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

Percentage Accurate: 86.1% → 99.4%

Time: 11.6s

Alternatives: 15

Speedup: 1.3×

• 23.4% 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: 86.1% 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 99.8%

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

   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 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := \frac{2}{z \cdot t}\\ t_3 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+213} \lor \neg \left(z \leq 4.9 \cdot 10^{+291}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (/ 2.0 (* z t))) (t_3 (+ -2.0 (/ 2.0 t))))
   (if (<= z -3.5e+108)
     t_3
     (if (<= z -3.7e-89)
       t_1
       (if (<= z 6.1e-120)
         t_2
         (if (<= z 9e-40)
           t_1
           (if (<= z 1.65e-11)
             t_2
             (if (or (<= z 7.2e+213) (not (<= z 4.9e+291))) t_1 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = 2.0 / (z * t);
	double t_3 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -3.5e+108) {
		tmp = t_3;
	} else if (z <= -3.7e-89) {
		tmp = t_1;
	} else if (z <= 6.1e-120) {
		tmp = t_2;
	} else if (z <= 9e-40) {
		tmp = t_1;
	} else if (z <= 1.65e-11) {
		tmp = t_2;
	} else if ((z <= 7.2e+213) || !(z <= 4.9e+291)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    t_2 = 2.0d0 / (z * t)
    t_3 = (-2.0d0) + (2.0d0 / t)
    if (z <= (-3.5d+108)) then
        tmp = t_3
    else if (z <= (-3.7d-89)) then
        tmp = t_1
    else if (z <= 6.1d-120) then
        tmp = t_2
    else if (z <= 9d-40) then
        tmp = t_1
    else if (z <= 1.65d-11) then
        tmp = t_2
    else if ((z <= 7.2d+213) .or. (.not. (z <= 4.9d+291))) then
        tmp = t_1
    else
        tmp = t_3
    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 t_2 = 2.0 / (z * t);
	double t_3 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -3.5e+108) {
		tmp = t_3;
	} else if (z <= -3.7e-89) {
		tmp = t_1;
	} else if (z <= 6.1e-120) {
		tmp = t_2;
	} else if (z <= 9e-40) {
		tmp = t_1;
	} else if (z <= 1.65e-11) {
		tmp = t_2;
	} else if ((z <= 7.2e+213) || !(z <= 4.9e+291)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	t_2 = 2.0 / (z * t)
	t_3 = -2.0 + (2.0 / t)
	tmp = 0
	if z <= -3.5e+108:
		tmp = t_3
	elif z <= -3.7e-89:
		tmp = t_1
	elif z <= 6.1e-120:
		tmp = t_2
	elif z <= 9e-40:
		tmp = t_1
	elif z <= 1.65e-11:
		tmp = t_2
	elif (z <= 7.2e+213) or not (z <= 4.9e+291):
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	t_2 = Float64(2.0 / Float64(z * t))
	t_3 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -3.5e+108)
		tmp = t_3;
	elseif (z <= -3.7e-89)
		tmp = t_1;
	elseif (z <= 6.1e-120)
		tmp = t_2;
	elseif (z <= 9e-40)
		tmp = t_1;
	elseif (z <= 1.65e-11)
		tmp = t_2;
	elseif ((z <= 7.2e+213) || !(z <= 4.9e+291))
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	t_2 = 2.0 / (z * t);
	t_3 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if (z <= -3.5e+108)
		tmp = t_3;
	elseif (z <= -3.7e-89)
		tmp = t_1;
	elseif (z <= 6.1e-120)
		tmp = t_2;
	elseif (z <= 9e-40)
		tmp = t_1;
	elseif (z <= 1.65e-11)
		tmp = t_2;
	elseif ((z <= 7.2e+213) || ~((z <= 4.9e+291)))
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+108], t$95$3, If[LessEqual[z, -3.7e-89], t$95$1, If[LessEqual[z, 6.1e-120], t$95$2, If[LessEqual[z, 9e-40], t$95$1, If[LessEqual[z, 1.65e-11], t$95$2, If[Or[LessEqual[z, 7.2e+213], N[Not[LessEqual[z, 4.9e+291]], $MachinePrecision]], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000002e108 or 7.2000000000000002e213 < z < 4.90000000000000004e291

