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

Percentage Accurate: 86.9% → 99.0%

Time: 13.1s

Alternatives: 17

Speedup: 0.9×

• 23.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.9% 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: 99.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(1 - t\right) \cdot \left(2 \cdot z\right)}{z \cdot t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;t\_1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{z \cdot t}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (- 1.0 t) (* 2.0 z))) (* z t))))
   (if (<= t_1 2e+305)
     (+ t_1 (/ x y))
     (/ (+ x (* y (+ (* 2.0 (/ (- 1.0 t) t)) (* 2.0 (/ 1.0 (* z t)))))) y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((1.0 - t) * (2.0 * z))) / (z * t);
	double tmp;
	if (t_1 <= 2e+305) {
		tmp = t_1 + (x / y);
	} else {
		tmp = (x + (y * ((2.0 * ((1.0 - t) / t)) + (2.0 * (1.0 / (z * t)))))) / 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) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 + ((1.0d0 - t) * (2.0d0 * z))) / (z * t)
    if (t_1 <= 2d+305) then
        tmp = t_1 + (x / y)
    else
        tmp = (x + (y * ((2.0d0 * ((1.0d0 - t) / t)) + (2.0d0 * (1.0d0 / (z * t)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((1.0 - t) * (2.0 * z))) / (z * t);
	double tmp;
	if (t_1 <= 2e+305) {
		tmp = t_1 + (x / y);
	} else {
		tmp = (x + (y * ((2.0 * ((1.0 - t) / t)) + (2.0 * (1.0 / (z * t)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((1.0 - t) * (2.0 * z))) / (z * t)
	tmp = 0
	if t_1 <= 2e+305:
		tmp = t_1 + (x / y)
	else:
		tmp = (x + (y * ((2.0 * ((1.0 - t) / t)) + (2.0 * (1.0 / (z * t)))))) / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(1.0 - t) * Float64(2.0 * z))) / Float64(z * t))
	tmp = 0.0
	if (t_1 <= 2e+305)
		tmp = Float64(t_1 + Float64(x / y));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(Float64(2.0 * Float64(Float64(1.0 - t) / t)) + Float64(2.0 * Float64(1.0 / Float64(z * t)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((1.0 - t) * (2.0 * z))) / (z * t);
	tmp = 0.0;
	if (t_1 <= 2e+305)
		tmp = t_1 + (x / y);
	else
		tmp = (x + (y * ((2.0 * ((1.0 - t) / t)) + (2.0 * (1.0 / (z * t)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(1.0 - t), $MachinePrecision] * N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+305], N[(t$95$1 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.9999999999999999e305

   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 1.9999999999999999e305 < (/.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 36.7%

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

   3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(1 - t\right) \cdot \left(2 \cdot z\right)}{z \cdot t} \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\frac{2 + \left(1 - t\right) \cdot \left(2 \cdot z\right)}{z \cdot t} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{z \cdot t}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 + N[(N[(1.0 - t), $MachinePrecision] * N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x + N[(y * -2.0), $MachinePrecision]), $MachinePrecision] / y), $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 y around 0 100.0%

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

   4. Taylor expanded in t around inf 93.5%

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

      1. +-commutative 93.5%

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

      2. *-commutative 93.5%

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

   6. Simplified 93.5%

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

4. Final simplification 99.1%

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

Alternative 3: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+16} \lor \neg \left(\frac{x}{y} \leq 2\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+16) (not (<= (/ x y) 2.0)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))
   (+ -2.0 (* (/ 1.0 t) (+ 2.0 (/ 2.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+16) || !((x / y) <= 2.0)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d+16)) .or. (.not. ((x / y) <= 2.0d0))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    else
        tmp = (-2.0d0) + ((1.0d0 / t) * (2.0d0 + (2.0d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+16) || !((x / y) <= 2.0)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+16) or not ((x / y) <= 2.0):
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	else:
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+16) || !(Float64(x / y) <= 2.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(1.0 / t) * Float64(2.0 + Float64(2.0 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+16) || ~(((x / y) <= 2.0)))
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	else
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+16], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2.0]], $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[(1.0 / t), $MachinePrecision] * N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e16 or 2 < (/.f64 x y)

