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+51], x, If[LessEqual[t, 2.05e+187], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+197], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.80000000000000013e41

   1. Initial program 90.7%

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

      1. associate-*r/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in x around 0 68.9%

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

      1. associate-/l* 73.3%

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

      2. associate-*r/ 73.3%

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

      3. neg-mul-1 73.3%

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

      4. *-rgt-identity 73.3%

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

      5. *-commutative 73.3%

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

      6. remove-double-neg 73.3%

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

      7. distribute-frac-neg 73.3%

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

      8. neg-mul-1 73.3%

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

      9. times-frac 73.3%

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

      10. metadata-eval 73.3%

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

      11. *-rgt-identity 73.3%

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

      12. associate-*r/ 73.4%

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

      13. associate-*l* 73.4%

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

      14. neg-mul-1 73.4%

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

      15. remove-double-neg 73.4%

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

      16. associate-/r/ 73.3%

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

      17. associate-*l/ 73.5%

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

      18. *-lft-identity 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in z around 0 62.1%

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

   if -1.80000000000000013e41 < t < -1.59999999999999999e-298 or 7.79999999999999998e-166 < t < 1e51 or 2.05e187 < t < 2.3000000000000001e197

   1. Initial program 97.6%

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

      1. associate-*r/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in x around inf 58.1%

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

   if -1.59999999999999999e-298 < t < 7.79999999999999998e-166

   1. Initial program 90.5%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 90.5%

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

      2. associate-*l/ 86.0%

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

      3. *-commutative 86.0%

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

      4. clear-num 86.0%

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

      5. un-div-inv 88.0%

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

   5. Applied egg-rr 88.0%

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

   6. Taylor expanded in z around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. associate-*r/ 72.8%

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

      3. distribute-rgt-neg-in 72.8%

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

      4. distribute-neg-frac 72.8%

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

   8. Simplified 72.8%

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

   if 1e51 < t < 2.05e187

   1. Initial program 93.6%

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

      1. associate-*r/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around inf 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*r/ 68.3%

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

   6. Simplified 68.3%

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

   if 2.3000000000000001e197 < t

   1. Initial program 86.6%

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

      1. associate-*r/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in t around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*r/ 78.6%

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

   6. Simplified 78.6%

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

      1. clear-num 78.6%

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

      2. div-inv 78.8%

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

   8. Applied egg-rr 78.8%

      \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;t \leq 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+187}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+197}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 4: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{+44} \lor \neg \left(t \leq 2.75 \cdot 10^{+54}\right) \land \left(t \leq 5 \cdot 10^{+186} \lor \neg \left(t \leq 1.8 \cdot 10^{+197}\right)\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.56e+44)
         (and (not (<= t 2.75e+54)) (or (<= t 5e+186) (not (<= t 1.8e+197)))))
   (* t (/ y a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.56e+44) || (!(t <= 2.75e+54) && ((t <= 5e+186) || !(t <= 1.8e+197)))) {
		tmp = t * (y / 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 ((t <= (-1.56d+44)) .or. (.not. (t <= 2.75d+54)) .and. (t <= 5d+186) .or. (.not. (t <= 1.8d+197))) then
        tmp = t * (y / 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 ((t <= -1.56e+44) || (!(t <= 2.75e+54) && ((t <= 5e+186) || !(t <= 1.8e+197)))) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.56e+44) or (not (t <= 2.75e+54) and ((t <= 5e+186) or not (t <= 1.8e+197))):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.56e+44) || (!(t <= 2.75e+54) && ((t <= 5e+186) || !(t <= 1.8e+197))))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.56e+44) || (~((t <= 2.75e+54)) && ((t <= 5e+186) || ~((t <= 1.8e+197)))))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.56e+44], And[N[Not[LessEqual[t, 2.75e+54]], $MachinePrecision], Or[LessEqual[t, 5e+186], N[Not[LessEqual[t, 1.8e+197]], $MachinePrecision]]]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.56e44 or 2.75000000000000013e54 < t < 4.99999999999999954e186 or 1.79999999999999991e197 < t

