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

Percentage Accurate: 85.8% → 99.3%

Time: 11.0s

Alternatives: 13

Speedup: 0.7×

• 23.0% 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: 85.8% 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: 99.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + \left(1 - t\right) \cdot \left(2 \cdot z\right)}{z \cdot t}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (- 1.0 t) (* 2.0 z))) (* 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 + ((1.0 - t) * (2.0 * z))) / (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 + ((1.0 - t) * (2.0 * z))) / (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 + ((1.0 - t) * (2.0 * z))) / (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(1.0 - t) * Float64(2.0 * z))) / 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 + ((1.0 - t) * (2.0 * z))) / (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[(1.0 - t), $MachinePrecision] * N[(2.0 * z), $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 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))) < +inf.0

   1. Initial program 99.8%

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

   if +inf.0 < (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) 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. Add Preprocessing

   3. 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%

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

Alternative 2: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+39} \lor \neg \left(\frac{x}{y} \leq 8 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+39) (not (<= (/ x y) 8e+87)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))
   (/ (+ (+ 2.0 (/ 2.0 z)) (* t (+ (/ x y) -2.0))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+39) || !((x / y) <= 8e+87)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -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) <= (-2d+39)) .or. (.not. ((x / y) <= 8d+87))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) + (t * ((x / y) + (-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) <= -2e+39) || !((x / y) <= 8e+87)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+39) or not ((x / y) <= 8e+87):
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	else:
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+39) || !(Float64(x / y) <= 8e+87))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) + Float64(t * Float64(Float64(x / y) + -2.0))) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+39) || ~(((x / y) <= 8e+87)))
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	else
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+39], N[Not[LessEqual[N[(x / y), $MachinePrecision], 8e+87]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999988e39 or 7.9999999999999997e87 < (/.f64 x y)

   1. Initial program 86.3%

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

   3. Taylor expanded in t around 0 99.0%

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

   if -1.99999999999999988e39 < (/.f64 x y) < 7.9999999999999997e87

   1. Initial program 89.9%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. associate-+r+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+39} \lor \neg \left(\frac{x}{y} \leq 8 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 466\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+14) (not (<= (/ x y) 466.0)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+14) || !((x / y) <= 466.0)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = -2.0 + ((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 (((x / y) <= (-2d+14)) .or. (.not. ((x / y) <= 466.0d0))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    else
        tmp = (-2.0d0) + ((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 (((x / y) <= -2e+14) || !((x / y) <= 466.0)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+14) or not ((x / y) <= 466.0):
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+14) || !(Float64(x / y) <= 466.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	else
		tmp = Float64(-2.0 + 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 (((x / y) <= -2e+14) || ~(((x / y) <= 466.0)))
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+14], N[Not[LessEqual[N[(x / y), $MachinePrecision], 466.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e14 or 466 < (/.f64 x y)

   1. Initial program 89.2%

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

   3. Taylor expanded in t around 0 98.7%

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

   if -2e14 < (/.f64 x y) < 466

   1. Initial program 87.7%

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

      1. add-cube-cbrt 86.5%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 86.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 86.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 86.4%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in x around 0 99.4%

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

      1. +-commutative 99.4%

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

      2. div-sub 99.5%

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

      3. *-inverses 99.5%

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

      4. *-lft-identity 99.5%

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

      5. *-lft-identity 99.5%

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

      6. sub-neg 99.5%

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

      7. metadata-eval 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. sub-neg 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. associate--l+ 99.5%