   1. Initial program 88.4%

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

   3. Taylor expanded in t around 0 97.8%

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

   if -1e16 < (/.f64 x y) < 2

   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 0 97.9%

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

      1. associate-*r/ 97.9%

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

      2. metadata-eval 97.9%

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

      3. associate-/l/ 98.0%

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

      4. +-commutative 98.0%

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

      5. div-sub 98.0%

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

      6. sub-neg 98.0%

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

      7. *-inverses 98.0%

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

      8. metadata-eval 98.0%

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

      9. distribute-lft-in 98.0%

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

      10. metadata-eval 98.0%

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

      11. associate-+l+ 98.0%

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

      12. +-commutative 98.0%

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

      13. associate-/l/ 97.9%

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

      14. +-commutative 97.9%

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

      15. associate-/l/ 98.0%

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

      16. *-rgt-identity 98.0%

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

      17. associate-*r/ 97.9%

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

      18. distribute-rgt-out 97.9%

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

   5. Simplified 97.9%

      \[\leadsto \color{blue}{-2 + \frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+16} \lor \neg \left(\frac{x}{y} \leq 2\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -3.15 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+27} \lor \neg \left(z \leq 4.4 \cdot 10^{+190}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -3.15e-80)
     t_1
     (if (<= z 2.5e-66)
       (/ (/ 2.0 t) z)
       (if (or (<= z 3.7e+27) (not (<= z 4.4e+190)))
         t_1
         (+ -2.0 (/ 2.0 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -3.15e-80) {
		tmp = t_1;
	} else if (z <= 2.5e-66) {
		tmp = (2.0 / t) / z;
	} else if ((z <= 3.7e+27) || !(z <= 4.4e+190)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-3.15d-80)) then
        tmp = t_1
    else if (z <= 2.5d-66) then
        tmp = (2.0d0 / t) / z
    else if ((z <= 3.7d+27) .or. (.not. (z <= 4.4d+190))) then
        tmp = t_1
    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 t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -3.15e-80) {
		tmp = t_1;
	} else if (z <= 2.5e-66) {
		tmp = (2.0 / t) / z;
	} else if ((z <= 3.7e+27) || !(z <= 4.4e+190)) {
		tmp = t_1;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -3.15e-80:
		tmp = t_1
	elif z <= 2.5e-66:
		tmp = (2.0 / t) / z
	elif (z <= 3.7e+27) or not (z <= 4.4e+190):
		tmp = t_1
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -3.15e-80)
		tmp = t_1;
	elseif (z <= 2.5e-66)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif ((z <= 3.7e+27) || !(z <= 4.4e+190))
		tmp = t_1;
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -3.15e-80)
		tmp = t_1;
	elseif (z <= 2.5e-66)
		tmp = (2.0 / t) / z;
	elseif ((z <= 3.7e+27) || ~((z <= 4.4e+190)))
		tmp = t_1;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -3.15e-80], t$95$1, If[LessEqual[z, 2.5e-66], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[z, 3.7e+27], N[Not[LessEqual[z, 4.4e+190]], $MachinePrecision]], t$95$1, N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.14999999999999983e-80 or 2.49999999999999981e-66 < z < 3.70000000000000002e27 or 4.4e190 < z

   1. Initial program 80.2%

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

   3. Taylor expanded in t around inf 74.5%

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

   if -3.14999999999999983e-80 < z < 2.49999999999999981e-66

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 67.1%

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

      1. associate-/l/ 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in z around 0 67.1%

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

      1. associate-/r* 67.2%

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

   8. Simplified 67.2%

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

   if 3.70000000000000002e27 < z < 4.4e190

   1. