Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2

Percentage Accurate: 86.3% → 99.4%

Time: 9.4s

Alternatives: 11

Speedup: 1.1×

• 23.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (* 2.0 z) (- 1.0 t))) (* z t)))))
   (if (<= t_1 INFINITY) t_1 (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(2.0 * z) * Float64(1.0 - t))) / Float64(z * t)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(2.0 * z), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x y) (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (-.f64 1 t))) (*.f64 t z))) < +inf.0

   1. Initial program 99.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   if +inf.0 < (+.f64 (/.f64 x y) (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (-.f64 1 t))) (*.f64 t z)))

   1. Initial program 0.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 97.6%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} + \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq \infty:\\ \;\;\;\;\frac{x}{y} + \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 2: 79.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{y} + 2 \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 0.47:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+37} \lor \neg \left(t \leq 1.75 \cdot 10^{+99}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (- (/ x y) 2.0)))
   (if (<= t -2.9e-21)
     t_2
     (if (<= t -1.5e-92)
       t_1
       (if (<= t -2.15e-144)
         (+ (/ x y) (* 2.0 (/ 1.0 t)))
         (if (<= t 0.47)
           t_1
           (if (or (<= t 1.9e+37) (not (<= t 1.75e+99)))
             t_2
             (+ -2.0 (/ (/ 2.0 t) z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.9e-21) {
		tmp = t_2;
	} else if (t <= -1.5e-92) {
		tmp = t_1;
	} else if (t <= -2.15e-144) {
		tmp = (x / y) + (2.0 * (1.0 / t));
	} else if (t <= 0.47) {
		tmp = t_1;
	} else if ((t <= 1.9e+37) || !(t <= 1.75e+99)) {
		tmp = t_2;
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = (x / y) - 2.0d0
    if (t <= (-2.9d-21)) then
        tmp = t_2
    else if (t <= (-1.5d-92)) then
        tmp = t_1
    else if (t <= (-2.15d-144)) then
        tmp = (x / y) + (2.0d0 * (1.0d0 / t))
    else if (t <= 0.47d0) then
        tmp = t_1
    else if ((t <= 1.9d+37) .or. (.not. (t <= 1.75d+99))) then
        tmp = t_2
    else
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.9e-21) {
		tmp = t_2;
	} else if (t <= -1.5e-92) {
		tmp = t_1;
	} else if (t <= -2.15e-144) {
		tmp = (x / y) + (2.0 * (1.0 / t));
	} else if (t <= 0.47) {
		tmp = t_1;
	} else if ((t <= 1.9e+37) || !(t <= 1.75e+99)) {
		tmp = t_2;
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -2.9e-21:
		tmp = t_2
	elif t <= -1.5e-92:
		tmp = t_1
	elif t <= -2.15e-144:
		tmp = (x / y) + (2.0 * (1.0 / t))
	elif t <= 0.47:
		tmp = t_1
	elif (t <= 1.9e+37) or not (t <= 1.75e+99):
		tmp = t_2
	else:
		tmp = -2.0 + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -2.9e-21)
		tmp = t_2;
	elseif (t <= -1.5e-92)
		tmp = t_1;
	elseif (t <= -2.15e-144)
		tmp = Float64(Float64(x / y) + Float64(2.0 * Float64(1.0 / t)));
	elseif (t <= 0.47)
		tmp = t_1;
	elseif ((t <= 1.9e+37) || !(t <= 1.75e+99))
		tmp = t_2;
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -2.9e-21)
		tmp = t_2;
	elseif (t <= -1.5e-92)
		tmp = t_1;
	elseif (t <= -2.15e-144)
		tmp = (x / y) + (2.0 * (1.0 / t));
	elseif (t <= 0.47)
		tmp = t_1;
	elseif ((t <= 1.9e+37) || ~((t <= 1.75e+99)))
		tmp = t_2;
	else
		tmp = -2.0 + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -2.9e-21], t$95$2, If[LessEqual[t, -1.5e-92], t$95$1, If[LessEqual[t, -2.15e-144], N[(N[(x / y), $MachinePrecision] + N[(2.0 * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.47], t$95$1, If[Or[LessEqual[t, 1.9e+37], N[Not[LessEqual[t, 1.75e+99]], $MachinePrecision]], t$95$2, N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9e-21 or 0.46999999999999997 < t < 1.89999999999999995e37 or 1.7499999999999999e99 < t