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. div-sub 100.0%

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

      2. sub-neg 100.0%

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

      3. *-inverses 100.0%

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

      4. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 80.9%

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

      1. sub-neg 80.9%

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

      2. metadata-eval 80.9%

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

      3. distribute-lft-in 80.9%

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

      4. associate-*r/ 80.9%

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

      5. metadata-eval 80.9%

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

      6. metadata-eval 80.9%

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

   7. Simplified 80.9%

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

   if -3.5000000000000002e108 < z < -3.6999999999999997e-89 or 6.1e-120 < z < 9.0000000000000002e-40 or 1.6500000000000001e-11 < z < 7.2000000000000002e213 or 4.90000000000000004e291 < z

   1. Initial program 87.8%

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

   2. Taylor expanded in t around inf 71.2%

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

   if -3.6999999999999997e-89 < z < 6.1e-120 or 9.0000000000000002e-40 < z < 1.6500000000000001e-11

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0 95.7%

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

   3. Taylor expanded in z around 0 95.7%

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

      1. associate-*r/ 95.7%

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

      2. metadata-eval 95.7%

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

      3. associate-/r* 95.8%

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

      4. *-rgt-identity 95.8%

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

      5. associate-*r/ 95.6%

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

      6. *-commutative 95.6%

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

      7. metadata-eval 95.6%

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

      8. associate-*r/ 95.6%

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

      9. associate-*r* 95.6%

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

      10. associate-*l/ 95.6%

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

      11. metadata-eval 95.6%

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

      12. distribute-rgt-in 95.7%

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

      13. associate-*l/ 95.8%

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

      14. *-lft-identity 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in z around 0 77.6%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+108}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-120}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-11}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+213} \lor \neg \left(z \leq 4.9 \cdot 10^{+291}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 3: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := \frac{\frac{2}{t}}{z}\\ t_3 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+214} \lor \neg \left(z \leq 4.5 \cdot 10^{+292}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (/ (/ 2.0 t) z)) (t_3 (+ -2.0 (/ 2.0 t))))
   (if (<= z -1.25e+108)
     t_3
     (if (<= z -2.15e-89)
       t_1
       (if (<= z 8.2e-119)
         t_2
         (if (<= z 9.2e-40)
           t_1
           (if (<= z 1.65e-11)
             t_2
             (if (or (<= z 1.02e+214) (not (<= z 4.5e+292))) t_1 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = (2.0 / t) / z;
	double t_3 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.25e+108) {
		tmp = t_3;
	} else if (z <= -2.15e-89) {
		tmp = t_1;
	} else if (z <= 8.2e-119) {
		tmp = t_2;
	} else if (z <= 9.2e-40) {
		tmp = t_1;
	} else if (z <= 1.65e-11) {
		tmp = t_2;
	} else if ((z <= 1.02e+214) || !(z <= 4.5e+292)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    t_2 = (2.0d0 / t) / z
    t_3 = (-2.0d0) + (2.0d0 / t)
    if (z <= (-1.25d+108)) then
        tmp = t_3
    else if (z <= (-2.15d-89)) then
        tmp = t_1
    else if (z <= 8.2d-119) then
        tmp = t_2
    else if (z <= 9.2d-40) then
        tmp = t_1
    else if (z <= 1.65d-11) then
        tmp = t_2
    else if ((z <= 1.02d+214) .or. (.not. (z <= 4.5d+292))) then
        tmp = t_1
    else
        tmp = t_3
    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 t_2 = (2.0 / t) / z;
	double t_3 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.25e+108) {
		tmp = t_3;
	} else if (z <= -2.15e-89) {
		tmp = t_1;
	} else if (z <= 8.2e-119) {
		tmp = t_2;
	} else if (z <= 9.2e-40) {
		tmp = t_1;
	} else if (z <= 1.65e-11) {
		tmp = t_2;
	} else if ((z <= 1.02e+214) || !(z <= 4.5e+292)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	t_2 = (2.0 / t) / z
	t_3 = -2.0 + (2.0 / t)
	tmp = 0
	if z <= -1.25e+108:
		tmp = t_3
	elif z <= -2.15e-89:
		tmp = t_1
	elif z <= 8.2e-119:
		tmp = t_2
	elif z <= 9.2e-40:
		tmp = t_1
	elif z <= 1.65e-11:
		tmp = t_2
	elif (z <= 1.02e+214) or not (z <= 4.5e+292):
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	t_2 = Float64(Float64(2.0 / t) / z)
	t_3 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -1.25e+108)
		tmp = t_3;
	elseif (z <= -2.15e-89)
		tmp = t_1;
	elseif (z <= 8.2e-119)
		tmp = t_2;
	elseif (z <= 9.2e-40)
		tmp = t_1;
	elseif (z <= 1.65e-11)
		tmp = t_2;
	elseif ((z <= 1.02e+214) || !(z <= 4.5e+292))
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	t_2 = (2.0 / t) / z;
	t_3 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if (z <= -1.25e+108)
		tmp = t_3;
	elseif (z <= -2.15e-89)
		tmp = t_1;
	elseif (z <= 8.2e-119)
		tmp = t_2;
	elseif (z <= 9.2e-40)
		tmp = t_1;
	elseif (z <= 1.65e-11)
		tmp = t_2;
	elseif ((z <= 1.02e+214) || ~((z <= 4.5e+292)))
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+108], t$95$3, If[LessEqual[z, -2.15e-89], t$95$1, If[LessEqual[z, 8.2e-119], t$95$2, If[LessEqual[z, 9.2e-40], t$95$1, If[LessEqual[z, 1.65e-11], t$95$2, If[Or[LessEqual[z, 1.02e+214], N[Not[LessEqual[z, 4.5e+292]], $MachinePrecision]], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999998e108 or 1.02e214 < z < 4.49999999999999984e292