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

      15. +-commutative 99.5%

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

      16. associate-+r- 99.5%

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

      17. metadata-eval 99.5%

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

      18. associate-*r/ 99.5%

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

      19. associate--l+ 99.5%

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

      20. sub-neg 99.5%

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

   7. Simplified 99.4%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 466\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-31}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq 8600000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -4.2e+132)
     t_2
     (if (<= z -1.25e-77)
       t_1
       (if (<= z 6.5e-31)
         (+ -2.0 (/ (/ 2.0 z) t))
         (if (<= z 8600000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -4.2e+132) {
		tmp = t_2;
	} else if (z <= -1.25e-77) {
		tmp = t_1;
	} else if (z <= 6.5e-31) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else if (z <= 8600000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    t_2 = (-2.0d0) + (2.0d0 / t)
    if (z <= (-4.2d+132)) then
        tmp = t_2
    else if (z <= (-1.25d-77)) then
        tmp = t_1
    else if (z <= 6.5d-31) then
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    else if (z <= 8600000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -4.2e+132) {
		tmp = t_2;
	} else if (z <= -1.25e-77) {
		tmp = t_1;
	} else if (z <= 6.5e-31) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else if (z <= 8600000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	t_2 = -2.0 + (2.0 / t)
	tmp = 0
	if z <= -4.2e+132:
		tmp = t_2
	elif z <= -1.25e-77:
		tmp = t_1
	elif z <= 6.5e-31:
		tmp = -2.0 + ((2.0 / z) / t)
	elif z <= 8600000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	t_2 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -4.2e+132)
		tmp = t_2;
	elseif (z <= -1.25e-77)
		tmp = t_1;
	elseif (z <= 6.5e-31)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	elseif (z <= 8600000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	t_2 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if (z <= -4.2e+132)
		tmp = t_2;
	elseif (z <= -1.25e-77)
		tmp = t_1;
	elseif (z <= 6.5e-31)
		tmp = -2.0 + ((2.0 / z) / t);
	elseif (z <= 8600000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+132], t$95$2, If[LessEqual[z, -1.25e-77], t$95$1, If[LessEqual[z, 6.5e-31], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8600000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999987e132 or 8.6e9 < z

   1. Initial program 73.2%

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

      1. add-cube-cbrt 72.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 72.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 72.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 72.4%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in x around 0 70.9%

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

      1. +-commutative 70.9%

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

      2. div-sub 71.0%

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

      3. *-inverses 71.0%

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

      4. *-lft-identity 71.0%

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

      5. *-lft-identity 71.0%

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

      6. sub-neg 71.0%

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

      7. metadata-eval 71.0%

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

      8. distribute-lft-in 71.0%

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

      9. metadata-eval 71.0%

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

      10. metadata-eval 71.0%

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

      11. sub-neg 71.0%

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

      12. associate-*r/ 71.0%

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

      13. metadata-eval 71.0%

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

      14. associate--l+ 71.0%

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

      15. +-commutative 71.0%

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

      16. associate-+r- 71.0%

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

      17. metadata-eval 71.0%

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

      18. associate-*r/ 71.0%

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

      19. associate--l+ 71.0%

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

      20. sub-neg 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in z around inf 70.8%

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

      1. sub-neg 70.8%

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

      2. associate-*r/ 70.8%

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

      3. metadata-eval 70.8%

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

      4. metadata-eval 70.8%

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

   10. Simplified 70.8%

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

   if -4.19999999999999987e132 < z < -1.24999999999999991e-77 or 6.49999999999999967e-31 < z < 8.6e9

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 78.0%

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

   if -1.24999999999999991e-77 < z < 6.49999999999999967e-31

   1. Initial program 98.9%

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

      1. add-cube-cbrt 98.0%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 97.9%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 97.9%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 97.9%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in x around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. div-sub 80.0%

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

      3. *-inverses 80.0%

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

      4. *-lft-identity 80.0%

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

      5. *-lft-identity 80.0%

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

      6. sub-neg 80.0%

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

      7. metadata-eval 80.0%

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

      8. distribute-lft-in 80.0%

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

      9. metadata-eval 80.0%

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

      10. metadata-eval 80.0%

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

      11. sub-neg 80.0%

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

      12. associate-*r/ 80.0%

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

      13. metadata-eval 80.0%

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

      14. associate--l+ 80.0%

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

      15. +-commutative 80.0%

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

      16. associate-+r- 80.0%

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

      17. metadata-eval 80.0%

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

      18. associate-*r/ 80.0%

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

      19. associate--l+ 80.0%

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

      20. sub-neg 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in z around 0 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-/r* 80.0%

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

   10. Simplified 80.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+132}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-31}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq 8600000000:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-31}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 1860000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -5.2e+129)
     t_2
     (if (<= z -9.2e-196)
       t_1
       (if (<= z 1.15e-31) (/ 2.0 (* z t)) (if (<= z 1860000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -5.2e+129) {
		tmp = t_2;
	} else if (z <= -9.2e-196) {
		tmp = t_1;
	} else if (z <= 1.15e-31) {
		tmp = 2.0 / (z * t);
	} else if (z <= 1860000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    t_2 = (-2.0d0) + (2.0d0 / t)
    if (z <= (-5.2d+129)) then
        tmp = t_2
    else if (z <= (-9.2d-196)) then
        tmp = t_1
    else if (z <= 1.15d-31) then
        tmp = 2.0d0 / (z * t)
    else if (z <= 1860000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -5.2e+129) {
		tmp = t_2;
	} else if (z <= -9.2e-196) {
		tmp = t_1;
	} else if (z <= 1.15e-31) {
		tmp = 2.0 / (z * t);
	} else if (z <= 1860000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	t_2 = -2.0 + (2.0 / t)
	tmp = 0
	if z <= -5.2e+129:
		tmp = t_2
	elif z <= -9.2e-196:
		tmp = t_1
	elif z <= 1.15e-31:
		tmp = 2.0 / (z * t)
	elif z <= 1860000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	t_2 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -5.2e+129)
		tmp = t_2;
	elseif (z <= -9.2e-196)
		tmp = t_1;
	elseif (z <= 1.15e-31)
		tmp = Float64(2.0 / Float64(z * t));
	elseif (z <= 1860000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	t_2 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if (z <= -5.2e+129)
		tmp = t_2;
	elseif (z <= -9.2e-196)
		tmp = t_1;
	elseif (z <= 1.15e-31)
		tmp = 2.0 / (z * t);
	elseif (z <= 1860000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+129], t$95$2, If[LessEqual[z, -9.2e-196], t$95$1, If[LessEqual[z, 1.15e-31], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1860000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000024e129 or 1.86e6 < z

   1. Initial program 73.2%

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

      1. add-cube-cbrt 72.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 72.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 72.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 72.4%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in x around 0 70.9%

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

      1. +-commutative 70.9%

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

      2. div-sub 71.0%

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

      3. *-inverses 71.0%

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

      4. *-lft-identity 71.0%

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

      5. *-lft-identity 71.0%

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

      6. sub-neg 71.0%

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

      7. metadata-eval 71.0%

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

      8. distribute-lft-in 71.0%

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

      9. metadata-eval 71.0%

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

      10. metadata-eval 71.0%

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

      11. sub-neg 71.0%

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

      12. associate-*r/ 71.0%

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

      13. metadata-eval 71.0%

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

      14. associate--l+ 71.0%

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

      15. +-commutative 71.0%

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

      16. associate-+r- 71.0%

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

      17. metadata-eval 71.0%

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

      18. associate-*r/ 71.0%

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

      19. associate--l+ 71.0%

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

      20. sub-neg 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in z around inf 70.8%

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

      1. sub-neg 70.8%

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

      2. associate-*r/ 70.8%

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

      3. metadata-eval 70.8%

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

      4. metadata-eval 70.8%

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

   10. Simplified 70.8%

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

   if -5.20000000000000024e129 < z < -9.2000000000000007e-196 or 1.1499999999999999e-31 < z < 1.86e6