   1. Initial program 65.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 84.8%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   if -2.9e-21 < t < -1.50000000000000007e-92 or -2.14999999999999995e-144 < t < 0.46999999999999997

   1. Initial program 99.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 85.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 85.6%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 85.6%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 85.6%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   if -1.50000000000000007e-92 < t < -2.14999999999999995e-144

   1. Initial program 100.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in z around inf 92.9%

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]

   3. Taylor expanded in t around 0 92.9%

      \[\leadsto \frac{x}{y} + 2 \cdot \color{blue}{\frac{1}{t}} \]

   if 1.89999999999999995e37 < t < 1.7499999999999999e99

   1. Initial program 99.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 99.8%

      \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{-2 \cdot \left(t \cdot z\right)}}{t \cdot z} \]
   3. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{\left(t \cdot z\right) \cdot -2}}{t \cdot z} \]

      2. associate-*l* 99.8%

         \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{t \cdot \left(z \cdot -2\right)}}{t \cdot z} \]

   4. Simplified 99.8%

      \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{t \cdot \left(z \cdot -2\right)}}{t \cdot z} \]

   5. Taylor expanded in t around 0 99.8%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} - 2\right)} \]
   6. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(-2\right)\right)} \]

      2. associate-*r/ 99.8%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(-2\right)\right) \]

      3. metadata-eval 99.8%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(-2\right)\right) \]

      4. metadata-eval 99.8%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \color{blue}{-2}\right) \]

   7. Simplified 99.8%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + -2\right)} \]

   8. Taylor expanded in x around 0 83.9%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} - 2} \]
   9. Step-by-step derivation

      1. sub-neg 83.9%

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + \left(-2\right)} \]

      2. associate-*r/ 83.9%

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(-2\right) \]

      3. metadata-eval 83.9%

         \[\leadsto \frac{\color{blue}{2}}{t \cdot z} + \left(-2\right) \]

      4. associate-/r* 83.9%

         \[\leadsto \color{blue}{\frac{\frac{2}{t}}{z}} + \left(-2\right) \]

      5. metadata-eval 83.9%

         \[\leadsto \frac{\frac{2}{t}}{z} + \color{blue}{-2} \]

      6. +-commutative 83.9%

         \[\leadsto \color{blue}{-2 + \frac{\frac{2}{t}}{z}} \]

   10. Simplified 83.9%

       \[\leadsto \color{blue}{-2 + \frac{\frac{2}{t}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{y} + 2 \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 0.47:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+37} \lor \neg \left(t \leq 1.75 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \]