   1. Initial program 90.8%

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

      1. associate-*r/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around inf 65.3%

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

      1. *-commutative 65.3%

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

      2. associate-*r/ 67.6%

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

   6. Simplified 67.6%

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

   if -1.56e44 < t < 2.75000000000000013e54 or 4.99999999999999954e186 < t < 1.79999999999999991e197

   1. Initial program 95.9%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in x around inf 50.5%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{+44} \lor \neg \left(t \leq 2.75 \cdot 10^{+54}\right) \land \left(t \leq 5 \cdot 10^{+186} \lor \neg \left(t \leq 1.8 \cdot 10^{+197}\right)\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+188} \lor \neg \left(t \leq 1.8 \cdot 10^{+197}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+40)
   (* y (/ t a))
   (if (<= t 2e+51)
     x
     (if (or (<= t 3.4e+188) (not (<= t 1.8e+197))) (* t (/ y a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+40) {
		tmp = y * (t / a);
	} else if (t <= 2e+51) {
		tmp = x;
	} else if ((t <= 3.4e+188) || !(t <= 1.8e+197)) {
		tmp = t * (y / 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 (t <= (-1.7d+40)) then
        tmp = y * (t / a)
    else if (t <= 2d+51) then
        tmp = x
    else if ((t <= 3.4d+188) .or. (.not. (t <= 1.8d+197))) then
        tmp = t * (y / 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 (t <= -1.7e+40) {
		tmp = y * (t / a);
	} else if (t <= 2e+51) {
		tmp = x;
	} else if ((t <= 3.4e+188) || !(t <= 1.8e+197)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+40:
		tmp = y * (t / a)
	elif t <= 2e+51:
		tmp = x
	elif (t <= 3.4e+188) or not (t <= 1.8e+197):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+40)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= 2e+51)
		tmp = x;
	elseif ((t <= 3.4e+188) || !(t <= 1.8e+197))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+40)
		tmp = y * (t / a);
	elseif (t <= 2e+51)
		tmp = x;
	elseif ((t <= 3.4e+188) || ~((t <= 1.8e+197)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+40], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+51], x, If[Or[LessEqual[t, 3.4e+188], N[Not[LessEqual[t, 1.8e+197]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.69999999999999994e40

   1. Initial program 90.7%

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

      1. associate-*r/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in x around 0 68.9%

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

      1. associate-/l* 73.3%

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

      2. associate-*r/ 73.3%

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

      3. neg-mul-1 73.3%

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

      4. *-rgt-identity 73.3%

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

      5. *-commutative 73.3%

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

      6. remove-double-neg 73.3%

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

      7. distribute-frac-neg 73.3%

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

      8. neg-mul-1 73.3%

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

      9. times-frac 73.3%

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

      10. metadata-eval 73.3%

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

      11. *-rgt-identity 73.3%

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

      12. associate-*r/ 73.4%

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

      13. associate-*l* 73.4%

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

      14. neg-mul-1 73.4%

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

      15. remove-double-neg 73.4%

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

      16. associate-/r/ 73.3%

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

      17. associate-*l/ 73.5%

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

      18. *-lft-identity 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in z around 0 62.1%

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

   if -1.69999999999999994e40 < t < 2e51 or 3.39999999999999995e188 < t < 1.79999999999999991e197