   1. Initial program 97.2%

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

   3. Taylor expanded in t around inf 70.4%

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

   if -9.2000000000000007e-196 < z < 1.1499999999999999e-31

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0 79.4%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+129}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-31}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 1860000:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.092:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.6 \cdot 10^{-171}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.02 \cdot 10^{+88}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -0.092)
   (/ x y)
   (if (<= (/ x y) 4.6e-171)
     -2.0
     (if (<= (/ x y) 1.02e+88) (/ 2.0 t) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -0.092) {
		tmp = x / y;
	} else if ((x / y) <= 4.6e-171) {
		tmp = -2.0;
	} else if ((x / y) <= 1.02e+88) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-0.092d0)) then
        tmp = x / y
    else if ((x / y) <= 4.6d-171) then
        tmp = -2.0d0
    else if ((x / y) <= 1.02d+88) then
        tmp = 2.0d0 / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -0.092) {
		tmp = x / y;
	} else if ((x / y) <= 4.6e-171) {
		tmp = -2.0;
	} else if ((x / y) <= 1.02e+88) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -0.092:
		tmp = x / y
	elif (x / y) <= 4.6e-171:
		tmp = -2.0
	elif (x / y) <= 1.02e+88:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -0.092)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4.6e-171)
		tmp = -2.0;
	elseif (Float64(x / y) <= 1.02e+88)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -0.092)
		tmp = x / y;
	elseif ((x / y) <= 4.6e-171)
		tmp = -2.0;
	elseif ((x / y) <= 1.02e+88)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -0.092], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.6e-171], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 1.02e+88], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -0.091999999999999998 or 1.01999999999999998e88 < (/.f64 x y)

   1. Initial program 87.2%

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

   3. Taylor expanded in x around inf 69.9%

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

   if -0.091999999999999998 < (/.f64 x y) < 4.59999999999999956e-171

   1. Initial program 88.9%

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

      1. add-cube-cbrt 87.6%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 87.6%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 87.6%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 87.6%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in x around 0 99.3%

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

      1. +-commutative 99.3%

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

      2. div-sub 99.3%

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

      3. *-inverses 99.3%

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

      4. *-lft-identity 99.3%

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

      5. *-lft-identity 99.3%

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

      6. sub-neg 99.3%

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

      7. metadata-eval 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. metadata-eval 99.3%

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

      10. metadata-eval 99.3%

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

      11. sub-neg 99.3%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. associate--l+ 99.3%

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

      15. +-commutative 99.3%

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

      16. associate-+r- 99.3%

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

      17. metadata-eval 99.3%

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

      18. associate-*r/ 99.3%

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

      19. associate--l+ 99.3%

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

      20. sub-neg 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in t around inf 37.1%

      \[\leadsto \color{blue}{-2} \]

   if 4.59999999999999956e-171 < (/.f64 x y) < 1.01999999999999998e88

   1. Initial program 90.2%

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

   3. Taylor expanded in t around 0 82.2%

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

      1. associate-*r/ 82.2%

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

      2. metadata-eval 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in z around inf 37.0%

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

Alternative 7: 88.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+49} \lor \neg \left(\frac{x}{y} \leq 8 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+49) (not (<= (/ x y) 8e+87)))
   (+ (/ x y) (/ 2.0 t))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+49) || !((x / y) <= 8e+87)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((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 (((x / y) <= (-5d+49)) .or. (.not. ((x / y) <= 8d+87))) then
        tmp = (x / y) + (2.0d0 / t)
    else
        tmp = (-2.0d0) + ((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 (((x / y) <= -5e+49) || !((x / y) <= 8e+87)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+49) or not ((x / y) <= 8e+87):
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+49) || !(Float64(x / y) <= 8e+87))
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	else
		tmp = Float64(-2.0 + 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 (((x / y) <= -5e+49) || ~(((x / y) <= 8e+87)))
		tmp = (x / y) + (2.0 / t);
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+49], N[Not[LessEqual[N[(x / y), $MachinePrecision], 8e+87]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.0000000000000004e49 or 7.9999999999999997e87 < (/.f64 x y)

   1. Initial program 86.8%

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

      1. add-cube-cbrt 86.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 86.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 86.4%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 86.4%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in t around 0 98.9%

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

      1. *-commutative 98.9%

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

   7. Simplified 98.9%

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

   8. Taylor expanded in z around inf 85.1%

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

      1. associate-*r/ 85.1%

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

      2. metadata-eval 85.1%

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

   10. Simplified 85.1%

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

   if -5.0000000000000004e49 < (/.f64 x y) < 7.9999999999999997e87

   1. Initial program 89.5%

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

      1. add-cube-cbrt 88.3%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 88.3%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 88.3%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 88.3%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in x around 0 95.2%