Alternative 3: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+162}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-94}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+249} \lor \neg \left(z \leq 2.6 \cdot 10^{+292}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -2.8e+203)
     t_1
     (if (<= z -4.1e+162)
       (/ 2.0 t)
       (if (<= z -1.85e-53)
         t_1
         (if (<= z 1e-94)
           (/ 2.0 (* z t))
           (if (or (<= z 4.2e+249) (not (<= z 2.6e+292))) t_1 (/ 2.0 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -2.8e+203) {
		tmp = t_1;
	} else if (z <= -4.1e+162) {
		tmp = 2.0 / t;
	} else if (z <= -1.85e-53) {
		tmp = t_1;
	} else if (z <= 1e-94) {
		tmp = 2.0 / (z * t);
	} else if ((z <= 4.2e+249) || !(z <= 2.6e+292)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-2.8d+203)) then
        tmp = t_1
    else if (z <= (-4.1d+162)) then
        tmp = 2.0d0 / t
    else if (z <= (-1.85d-53)) then
        tmp = t_1
    else if (z <= 1d-94) then
        tmp = 2.0d0 / (z * t)
    else if ((z <= 4.2d+249) .or. (.not. (z <= 2.6d+292))) then
        tmp = t_1
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -2.8e+203) {
		tmp = t_1;
	} else if (z <= -4.1e+162) {
		tmp = 2.0 / t;
	} else if (z <= -1.85e-53) {
		tmp = t_1;
	} else if (z <= 1e-94) {
		tmp = 2.0 / (z * t);
	} else if ((z <= 4.2e+249) || !(z <= 2.6e+292)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -2.8e+203:
		tmp = t_1
	elif z <= -4.1e+162:
		tmp = 2.0 / t
	elif z <= -1.85e-53:
		tmp = t_1
	elif z <= 1e-94:
		tmp = 2.0 / (z * t)
	elif (z <= 4.2e+249) or not (z <= 2.6e+292):
		tmp = t_1
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -2.8e+203)
		tmp = t_1;
	elseif (z <= -4.1e+162)
		tmp = Float64(2.0 / t);
	elseif (z <= -1.85e-53)
		tmp = t_1;
	elseif (z <= 1e-94)
		tmp = Float64(2.0 / Float64(z * t));
	elseif ((z <= 4.2e+249) || !(z <= 2.6e+292))
		tmp = t_1;
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -2.8e+203)
		tmp = t_1;
	elseif (z <= -4.1e+162)
		tmp = 2.0 / t;
	elseif (z <= -1.85e-53)
		tmp = t_1;
	elseif (z <= 1e-94)
		tmp = 2.0 / (z * t);
	elseif ((z <= 4.2e+249) || ~((z <= 2.6e+292)))
		tmp = t_1;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -2.8e+203], t$95$1, If[LessEqual[z, -4.1e+162], N[(2.0 / t), $MachinePrecision], If[LessEqual[z, -1.85e-53], t$95$1, If[LessEqual[z, 1e-94], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.2e+249], N[Not[LessEqual[z, 2.6e+292]], $MachinePrecision]], t$95$1, N[(2.0 / t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7999999999999999e203 or -4.0999999999999999e162 < z < -1.84999999999999991e-53 or 9.9999999999999996e-95 < z < 4.1999999999999997e249 or 2.5999999999999999e292 < z

   1. Initial program 74.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 69.1%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   if -2.7999999999999999e203 < z < -4.0999999999999999e162 or 4.1999999999999997e249 < z < 2.5999999999999999e292

   1. Initial program 84.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 79.7%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 79.7%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 79.7%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   5. Taylor expanded in z around inf 79.7%

      \[\leadsto \color{blue}{\frac{2}{t}} \]