   1. Initial program 95.9%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in x around inf 50.5%

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

   if 2e51 < t < 3.39999999999999995e188 or 1.79999999999999991e197 < t

   1. Initial program 90.9%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. associate-*r/ 72.3%

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

   6. Simplified 72.3%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+188} \lor \neg \left(t \leq 1.8 \cdot 10^{+197}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+188}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+197}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.3e+44)
   (* y (/ t a))
   (if (<= t 4.2e+51)
     x
     (if (<= t 3.4e+188) (* t (/ y a)) (if (<= t 1.9e+197) x (/ t (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+44) {
		tmp = y * (t / a);
	} else if (t <= 4.2e+51) {
		tmp = x;
	} else if (t <= 3.4e+188) {
		tmp = t * (y / a);
	} else if (t <= 1.9e+197) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	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 <= (-3.3d+44)) then
        tmp = y * (t / a)
    else if (t <= 4.2d+51) then
        tmp = x
    else if (t <= 3.4d+188) then
        tmp = t * (y / a)
    else if (t <= 1.9d+197) then
        tmp = x
    else
        tmp = t / (a / y)
    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 <= -3.3e+44) {
		tmp = y * (t / a);
	} else if (t <= 4.2e+51) {
		tmp = x;
	} else if (t <= 3.4e+188) {
		tmp = t * (y / a);
	} else if (t <= 1.9e+197) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.3e+44:
		tmp = y * (t / a)
	elif t <= 4.2e+51:
		tmp = x
	elif t <= 3.4e+188:
		tmp = t * (y / a)
	elif t <= 1.9e+197:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.3e+44)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= 4.2e+51)
		tmp = x;
	elseif (t <= 3.4e+188)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 1.9e+197)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.3e+44)
		tmp = y * (t / a);
	elseif (t <= 4.2e+51)
		tmp = x;
	elseif (t <= 3.4e+188)
		tmp = t * (y / a);
	elseif (t <= 1.9e+197)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.3e+44], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+51], x, If[LessEqual[t, 3.4e+188], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+197], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.30000000000000013e44

   1. Initial program 90.7%

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

      1. associate-*r/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in x around 0 68.9%

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

      1. associate-/l* 73.3%

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

      2. associate-*r/ 73.3%

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

      3. neg-mul-1 73.3%

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

      4. *-rgt-identity 73.3%

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

      5. *-commutative 73.3%

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

      6. remove-double-neg 73.3%

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

      7. distribute-frac-neg 73.3%

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

      8. neg-mul-1 73.3%

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

      9. times-frac 73.3%

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

      10. metadata-eval 73.3%

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

      11. *-rgt-identity 73.3%

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

      12. associate-*r/ 73.4%

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

      13. associate-*l* 73.4%

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

      14. neg-mul-1 73.4%

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

      15. remove-double-neg 73.4%

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

      16. associate-/r/ 73.3%

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

      17. associate-*l/ 73.5%

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

      18. *-lft-identity 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in z around 0 62.1%

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

   if -3.30000000000000013e44 < t < 4.2000000000000002e51 or 3.39999999999999995e188 < t < 1.9000000000000001e197

   1. Initial program 95.9%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in x around inf 50.5%

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

   if 4.2000000000000002e51 < t < 3.39999999999999995e188

   1. Initial program 93.6%

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

      1. associate-*r/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around inf 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*r/ 68.3%

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

   6. Simplified 68.3%

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

   if 1.9000000000000001e197 < t

   1. Initial program 86.6%

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

      1. associate-*r/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in t around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*r/ 78.6%

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

   6. Simplified 78.6%

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

      1. clear-num 78.6%

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

      2. div-inv 78.8%

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

   8. Applied egg-rr 78.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+188}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+197}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+100} \lor \neg \left(y \leq 2.6 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.9e+100) (not (<= y 2.6e+105)))
   (* (/ y a) (- t z))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e+100) || !(y <= 2.6e+105)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (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 ((y <= (-2.9d+100)) .or. (.not. (y <= 2.6d+105))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + (t * (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 ((y <= -2.9e+100) || !(y <= 2.6e+105)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.9e+100) or not (y <= 2.6e+105):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.9e+100) || !(y <= 2.6e+105))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.9e+100) || ~((y <= 2.6e+105)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.9e+100], N[Not[LessEqual[y, 2.6e+105]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e100 or 2.6000000000000002e105 < y

   1. Initial program 84.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. frac-2neg 99.9%

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

      2. div-inv 99.8%

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

      3. distribute-neg-frac 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. un-div-inv 99.9%