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

      1. +-commutative 95.2%

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

      2. div-sub 95.2%

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

      3. *-inverses 95.2%

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

      4. *-lft-identity 95.2%

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

      5. *-lft-identity 95.2%

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

      6. sub-neg 95.2%

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

      7. metadata-eval 95.2%

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

      8. distribute-lft-in 95.2%

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

      9. metadata-eval 95.2%

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

      10. metadata-eval 95.2%

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

      11. sub-neg 95.2%

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

      12. associate-*r/ 95.2%

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

      13. metadata-eval 95.2%

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

      14. associate--l+ 95.2%

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

      15. +-commutative 95.2%

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

      16. associate-+r- 95.2%

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

      17. metadata-eval 95.2%

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

      18. associate-*r/ 95.2%

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

      19. associate--l+ 95.2%

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

      20. sub-neg 95.2%

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

   7. Simplified 95.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+49} \lor \neg \left(\frac{x}{y} \leq 8 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3400000 \lor \neg \left(\frac{x}{y} \leq 10^{+88}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3400000.0) (not (<= (/ x y) 1e+88)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3400000.0) || !((x / y) <= 1e+88)) {
		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) <= (-3400000.0d0)) .or. (.not. ((x / y) <= 1d+88))) 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) <= -3400000.0) || !((x / y) <= 1e+88)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3400000.0) or not ((x / y) <= 1e+88):
		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) <= -3400000.0) || !(Float64(x / y) <= 1e+88))
		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) <= -3400000.0) || ~(((x / y) <= 1e+88)))
		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], -3400000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+88]], $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) < -3.4e6 or 9.99999999999999959e87 < (/.f64 x y)

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf 70.6%

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

   if -3.4e6 < (/.f64 x y) < 9.99999999999999959e87

   1. Initial program 89.5%

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

      1. add-cube-cbrt 88.3%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 88.2%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 88.2%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 88.2%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in x around 0 97.7%

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

      1. +-commutative 97.7%

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

      2. div-sub 97.7%

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

      3. *-inverses 97.7%

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

      4. *-lft-identity 97.7%

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

      5. *-lft-identity 97.7%

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

      6. sub-neg 97.7%

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

      7. metadata-eval 97.7%

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

      8. distribute-lft-in 97.7%

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

      9. metadata-eval 97.7%

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

      10. metadata-eval 97.7%

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

      11. sub-neg 97.7%

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

      12. associate-*r/ 97.7%

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

      13. metadata-eval 97.7%

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

      14. associate--l+ 97.7%

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

      15. +-commutative 97.7%

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

      16. associate-+r- 97.7%

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

      17. metadata-eval 97.7%

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

      18. associate-*r/ 97.7%

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

      19. associate--l+ 97.7%

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

      20. sub-neg 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in z around inf 56.7%

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

      1. sub-neg 56.7%

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

      2. associate-*r/ 56.7%

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

      3. metadata-eval 56.7%

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

      4. metadata-eval 56.7%

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

   10. Simplified 56.7%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3400000 \lor \neg \left(\frac{x}{y} \leq 10^{+88}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1950000:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.05 \cdot 10^{+88}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1950000.0)
   (- (/ x y) 2.0)
   (if (<= (/ x y) 1.05e+88) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1950000.0) {
		tmp = (x / y) - 2.0;
	} else if ((x / y) <= 1.05e+88) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	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) <= (-1950000.0d0)) then
        tmp = (x / y) - 2.0d0
    else if ((x / y) <= 1.05d+88) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1950000.0) {
		tmp = (x / y) - 2.0;
	} else if ((x / y) <= 1.05e+88) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1950000.0:
		tmp = (x / y) - 2.0
	elif (x / y) <= 1.05e+88:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1950000.0)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (Float64(x / y) <= 1.05e+88)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1950000.0)
		tmp = (x / y) - 2.0;
	elseif ((x / y) <= 1.05e+88)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1950000.0], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.05e+88], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.95e6

   1. Initial program 91.4%

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

   3. Taylor expanded in t around inf 62.3%

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

   if -1.95e6 < (/.f64 x y) < 1.05e88

   1. Initial program 89.5%

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

      1. add-cube-cbrt 88.3%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 88.2%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 88.2%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 88.2%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in x around 0 97.7%