   if -1.84999999999999991e-53 < z < 9.9999999999999996e-95

   1. Initial program 98.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 76.1%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 76.1%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 76.1%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 76.1%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   5. Taylor expanded in z around 0 76.2%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+203}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+162}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 10^{-94}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+249} \lor \neg \left(z \leq 2.6 \cdot 10^{+292}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 4: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{z \cdot t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-58}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 (* z t)))) (t_2 (- (/ x y) 2.0)))
   (if (<= t -1.15e+153)
     t_2
     (if (<= t -5.5e-108)
       t_1
       (if (<= t 1.32e-58)
         (/ (+ 2.0 (/ 2.0 z)) t)
         (if (<= t 7.6e+137) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / (z * t));
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.15e+153) {
		tmp = t_2;
	} else if (t <= -5.5e-108) {
		tmp = t_1;
	} else if (t <= 1.32e-58) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if (t <= 7.6e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) + (2.0d0 / (z * t))
    t_2 = (x / y) - 2.0d0
    if (t <= (-1.15d+153)) then
        tmp = t_2
    else if (t <= (-5.5d-108)) then
        tmp = t_1
    else if (t <= 1.32d-58) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else if (t <= 7.6d+137) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / (z * t));
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.15e+153) {
		tmp = t_2;
	} else if (t <= -5.5e-108) {
		tmp = t_1;
	} else if (t <= 1.32e-58) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if (t <= 7.6e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / (z * t))
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -1.15e+153:
		tmp = t_2
	elif t <= -5.5e-108:
		tmp = t_1
	elif t <= 1.32e-58:
		tmp = (2.0 + (2.0 / z)) / t
	elif t <= 7.6e+137:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)))
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.15e+153)
		tmp = t_2;
	elseif (t <= -5.5e-108)
		tmp = t_1;
	elseif (t <= 1.32e-58)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	elseif (t <= 7.6e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / (z * t));
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.15e+153)
		tmp = t_2;
	elseif (t <= -5.5e-108)
		tmp = t_1;
	elseif (t <= 1.32e-58)
		tmp = (2.0 + (2.0 / z)) / t;
	elseif (t <= 7.6e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.15e+153], t$95$2, If[LessEqual[t, -5.5e-108], t$95$1, If[LessEqual[t, 1.32e-58], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 7.6e+137], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1500000000000001e153 or 7.59999999999999926e137 < t

   1. Initial program 47.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 98.6%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   if -1.1500000000000001e153 < t < -5.50000000000000031e-108 or 1.31999999999999993e-58 < t < 7.59999999999999926e137

   1. Initial program 92.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in z around 0 75.4%

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]

   if -5.50000000000000031e-108 < t < 1.31999999999999993e-58

   1. Initial program 98.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 87.8%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 87.8%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 87.8%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 87.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-58}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 5: 80.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -5 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.82:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+38} \lor \neg \left(t \leq 1.25 \cdot 10^{+97}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -5e-18)
     t_1
     (if (<= t 0.82)
       (/ (+ 2.0 (/ 2.0 z)) t)
       (if (or (<= t 2.5e+38) (not (<= t 1.25e+97)))
         t_1
         (+ -2.0 (/ (/ 2.0 t) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -5e-18) {
		tmp = t_1;
	} else if (t <= 0.82) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if ((t <= 2.5e+38) || !(t <= 1.25e+97)) {
		tmp = t_1;
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-5d-18)) then
        tmp = t_1
    else if (t <= 0.82d0) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else if ((t <= 2.5d+38) .or. (.not. (t <= 1.25d+97))) then
        tmp = t_1
    else
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -5e-18) {
		tmp = t_1;
	} else if (t <= 0.82) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if ((t <= 2.5e+38) || !(t <= 1.25e+97)) {
		tmp = t_1;
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -5e-18:
		tmp = t_1
	elif t <= 0.82:
		tmp = (2.0 + (2.0 / z)) / t
	elif (t <= 2.5e+38) or not (t <= 1.25e+97):
		tmp = t_1
	else:
		tmp = -2.0 + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -5e-18)
		tmp = t_1;
	elseif (t <= 0.82)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	elseif ((t <= 2.5e+38) || !(t <= 1.25e+97))
		tmp = t_1;
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -5e-18)
		tmp = t_1;
	elseif (t <= 0.82)
		tmp = (2.0 + (2.0 / z)) / t;
	elseif ((t <= 2.5e+38) || ~((t <= 1.25e+97)))
		tmp = t_1;
	else
		tmp = -2.0 + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -5e-18], t$95$1, If[LessEqual[t, 0.82], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[t, 2.5e+38], N[Not[LessEqual[t, 1.25e+97]], $MachinePrecision]], t$95$1, N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.00000000000000036e-18 or 0.819999999999999951 < t < 2.49999999999999985e38 or 1.25e97 < t

   1. Initial program 65.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 84.8%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   if -5.00000000000000036e-18 < t < 0.819999999999999951

   1. Initial program 99.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 81.6%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 81.6%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 81.6%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   if 2.49999999999999985e38 < t < 1.25e97