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

      2. clear-num 99.8%

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

      3. add-sqr-sqrt 37.8%

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

      4. sqrt-unprod 41.3%

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

      5. sqr-neg 41.3%

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

      6. sqrt-unprod 8.1%

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

      7. add-sqr-sqrt 11.6%

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

      8. add-sqr-sqrt 3.5%

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

      9. sqrt-unprod 42.0%

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

      10. sqr-neg 42.0%

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

      11. sqrt-unprod 55.0%

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

      12. add-sqr-sqrt 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in x around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. neg-sub0 75.9%

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

      3. associate-*l/ 82.5%

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

      4. sub-neg 82.5%

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

      5. distribute-rgt-out 62.8%

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

      6. distribute-lft-neg-out 62.8%

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

      7. unsub-neg 62.8%

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

      8. associate-+l- 62.8%

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

      9. neg-sub0 62.8%

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

      10. distribute-lft-neg-in 62.8%

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

      11. distribute-rgt-out 82.5%

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

      12. +-commutative 82.5%

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

      13. sub-neg 82.5%

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

   10. Simplified 82.5%

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

   if -2.9e100 < y < 2.6000000000000002e105

   1. Initial program 98.8%

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

      1. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 79.0%

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

      1. cancel-sign-sub-inv 79.0%

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

      2. metadata-eval 79.0%

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

      3. *-lft-identity 79.0%

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

      4. +-commutative 79.0%

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

      5. *-commutative 79.0%

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

      6. associate-*r/ 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+100} \lor \neg \left(y \leq 2.6 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+40} \lor \neg \left(t \leq 550000000000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e+40) (not (<= t 550000000000.0)))
   (+ x (* t (/ y a)))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+40) || !(t <= 550000000000.0)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (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 ((t <= (-2.5d+40)) .or. (.not. (t <= 550000000000.0d0))) then
        tmp = x + (t * (y / a))
    else
        tmp = x - (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 ((t <= -2.5e+40) || !(t <= 550000000000.0)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e+40) or not (t <= 550000000000.0):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e+40) || !(t <= 550000000000.0))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e+40) || ~((t <= 550000000000.0)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e+40], N[Not[LessEqual[t, 550000000000.0]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.50000000000000002e40 or 5.5e11 < t

   1. Initial program 92.1%

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

      1. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 85.4%

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

      1. cancel-sign-sub-inv 85.4%

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

      2. metadata-eval 85.4%

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

      3. *-lft-identity 85.4%

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

      4. +-commutative 85.4%

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

      5. *-commutative 85.4%

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

      6. associate-*r/ 90.2%

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

   6. Simplified 90.2%

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

   if -2.50000000000000002e40 < t < 5.5e11

   1. Initial program 95.5%

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

      1. associate-*r/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around inf 92.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+40} \lor \neg \left(t \leq 550000000000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 9: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+43} \lor \neg \left(t \leq 1.1 \cdot 10^{+25}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.2e+43) (not (<= t 1.1e+25)))
   (+ x (* t (/ y a)))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+43) || !(t <= 1.1e+25)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.2d+43)) .or. (.not. (t <= 1.1d+25))) then
        tmp = x + (t * (y / a))
    else
        tmp = x - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+43) || !(t <= 1.1e+25)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.2e+43) or not (t <= 1.1e+25):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.2e+43) || !(t <= 1.1e+25))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.2e+43) || ~((t <= 1.1e+25)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.2e+43], N[Not[LessEqual[t, 1.1e+25]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.2000000000000001e43 or 1.1e25 < t