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. div-sub 100.0%

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

      2. sub-neg 100.0%

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

      3. *-inverses 100.0%

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

      4. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 80.9%

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

      1. sub-neg 80.9%

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

      2. metadata-eval 80.9%

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

      3. distribute-lft-in 80.9%

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

      4. associate-*r/ 80.9%

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

      5. metadata-eval 80.9%

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

      6. metadata-eval 80.9%

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

   7. Simplified 80.9%

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

   if -1.24999999999999998e108 < z < -2.14999999999999993e-89 or 8.20000000000000041e-119 < z < 9.2e-40 or 1.6500000000000001e-11 < z < 1.02e214 or 4.49999999999999984e292 < z

   1. Initial program 87.8%

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

   2. Taylor expanded in t around inf 71.2%

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

   if -2.14999999999999993e-89 < z < 8.20000000000000041e-119 or 9.2e-40 < z < 1.6500000000000001e-11

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0 95.7%

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

   3. Taylor expanded in z around 0 95.7%

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

      1. associate-*r/ 95.7%

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

      2. metadata-eval 95.7%

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

      3. associate-/r* 95.8%

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

      4. *-rgt-identity 95.8%

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

      5. associate-*r/ 95.6%

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

      6. *-commutative 95.6%

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

      7. metadata-eval 95.6%

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

      8. associate-*r/ 95.6%

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

      9. associate-*r* 95.6%

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

      10. associate-*l/ 95.6%

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

      11. metadata-eval 95.6%

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

      12. distribute-rgt-in 95.7%

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

      13. associate-*l/ 95.8%

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

      14. *-lft-identity 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in z around 0 77.6%

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

      1. associate-/r* 77.7%

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

   8. Simplified 77.7%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+108}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+214} \lor \neg \left(z \leq 4.5 \cdot 10^{+292}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 4: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} + \frac{2}{t}\\ t_3 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.44 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t))
        (t_2 (+ (/ x y) (/ 2.0 t)))
        (t_3 (- (/ x y) 2.0)))
   (if (<= t -1.5e+19)
     t_3
     (if (<= t -5.4e-57)
       t_1
       (if (<= t -1.44e-157)
         t_2
         (if (<= t 1.3e-276)
           t_1
           (if (<= t 5.3e-96) t_2 (if (<= t 1.45e-16) t_1 t_3))))))))