   1. Initial program 99.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 99.8%

      \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{-2 \cdot \left(t \cdot z\right)}}{t \cdot z} \]
   3. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{\left(t \cdot z\right) \cdot -2}}{t \cdot z} \]

      2. associate-*l* 99.8%

         \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{t \cdot \left(z \cdot -2\right)}}{t \cdot z} \]

   4. Simplified 99.8%

      \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{t \cdot \left(z \cdot -2\right)}}{t \cdot z} \]

   5. Taylor expanded in t around 0 99.8%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} - 2\right)} \]
   6. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(-2\right)\right)} \]

      2. associate-*r/ 99.8%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(-2\right)\right) \]

      3. metadata-eval 99.8%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(-2\right)\right) \]

      4. metadata-eval 99.8%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \color{blue}{-2}\right) \]

   7. Simplified 99.8%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + -2\right)} \]

   8. Taylor expanded in x around 0 83.9%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} - 2} \]
   9. Step-by-step derivation

      1. sub-neg 83.9%

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + \left(-2\right)} \]

      2. associate-*r/ 83.9%

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(-2\right) \]

      3. metadata-eval 83.9%

         \[\leadsto \frac{\color{blue}{2}}{t \cdot z} + \left(-2\right) \]

      4. associate-/r* 83.9%

         \[\leadsto \color{blue}{\frac{\frac{2}{t}}{z}} + \left(-2\right) \]

      5. metadata-eval 83.9%

         \[\leadsto \frac{\frac{2}{t}}{z} + \color{blue}{-2} \]

      6. +-commutative 83.9%

         \[\leadsto \color{blue}{-2 + \frac{\frac{2}{t}}{z}} \]

   10. Simplified 83.9%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 0.82:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+38} \lor \neg \left(t \leq 1.25 \cdot 10^{+97}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \]

Alternative 6: 69.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0013 \lor \neg \left(\frac{x}{y} \leq 9.8 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -0.0013) (not (<= (/ x y) 9.8e+154)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.0013) || !((x / y) <= 9.8e+154)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-0.0013d0)) .or. (.not. ((x / y) <= 9.8d+154))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.0013) || !((x / y) <= 9.8e+154)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -0.0013) or not ((x / y) <= 9.8e+154):
		tmp = (x / y) - 2.0
	else:
		tmp = -2.0 + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -0.0013) || !(Float64(x / y) <= 9.8e+154))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -0.0013) || ~(((x / y) <= 9.8e+154)))
		tmp = (x / y) - 2.0;
	else
		tmp = -2.0 + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -0.0013], N[Not[LessEqual[N[(x / y), $MachinePrecision], 9.8e+154]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -0.0012999999999999999 or 9.8000000000000003e154 < (/.f64 x y)

   1. Initial program 81.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 73.6%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   if -0.0012999999999999999 < (/.f64 x y) < 9.8000000000000003e154

   1. Initial program 84.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 57.0%

      \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{-2 \cdot \left(t \cdot z\right)}}{t \cdot z} \]
   3. Step-by-step derivation

      1. *-commutative 57.0%

         \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{\left(t \cdot z\right) \cdot -2}}{t \cdot z} \]

      2. associate-*l* 57.0%

         \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{t \cdot \left(z \cdot -2\right)}}{t \cdot z} \]

   4. Simplified 57.0%

      \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{t \cdot \left(z \cdot -2\right)}}{t \cdot z} \]

   5. Taylor expanded in t around 0 72.1%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} - 2\right)} \]
   6. Step-by-step derivation

      1. sub-neg 72.1%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(-2\right)\right)} \]

      2. associate-*r/ 72.1%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(-2\right)\right) \]

      3. metadata-eval 72.1%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(-2\right)\right) \]

      4. metadata-eval 72.1%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \color{blue}{-2}\right) \]

   7. Simplified 72.1%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + -2\right)} \]

   8. Taylor expanded in x around 0 70.2%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} - 2} \]
   9. Step-by-step derivation