   1. Initial program 92.1%

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

      1. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 85.4%

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

      1. cancel-sign-sub-inv 85.4%

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

      2. metadata-eval 85.4%

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

      3. *-lft-identity 85.4%

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

      4. +-commutative 85.4%

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

      5. *-commutative 85.4%

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

      6. associate-*r/ 90.2%

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

   6. Simplified 90.2%

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

   if -8.2000000000000001e43 < t < 1.1e25

   1. Initial program 95.5%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around inf 92.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+43} \lor \neg \left(t \leq 1.1 \cdot 10^{+25}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 10: 68.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.4 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.4e+154) x (if (<= a 2.6e+37) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.4e+154) {
		tmp = x;
	} else if (a <= 2.6e+37) {
		tmp = (y / a) * (t - z);
	} 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 (a <= (-9.4d+154)) then
        tmp = x
    else if (a <= 2.6d+37) then
        tmp = (y / a) * (t - z)
    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 (a <= -9.4e+154) {
		tmp = x;
	} else if (a <= 2.6e+37) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.4e+154:
		tmp = x
	elif a <= 2.6e+37:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.4e+154)
		tmp = x;
	elseif (a <= 2.6e+37)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.4e+154)
		tmp = x;
	elseif (a <= 2.6e+37)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.4e+154], x, If[LessEqual[a, 2.6e+37], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.39999999999999966e154 or 2.5999999999999999e37 < a

   1. Initial program 88.5%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 72.9%

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

   if -9.39999999999999966e154 < a < 2.5999999999999999e37

   1. Initial program 97.1%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

      1. frac-2neg 93.7%

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

      2. div-inv 93.5%

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

      3. distribute-neg-frac 93.5%

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

   5. Applied egg-rr 93.5%

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

      1. un-div-inv 93.7%

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

      2. clear-num 93.6%

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

      3. add-sqr-sqrt 50.5%

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

      4. sqrt-unprod 52.7%

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

      5. sqr-neg 52.7%

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

      6. sqrt-unprod 9.2%

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

      7. add-sqr-sqrt 21.0%

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

      8. add-sqr-sqrt 11.7%

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

      9. sqrt-unprod 55.6%

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

      10. sqr-neg 55.6%

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

      11. sqrt-unprod 51.4%

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

      12. add-sqr-sqrt 93.6%

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

   7. Applied egg-rr 93.6%

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

   8. Taylor expanded in x around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. neg-sub0 75.6%

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

      3. associate-*l/ 73.6%

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

      4. sub-neg 73.6%

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

      5. distribute-rgt-out 63.2%

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

      6. distribute-lft-neg-out 63.2%

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

      7. unsub-neg 63.2%

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

      8. associate-+l- 63.2%

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

      9. neg-sub0 63.2%

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

      10. distribute-lft-neg-in 63.2%

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

      11. distribute-rgt-out 73.6%

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

      12. +-commutative 73.6%

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

      13. sub-neg 73.6%

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

   10. Simplified 73.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.4 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 95.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.4 \cdot 10^{-112}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2.4e-112) (+ x (* y (/ (- t z) a))) (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.4e-112) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 2.4d-112) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + ((y / a) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.4e-112) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.4e-112:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.4e-112)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 2.4e-112)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.4e-112], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.4000000000000001e-112

   1. Initial program 93.8%

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

      1. associate-*r/ 97.1%

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

   3. Simplified 97.1%

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

   if 2.4000000000000001e-112 < t

   1. Initial program 94.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.4 \cdot 10^{-112}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 12: 93.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{t - z}{a} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. associate-*r/ 95.8%

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

3. Simplified 95.8%

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

4. Final simplification 95.8%

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

Alternative 13: 39.5% accurate, 9.0× 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 94.1%

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

   1. associate-*r/ 95.8%

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

3. Simplified 95.8%

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

4. Taylor expanded in x around inf 41.2%

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

5. Final simplification 41.2%

   \[\leadsto x \]

Developer target: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{t_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (- x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (- x (/ (* y (- z t)) a))
       (- x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x - (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x - ((y * (z - t)) / a)
    else
        tmp = x - (y / 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 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x - (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x - ((y * (z - t)) / a)
	else:
		tmp = x - (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x - Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x - Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x - Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x - (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x - ((y * (z - t)) / a);
	else
		tmp = x - (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x - N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))