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 / t);
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.5e+19) {
		tmp = t_3;
	} else if (t <= -5.4e-57) {
		tmp = t_1;
	} else if (t <= -1.44e-157) {
		tmp = t_2;
	} else if (t <= 1.3e-276) {
		tmp = t_1;
	} else if (t <= 5.3e-96) {
		tmp = t_2;
	} else if (t <= 1.45e-16) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = (x / y) + (2.0d0 / t)
    t_3 = (x / y) - 2.0d0
    if (t <= (-1.5d+19)) then
        tmp = t_3
    else if (t <= (-5.4d-57)) then
        tmp = t_1
    else if (t <= (-1.44d-157)) then
        tmp = t_2
    else if (t <= 1.3d-276) then
        tmp = t_1
    else if (t <= 5.3d-96) then
        tmp = t_2
    else if (t <= 1.45d-16) then
        tmp = t_1
    else
        tmp = t_3
    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 / t);
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.5e+19) {
		tmp = t_3;
	} else if (t <= -5.4e-57) {
		tmp = t_1;
	} else if (t <= -1.44e-157) {
		tmp = t_2;
	} else if (t <= 1.3e-276) {
		tmp = t_1;
	} else if (t <= 5.3e-96) {
		tmp = t_2;
	} else if (t <= 1.45e-16) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) + (2.0 / t)
	t_3 = (x / y) - 2.0
	tmp = 0
	if t <= -1.5e+19:
		tmp = t_3
	elif t <= -5.4e-57:
		tmp = t_1
	elif t <= -1.44e-157:
		tmp = t_2
	elif t <= 1.3e-276:
		tmp = t_1
	elif t <= 5.3e-96:
		tmp = t_2
	elif t <= 1.45e-16:
		tmp = t_1
	else:
		tmp = t_3
	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) + Float64(2.0 / t))
	t_3 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.5e+19)
		tmp = t_3;
	elseif (t <= -5.4e-57)
		tmp = t_1;
	elseif (t <= -1.44e-157)
		tmp = t_2;
	elseif (t <= 1.3e-276)
		tmp = t_1;
	elseif (t <= 5.3e-96)
		tmp = t_2;
	elseif (t <= 1.45e-16)
		tmp = t_1;
	else
		tmp = t_3;
	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 / t);
	t_3 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.5e+19)
		tmp = t_3;
	elseif (t <= -5.4e-57)
		tmp = t_1;
	elseif (t <= -1.44e-157)
		tmp = t_2;
	elseif (t <= 1.3e-276)
		tmp = t_1;
	elseif (t <= 5.3e-96)
		tmp = t_2;
	elseif (t <= 1.45e-16)
		tmp = t_1;
	else
		tmp = t_3;
	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] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.5e+19], t$95$3, If[LessEqual[t, -5.4e-57], t$95$1, If[LessEqual[t, -1.44e-157], t$95$2, If[LessEqual[t, 1.3e-276], t$95$1, If[LessEqual[t, 5.3e-96], t$95$2, If[LessEqual[t, 1.45e-16], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5e19 or 1.4499999999999999e-16 < t

   1. Initial program 78.6%

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

   2. Taylor expanded in t around inf 78.4%

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

   if -1.5e19 < t < -5.4000000000000004e-57 or -1.43999999999999996e-157 < t < 1.29999999999999992e-276 or 5.3000000000000001e-96 < t < 1.4499999999999999e-16

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 91.0%

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

      1. associate-*r/ 91.0%

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

      2. metadata-eval 91.0%

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

   4. Simplified 91.0%

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

   if -5.4000000000000004e-57 < t < -1.43999999999999996e-157 or 1.29999999999999992e-276 < t < 5.3000000000000001e-96

   1. Initial program 96.1%

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

   2. Taylor expanded in t around 0 96.1%

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

   3. Taylor expanded in z around inf 80.9%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-57}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq -1.44 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-276}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-16}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 5: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{\frac{2}{t}}{z}\\ t_2 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ (/ 2.0 t) z))) (t_2 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -3.6e-89)
     t_2
     (if (<= z 7.9e-119)
       t_1
       (if (<= z 1.55e-43) (- (/ x y) 2.0) (if (<= z 8.5e-11) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + ((2.0 / t) / z);
	double t_2 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -3.6e-89) {
		tmp = t_2;
	} else if (z <= 7.9e-119) {
		tmp = t_1;
	} else if (z <= 1.55e-43) {
		tmp = (x / y) - 2.0;
	} else if (z <= 8.5e-11) {
		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 = (-2.0d0) + ((2.0d0 / t) / z)
    t_2 = (x / y) + ((-2.0d0) + (2.0d0 / t))
    if (z <= (-3.6d-89)) then
        tmp = t_2
    else if (z <= 7.9d-119) then
        tmp = t_1
    else if (z <= 1.55d-43) then
        tmp = (x / y) - 2.0d0
    else if (z <= 8.5d-11) 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 = -2.0 + ((2.0 / t) / z);
	double t_2 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -3.6e-89) {
		tmp = t_2;
	} else if (z <= 7.9e-119) {
		tmp = t_1;
	} else if (z <= 1.55e-43) {
		tmp = (x / y) - 2.0;
	} else if (z <= 8.5e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + ((2.0 / t) / z)
	t_2 = (x / y) + (-2.0 + (2.0 / t))
	tmp = 0
	if z <= -3.6e-89:
		tmp = t_2
	elif z <= 7.9e-119:
		tmp = t_1
	elif z <= 1.55e-43:
		tmp = (x / y) - 2.0
	elif z <= 8.5e-11:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(Float64(2.0 / t) / z))
	t_2 = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)))
	tmp = 0.0
	if (z <= -3.6e-89)
		tmp = t_2;
	elseif (z <= 7.9e-119)
		tmp = t_1;
	elseif (z <= 1.55e-43)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (z <= 8.5e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + ((2.0 / t) / z);
	t_2 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if (z <= -3.6e-89)
		tmp = t_2;
	elseif (z <= 7.9e-119)
		tmp = t_1;
	elseif (z <= 1.55e-43)
		tmp = (x / y) - 2.0;
	elseif (z <= 8.5e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e-89], t$95$2, If[LessEqual[z, 7.9e-119], t$95$1, If[LessEqual[z, 1.55e-43], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[z, 8.5e-11], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.60000000000000007e-89 or 8.50000000000000037e-11 < z