      1. sub-neg 70.2%

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + \left(-2\right)} \]

      2. associate-*r/ 70.2%

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(-2\right) \]

      3. metadata-eval 70.2%

         \[\leadsto \frac{\color{blue}{2}}{t \cdot z} + \left(-2\right) \]

      4. associate-/r* 70.1%

         \[\leadsto \color{blue}{\frac{\frac{2}{t}}{z}} + \left(-2\right) \]

      5. metadata-eval 70.1%

         \[\leadsto \frac{\frac{2}{t}}{z} + \color{blue}{-2} \]

      6. +-commutative 70.1%

         \[\leadsto \color{blue}{-2 + \frac{\frac{2}{t}}{z}} \]

   10. Simplified 70.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0013 \lor \neg \left(\frac{x}{y} \leq 9.8 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \]

Alternative 7: 92.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-27} \lor \neg \left(z \leq 4.7 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} + 2 \cdot \frac{1 - t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e-27) (not (<= z 4.7e-19)))
   (+ (/ x y) (* 2.0 (/ (- 1.0 t) t)))
   (+ (/ x y) (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-27) || !(z <= 4.7e-19)) {
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9d-27)) .or. (.not. (z <= 4.7d-19))) then
        tmp = (x / y) + (2.0d0 * ((1.0d0 - t) / t))
    else
        tmp = (x / y) + (2.0d0 / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-27) || !(z <= 4.7e-19)) {
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e-27) or not (z <= 4.7e-19):
		tmp = (x / y) + (2.0 * ((1.0 - t) / t))
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e-27) || !(z <= 4.7e-19))
		tmp = Float64(Float64(x / y) + Float64(2.0 * Float64(Float64(1.0 - t) / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9e-27) || ~((z <= 4.7e-19)))
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e-27], N[Not[LessEqual[z, 4.7e-19]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000003e-27 or 4.7e-19 < z

   1. Initial program 72.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in z around inf 97.7%

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]

   if -9.0000000000000003e-27 < z < 4.7e-19

   1. Initial program 98.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in z around 0 87.8%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-27} \lor \neg \left(z \leq 4.7 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} + 2 \cdot \frac{1 - t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 8: 98.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 2.05 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x}{y} + 2 \cdot \frac{1 - t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{z \cdot t} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 2.05e-17)))
   (+ (/ x y) (* 2.0 (/ (- 1.0 t) t)))
   (+ (/ x y) (+ (/ 2.0 (* z t)) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 2.05e-17)) {
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	} else {
		tmp = (x / y) + ((2.0 / (z * t)) + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 2.05d-17))) then
        tmp = (x / y) + (2.0d0 * ((1.0d0 - t) / t))
    else
        tmp = (x / y) + ((2.0d0 / (z * t)) + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 2.05e-17)) {
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	} else {
		tmp = (x / y) + ((2.0 / (z * t)) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 2.05e-17):
		tmp = (x / y) + (2.0 * ((1.0 - t) / t))
	else:
		tmp = (x / y) + ((2.0 / (z * t)) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 2.05e-17))
		tmp = Float64(Float64(x / y) + Float64(2.0 * Float64(Float64(1.0 - t) / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / Float64(z * t)) + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 2.05e-17)))
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	else
		tmp = (x / y) + ((2.0 / (z * t)) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 2.05e-17]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 2.05e-17 < z

   1. Initial program 72.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in z around inf 98.3%

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]

   if -1 < z < 2.05e-17

   1. Initial program 99.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 98.5%

      \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{-2 \cdot \left(t \cdot z\right)}}{t \cdot z} \]
   3. Step-by-step derivation

      1. *-commutative 98.5%

         \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{\left(t \cdot z\right) \cdot -2}}{t \cdot z} \]

      2. associate-*l* 98.5%

         \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{t \cdot \left(z \cdot -2\right)}}{t \cdot z} \]