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

      1. +-commutative 97.7%

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

      2. div-sub 97.7%

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

      3. *-inverses 97.7%

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

      4. *-lft-identity 97.7%

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

      5. *-lft-identity 97.7%

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

      6. sub-neg 97.7%

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

      7. metadata-eval 97.7%

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

      8. distribute-lft-in 97.7%

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

      9. metadata-eval 97.7%

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

      10. metadata-eval 97.7%

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

      11. sub-neg 97.7%

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

      12. associate-*r/ 97.7%

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

      13. metadata-eval 97.7%

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

      14. associate--l+ 97.7%

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

      15. +-commutative 97.7%

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

      16. associate-+r- 97.7%

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

      17. metadata-eval 97.7%

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

      18. associate-*r/ 97.7%

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

      19. associate--l+ 97.7%

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

      20. sub-neg 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in z around inf 56.7%

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

      1. sub-neg 56.7%

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

      2. associate-*r/ 56.7%

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

      3. metadata-eval 56.7%

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

      4. metadata-eval 56.7%

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

   10. Simplified 56.7%

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

   if 1.05e88 < (/.f64 x y)

   1. Initial program 82.0%

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

   3. Taylor expanded in x around inf 80.5%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1950000:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.05 \cdot 10^{+88}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+14} \lor \neg \left(t \leq 4.4 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.1e+14) (not (<= t 4.4e-6)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e+14) || !(t <= 4.4e-6)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (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 <= (-1.1d+14)) .or. (.not. (t <= 4.4d-6))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (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 <= -1.1e+14) || !(t <= 4.4e-6)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.1e+14) or not (t <= 4.4e-6):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.1e+14) || !(t <= 4.4e-6))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = 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 <= -1.1e+14) || ~((t <= 4.4e-6)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.1e+14], N[Not[LessEqual[t, 4.4e-6]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e14 or 4.4000000000000002e-6 < t

   1. Initial program 75.7%

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

   3. Taylor expanded in t around inf 78.8%

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

   if -1.1e14 < t < 4.4000000000000002e-6

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 80.6%

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

      1. associate-*r/ 80.6%

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

      2. metadata-eval 80.6%

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

   5. Simplified 80.6%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+14} \lor \neg \left(t \leq 4.4 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-6} \lor \neg \left(z \leq 1.2 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.25e-6) (not (<= z 1.2e-30)))
   (+ (/ x y) (/ 2.0 t))
   (+ -2.0 (/ (/ 2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.25e-6) || !(z <= 1.2e-30)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -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 ((z <= (-2.25d-6)) .or. (.not. (z <= 1.2d-30))) then
        tmp = (x / y) + (2.0d0 / t)
    else
        tmp = (-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 ((z <= -2.25e-6) || !(z <= 1.2e-30)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.25e-6) or not (z <= 1.2e-30):
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = -2.0 + ((2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.25e-6) || !(z <= 1.2e-30))
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.25e-6) || ~((z <= 1.2e-30)))
		tmp = (x / y) + (2.0 / t);
	else
		tmp = -2.0 + ((2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.25e-6], N[Not[LessEqual[z, 1.2e-30]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.25000000000000006e-6 or 1.19999999999999992e-30 < z

   1. Initial program 78.6%

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

      1. add-cube-cbrt 77.8%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 77.8%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 77.8%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 77.8%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in t around 0 79.0%

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

      1. *-commutative 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in z around inf 77.7%

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

      1. associate-*r/ 77.7%

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

      2. metadata-eval 77.7%

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

   10. Simplified 77.7%

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

   if -2.25000000000000006e-6 < z < 1.19999999999999992e-30

   1. Initial program 99.0%

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

      1. add-cube-cbrt 98.0%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 98.0%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 98.0%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 98.0%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in x around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. div-sub 78.4%