   1. Initial program 81.5%

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

   2. Taylor expanded in z around inf 94.6%

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

      1. div-sub 94.6%

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

      2. sub-neg 94.6%

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

      3. *-inverses 94.6%

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

      4. metadata-eval 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in x around 0 94.6%

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

      1. +-commutative 94.6%

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

      2. sub-neg 94.6%

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

      3. metadata-eval 94.6%

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

      4. distribute-lft-in 94.6%

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

      5. associate-*r/ 94.6%

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

      6. metadata-eval 94.6%

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

      7. metadata-eval 94.6%

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

   7. Simplified 94.6%

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

   if -3.60000000000000007e-89 < z < 7.9e-119 or 1.55e-43 < z < 8.50000000000000037e-11

   1. Initial program 97.7%

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

   2. Taylor expanded in t around inf 97.5%

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

      1. *-commutative 97.5%

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

      2. associate-*l* 97.5%

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

   4. Simplified 97.5%

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

   5. Taylor expanded in t around 0 97.5%

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

      1. sub-neg 97.5%

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

      2. associate-*r/ 97.5%

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

      3. metadata-eval 97.5%

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

      4. metadata-eval 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in x around 0 80.0%

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

      1. sub-neg 80.0%

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

      2. associate-*r/ 80.0%

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

      3. metadata-eval 80.0%

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

      4. associate-/r* 80.1%

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

      5. metadata-eval 80.1%

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

      6. +-commutative 80.1%

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

   10. Simplified 80.1%

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

   if 7.9e-119 < z < 1.55e-43

   1. Initial program 99.7%

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

   2. Taylor expanded in t around inf 82.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{-119}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]

Alternative 6: 74.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+100} \lor \neg \left(\frac{x}{y} \leq 3.1 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+100) (not (<= (/ x y) 3.1e+46)))
   (+ (/ x y) (/ 2.0 t))
   (+ -2.0 (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+100) || !((x / y) <= 3.1e+46)) {
		tmp = (x / y) + (2.0 / t);
	} 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) <= (-4d+100)) .or. (.not. ((x / y) <= 3.1d+46))) then
        tmp = (x / y) + (2.0d0 / t)
    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) <= -4e+100) || !((x / y) <= 3.1e+46)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e+100) or not ((x / y) <= 3.1e+46):
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = -2.0 + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e+100) || !(Float64(x / y) <= 3.1e+46))
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	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) <= -4e+100) || ~(((x / y) <= 3.1e+46)))
		tmp = (x / y) + (2.0 / t);
	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], -4e+100], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.1e+46]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $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) < -4.00000000000000006e100 or 3.09999999999999975e46 < (/.f64 x y)

   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 t around 0 98.1%

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

   3. Taylor expanded in z around inf 82.5%

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

   if -4.00000000000000006e100 < (/.f64 x y) < 3.09999999999999975e46

   1. Initial program 85.6%

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

   2. Taylor expanded in t around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. associate-*l* 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in t around 0 75.2%

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

      1. sub-neg 75.2%

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

      2. associate-*r/ 75.2%

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

      3. metadata-eval 75.2%

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

      4. metadata-eval 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in x around 0 71.4%

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

      1. sub-neg 71.4%

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

      2. associate-*r/ 71.4%

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

      3. metadata-eval 71.4%

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

      4. associate-/r* 71.4%

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

      5. metadata-eval 71.4%

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

      6. +-commutative 71.4%

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

   10. Simplified 71.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+100} \lor \neg \left(\frac{x}{y} \leq 3.1 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \]