   4. Simplified 98.5%

      \[\leadsto \frac{x}{y} + \frac{2 + \color{blue}{t \cdot \left(z \cdot -2\right)}}{t \cdot z} \]

   5. Taylor expanded in t around 0 98.5%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} - 2\right)} \]
   6. Step-by-step derivation

      1. sub-neg 98.5%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(-2\right)\right)} \]

      2. associate-*r/ 98.5%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(-2\right)\right) \]

      3. metadata-eval 98.5%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(-2\right)\right) \]

      4. metadata-eval 98.5%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \color{blue}{-2}\right) \]

   7. Simplified 98.5%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 2.05 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x}{y} + 2 \cdot \frac{1 - t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{z \cdot t} + -2\right)\\ \end{array} \]

Alternative 9: 47.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7500 \lor \neg \left(\frac{x}{y} \leq 1.6 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -7500.0) (not (<= (/ x y) 1.6e+43))) (/ x y) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -7500.0) || !((x / y) <= 1.6e+43)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-7500.0d0)) .or. (.not. ((x / y) <= 1.6d+43))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -7500.0) || !((x / y) <= 1.6e+43)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -7500.0) or not ((x / y) <= 1.6e+43):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -7500.0) || !(Float64(x / y) <= 1.6e+43))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -7500.0) || ~(((x / y) <= 1.6e+43)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -7500.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.6e+43]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -7500 or 1.60000000000000007e43 < (/.f64 x y)

   1. Initial program 81.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in x around inf 70.3%

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

   if -7500 < (/.f64 x y) < 1.60000000000000007e43

   1. Initial program 85.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 64.9%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 64.9%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 64.9%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 64.9%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   5. Taylor expanded in z around inf 29.7%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7500 \lor \neg \left(\frac{x}{y} \leq 1.6 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 10: 60.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-144} \lor \neg \left(t \leq 4.8 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.8e-144) (not (<= t 4.8e-63))) (- (/ x y) 2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-144) || !(t <= 4.8e-63)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.8d-144)) .or. (.not. (t <= 4.8d-63))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-144) || !(t <= 4.8e-63)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.8e-144) or not (t <= 4.8e-63):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.8e-144) || !(t <= 4.8e-63))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.8e-144) || ~((t <= 4.8e-63)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.8e-144], N[Not[LessEqual[t, 4.8e-63]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999998e-144 or 4.8000000000000001e-63 < t

   1. Initial program 75.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 70.3%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   if -2.79999999999999998e-144 < t < 4.8000000000000001e-63

   1. Initial program 98.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 90.0%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 90.0%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 90.0%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   5. Taylor expanded in z around inf 47.1%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-144} \lor \neg \left(t \leq 4.8 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 11: 20.2% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \frac{2}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ 2.0 t))

C

double code(double x, double y, double z, double t) {
	return 2.0 / t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 2.0d0 / t
end function

Java

public static double code(double x, double y, double z, double t) {
	return 2.0 / t;
}

Python

def code(x, y, z, t):
	return 2.0 / t

Julia

function code(x, y, z, t)
	return Float64(2.0 / t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 2.0 / t;
end

Wolfram

code[x_, y_, z_, t_] := N[(2.0 / t), $MachinePrecision]

Derivation

1. Initial program 83.5%

   \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

2. Taylor expanded in t around 0 51.1%

   \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
3. Step-by-step derivation

   1. associate-*r/ 51.1%

      \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

   2. metadata-eval 51.1%

      \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

4. Simplified 51.1%

   \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

5. Taylor expanded in z around inf 22.4%

   \[\leadsto \color{blue}{\frac{2}{t}} \]

6. Final simplification 22.4%

   \[\leadsto \frac{2}{t} \]

Developer target: 99.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((2.0d0 / z) + 2.0d0) / t) - (2.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
}

Python

def code(x, y, z, t):
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(2.0 / z) + 2.0) / t) - Float64(2.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(2.0 / z), $MachinePrecision] + 2.0), $MachinePrecision] / t), $MachinePrecision] - N[(2.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))