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

      3. *-inverses 78.4%

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

      4. *-lft-identity 78.4%

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

      5. *-lft-identity 78.4%

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

      6. sub-neg 78.4%

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

      7. metadata-eval 78.4%

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

      8. distribute-lft-in 78.4%

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

      9. metadata-eval 78.4%

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

      10. metadata-eval 78.4%

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

      11. sub-neg 78.4%

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

      12. associate-*r/ 78.4%

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

      13. metadata-eval 78.4%

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

      14. associate--l+ 78.4%

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

      15. +-commutative 78.4%

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

      16. associate-+r- 78.4%

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

      17. metadata-eval 78.4%

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

      18. associate-*r/ 78.4%

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

      19. associate--l+ 78.4%

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

      20. sub-neg 78.4%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in z around 0 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-/r* 78.0%

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

   10. Simplified 78.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-6} \lor \neg \left(z \leq 1.2 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 4.5e-6) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 4.5e-6) {
		tmp = 2.0 / t;
	} else {
		tmp = -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 (t <= (-1.0d0)) then
        tmp = -2.0d0
    else if (t <= 4.5d-6) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 4.5e-6) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.0:
		tmp = -2.0
	elif t <= 4.5e-6:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 4.5e-6)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 4.5e-6)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.0], -2.0, If[LessEqual[t, 4.5e-6], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 4.50000000000000011e-6 < t

   1. Initial program 76.2%

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

      1. add-cube-cbrt 75.3%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

      2. pow3 75.3%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

      3. *-commutative 75.3%

         \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

   4. Applied egg-rr 75.3%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

   5. Taylor expanded in x around 0 57.1%

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

      1. +-commutative 57.1%

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

      2. div-sub 57.1%

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

      3. *-inverses 57.1%

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

      4. *-lft-identity 57.1%

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

      5. *-lft-identity 57.1%

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

      6. sub-neg 57.1%

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

      7. metadata-eval 57.1%

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

      8. distribute-lft-in 57.1%

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

      9. metadata-eval 57.1%

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

      10. metadata-eval 57.1%

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

      11. sub-neg 57.1%

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

      12. associate-*r/ 57.1%

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

      13. metadata-eval 57.1%

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

      14. associate--l+ 57.1%

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

      15. +-commutative 57.1%

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

      16. associate-+r- 57.1%

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

      17. metadata-eval 57.1%

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

      18. associate-*r/ 57.1%

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

      19. associate--l+ 57.1%

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

      20. sub-neg 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in t around inf 35.0%

      \[\leadsto \color{blue}{-2} \]

   if -1 < t < 4.50000000000000011e-6

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 80.3%

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

      1. associate-*r/ 80.3%

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

      2. metadata-eval 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in z around inf 39.6%

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

Alternative 13: 20.3% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := -2.0

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. Add Preprocessing
3. Step-by-step derivation

   1. add-cube-cbrt 87.6%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{\left(\sqrt[3]{t \cdot z} \cdot \sqrt[3]{t \cdot z}\right) \cdot \sqrt[3]{t \cdot z}}} \]

   2. pow3 87.6%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{t \cdot z}\right)}^{3}}} \]

   3. *-commutative 87.6%

      \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{{\left(\sqrt[3]{\color{blue}{z \cdot t}}\right)}^{3}} \]

4. Applied egg-rr 87.6%

   \[\leadsto \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{\color{blue}{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}} \]

5. Taylor expanded in x around 0 70.0%

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

   1. +-commutative 70.0%

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

   2. div-sub 70.0%

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

   3. *-inverses 70.0%

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

   4. *-lft-identity 70.0%

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

   5. *-lft-identity 70.0%

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

   6. sub-neg 70.0%

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

   7. metadata-eval 70.0%

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

   8. distribute-lft-in 70.0%

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

   9. metadata-eval 70.0%

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

   10. metadata-eval 70.0%

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

   11. sub-neg 70.0%

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

   12. associate-*r/ 70.0%

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

   13. metadata-eval 70.0%

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

   14. associate--l+ 70.0%

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

   15. +-commutative 70.0%

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

   16. associate-+r- 70.0%

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

   17. metadata-eval 70.0%

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

   18. associate-*r/ 70.0%

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

   19. associate--l+ 70.0%

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

   20. sub-neg 70.0%

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

7. Simplified 70.0%

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

8. Taylor expanded in t around inf 17.5%

   \[\leadsto \color{blue}{-2} \]
9. Add Preprocessing

Developer Target 1: 99.0% 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 2024158 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

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