Alternative 7: 98.3% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0)))
   (+ (/ x y) (+ -2.0 (/ 2.0 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 <= 1.0)) {
		tmp = (x / y) + (-2.0 + (2.0 / 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 <= 1.0d0))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / 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 <= 1.0)) {
		tmp = (x / y) + (-2.0 + (2.0 / 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 <= 1.0):
		tmp = (x / y) + (-2.0 + (2.0 / 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 <= 1.0))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / 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 <= 1.0)))
		tmp = (x / y) + (-2.0 + (2.0 / 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, 1.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / 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 1 < z

   1. Initial program 77.5%

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

   2. Taylor expanded in z around inf 99.3%

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

      1. div-sub 99.3%

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

      2. sub-neg 99.3%

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

      3. *-inverses 99.3%

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

      4. metadata-eval 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.3%

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

      1. +-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. associate-*r/ 99.3%

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

      6. metadata-eval 99.3%

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

      7. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

   if -1 < z < 1

   1. Initial program 98.3%

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

   2. Taylor expanded in t around inf 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l* 97.1%

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

   4. Simplified 97.1%

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

   5. Taylor expanded in t around 0 97.1%

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

      1. sub-neg 97.1%

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

      2. associate-*r/ 97.1%

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

      3. metadata-eval 97.1%

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

      4. metadata-eval 97.1%

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

   7. Simplified 97.1%

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

4. Final simplification 98.1%

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

Alternative 8: 98.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.86 \lor \neg \left(t \leq 8.5 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{z \cdot t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.86) (not (<= t 8.5e-30)))
   (+ (/ x y) (+ (/ 2.0 (* z t)) -2.0))
   (+ (/ x y) (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.86) || !(t <= 8.5e-30)) {
		tmp = (x / y) + ((2.0 / (z * t)) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 + (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 ((t <= (-0.86d0)) .or. (.not. (t <= 8.5d-30))) then
        tmp = (x / y) + ((2.0d0 / (z * t)) + (-2.0d0))
    else
        tmp = (x / y) + ((2.0d0 + (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 ((t <= -0.86) || !(t <= 8.5e-30)) {
		tmp = (x / y) + ((2.0 / (z * t)) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.86) or not (t <= 8.5e-30):
		tmp = (x / y) + ((2.0 / (z * t)) + -2.0)
	else:
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.86) || !(t <= 8.5e-30))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / Float64(z * t)) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -0.86) || ~((t <= 8.5e-30)))
		tmp = (x / y) + ((2.0 / (z * t)) + -2.0);
	else
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.86], N[Not[LessEqual[t, 8.5e-30]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.859999999999999987 or 8.49999999999999931e-30 < t

   1. Initial program 79.7%

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

   2. Taylor expanded in t around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-*l* 78.4%

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

   4. Simplified 78.4%

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

   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%

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

   if -0.859999999999999987 < t < 8.49999999999999931e-30

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0 98.1%

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

   3. Taylor expanded in z around 0 98.2%

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

      1. associate-*r/ 98.2%

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

      2. metadata-eval 98.2%

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

      3. associate-/r* 98.2%

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

      4. *-rgt-identity 98.2%

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

      5. associate-*r/ 98.2%

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

      6. *-commutative 98.2%

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

      7. metadata-eval 98.2%

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

      8. associate-*r/ 98.2%

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

      9. associate-*r* 98.2%

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

      10. associate-*l/ 98.2%

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

      11. metadata-eval 98.2%

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

      12. distribute-rgt-in 98.2%

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

      13. associate-*l/ 98.3%

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

      14. *-lft-identity 98.3%

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

   5. Simplified 98.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.86 \lor \neg \left(t \leq 8.5 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{z \cdot t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 9: 71.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.85 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.56 \cdot 10^{+47}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.85e+100)
   (/ x y)
   (if (<= (/ x y) 1.56e+47) (+ -2.0 (/ (/ 2.0 t) z)) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.85e+100) {
		tmp = x / y;
	} else if ((x / y) <= 1.56e+47) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else {
		tmp = (x / y) - 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 ((x / y) <= (-1.85d+100)) then
        tmp = x / y
    else if ((x / y) <= 1.56d+47) then
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.85e+100) {
		tmp = x / y;
	} else if ((x / y) <= 1.56e+47) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.85e+100:
		tmp = x / y
	elif (x / y) <= 1.56e+47:
		tmp = -2.0 + ((2.0 / t) / z)
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.85e+100)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.56e+47)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.85e+100)
		tmp = x / y;
	elseif ((x / y) <= 1.56e+47)
		tmp = -2.0 + ((2.0 / t) / z);
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.85e+100], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.56e+47], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.8500000000000001e100

   1. Initial program 90.2%

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

   2. Taylor expanded in x around inf 74.2%

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

   if -1.8500000000000001e100 < (/.f64 x y) < 1.55999999999999998e47

   1. Initial program 85.6%

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

   2. Taylor expanded in t around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. associate-*l* 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in t around 0 75.2%

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

      1. sub-neg 75.2%

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

      2. associate-*r/ 75.2%

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

      3. metadata-eval 75.2%

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

      4. metadata-eval 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in x around 0 71.4%

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

      1. sub-neg 71.4%

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

      2. associate-*r/ 71.4%

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

      3. metadata-eval 71.4%

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

      4. associate-/r* 71.4%

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

      5. metadata-eval 71.4%

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

      6. +-commutative 71.4%

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

   10. Simplified 71.4%

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

   if 1.55999999999999998e47 < (/.f64 x y)

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 75.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.85 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.56 \cdot 10^{+47}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 10: 65.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.5 \cdot 10^{+34} \lor \neg \left(\frac{x}{y} \leq 1300000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5.5e+34) (not (<= (/ x y) 1300000.0)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.5e+34) || !((x / y) <= 1300000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (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) <= (-5.5d+34)) .or. (.not. ((x / y) <= 1300000.0d0))) then
        tmp = x / y
    else
        tmp = (-2.0d0) + (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) <= -5.5e+34) || !((x / y) <= 1300000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5.5e+34) or not ((x / y) <= 1300000.0):
		tmp = x / y
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5.5e+34) || !(Float64(x / y) <= 1300000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5.5e+34) || ~(((x / y) <= 1300000.0)))
		tmp = x / y;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5.5e+34], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1300000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.4999999999999996e34 or 1.3e6 < (/.f64 x y)

   1. Initial program 91.1%

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

   2. Taylor expanded in x around inf 67.3%

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

   if -5.4999999999999996e34 < (/.f64 x y) < 1.3e6

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf 59.0%

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

      1. div-sub 59.0%

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

      2. sub-neg 59.0%

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

      3. *-inverses 59.0%

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

      4. metadata-eval 59.0%

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

   4. Simplified 59.0%

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

   5. Taylor expanded in x around 0 58.7%

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

      1. sub-neg 58.7%

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

      2. metadata-eval 58.7%

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

      3. distribute-lft-in 58.7%

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

      4. associate-*r/ 58.7%

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

      5. metadata-eval 58.7%

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

      6. metadata-eval 58.7%

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

   7. Simplified 58.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.5 \cdot 10^{+34} \lor \neg \left(\frac{x}{y} \leq 1300000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 11: 92.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.115 \lor \neg \left(z \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.115) (not (<= z 2e-5)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.115) || !(z <= 2e-5)) {
		tmp = (x / y) + (-2.0 + (2.0 / 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 <= (-0.115d0)) .or. (.not. (z <= 2d-5))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / 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 <= -0.115) || !(z <= 2e-5)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.115) or not (z <= 2e-5):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.115) || !(z <= 2e-5))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / 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 <= -0.115) || ~((z <= 2e-5)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.115], N[Not[LessEqual[z, 2e-5]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / 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 < -0.115000000000000005 or 2.00000000000000016e-5 < z

   1. Initial program 77.5%

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

   2. Taylor expanded in z around inf 99.3%

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

      1. div-sub 99.3%

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

      2. sub-neg 99.3%

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

      3. *-inverses 99.3%

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

      4. metadata-eval 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.3%

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

      1. +-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. associate-*r/ 99.3%

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

      6. metadata-eval 99.3%

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

      7. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

   if -0.115000000000000005 < z < 2.00000000000000016e-5

   1. Initial program 98.3%

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

   2. Taylor expanded in z around 0 91.4%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.115 \lor \neg \left(z \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 12: 92.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.11 \lor \neg \left(z \leq 1.3 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.11) (not (<= z 1.3e-5)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.11) || !(z <= 1.3e-5)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((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 ((z <= (-0.11d0)) .or. (.not. (z <= 1.3d-5))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + ((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 ((z <= -0.11) || !(z <= 1.3e-5)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.11) or not (z <= 1.3e-5):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.11) || !(z <= 1.3e-5))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.11) || ~((z <= 1.3e-5)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.11], N[Not[LessEqual[z, 1.3e-5]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.110000000000000001 or 1.29999999999999992e-5 < z

   1. Initial program 77.5%

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

   2. Taylor expanded in z around inf 99.3%

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

      1. div-sub 99.3%

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

      2. sub-neg 99.3%

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

      3. *-inverses 99.3%

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

      4. metadata-eval 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.3%

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

      1. +-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. associate-*r/ 99.3%

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

      6. metadata-eval 99.3%

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

      7. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

   if -0.110000000000000001 < z < 1.29999999999999992e-5

   1. Initial program 98.3%

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

   2. Taylor expanded in z around 0 91.4%

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

      1. associate-/r* 91.4%

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

   4. Simplified 91.4%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.11 \lor \neg \left(z \leq 1.3 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]

Alternative 13: 65.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.35 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 60000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.35e+35)
   (/ x y)
   (if (<= (/ x y) 60000.0) (+ -2.0 (/ 2.0 t)) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.35e+35) {
		tmp = x / y;
	} else if ((x / y) <= 60000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) - 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 ((x / y) <= (-1.35d+35)) then
        tmp = x / y
    else if ((x / y) <= 60000.0d0) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.35e+35) {
		tmp = x / y;
	} else if ((x / y) <= 60000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.35e+35:
		tmp = x / y
	elif (x / y) <= 60000.0:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.35e+35)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 60000.0)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.35e+35)
		tmp = x / y;
	elseif ((x / y) <= 60000.0)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.35e+35], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 60000.0], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.35000000000000001e35

   1. Initial program 88.2%

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

   2. Taylor expanded in x around inf 68.2%

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

   if -1.35000000000000001e35 < (/.f64 x y) < 6e4

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf 59.0%

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

      1. div-sub 59.0%

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

      2. sub-neg 59.0%

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

      3. *-inverses 59.0%

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

      4. metadata-eval 59.0%

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

   4. Simplified 59.0%

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

   5. Taylor expanded in x around 0 58.7%

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

      1. sub-neg 58.7%

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

      2. metadata-eval 58.7%

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

      3. distribute-lft-in 58.7%

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

      4. associate-*r/ 58.7%

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

      5. metadata-eval 58.7%

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

      6. metadata-eval 58.7%

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

   7. Simplified 58.7%

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

   if 6e4 < (/.f64 x y)

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 66.9%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.35 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 60000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 14: 47.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.2 \cdot 10^{+41} \lor \neg \left(\frac{x}{y} \leq 11500000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.2e+41) (not (<= (/ x y) 11500000.0)))
   (/ x y)
   (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.2e+41) || !((x / y) <= 11500000.0)) {
		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) <= (-1.2d+41)) .or. (.not. ((x / y) <= 11500000.0d0))) 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) <= -1.2e+41) || !((x / y) <= 11500000.0)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.2e+41) or not ((x / y) <= 11500000.0):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.2e+41) || !(Float64(x / y) <= 11500000.0))
		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) <= -1.2e+41) || ~(((x / y) <= 11500000.0)))
		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], -1.2e+41], N[Not[LessEqual[N[(x / y), $MachinePrecision], 11500000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.2000000000000001e41 or 1.15e7 < (/.f64 x y)

   1. Initial program 91.1%

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

   2. Taylor expanded in x around inf 67.3%

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

   if -1.2000000000000001e41 < (/.f64 x y) < 1.15e7

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf 59.0%

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

      1. div-sub 59.0%

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

      2. sub-neg 59.0%

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

      3. *-inverses 59.0%

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

      4. metadata-eval 59.0%

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

   4. Simplified 59.0%

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

   5. Taylor expanded in t around 0 27.3%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.2 \cdot 10^{+41} \lor \neg \left(\frac{x}{y} \leq 11500000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 15: 19.4% 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 88.5%

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

2. Taylor expanded in z around inf 67.4%

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

   1. div-sub 67.4%

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

   2. sub-neg 67.4%

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

   3. *-inverses 67.4%

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

   4. metadata-eval 67.4%

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

4. Simplified 67.4%

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

5. Taylor expanded in t around 0 19.0%

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

6. Final simplification 19.0%

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

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 2023308 
(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))))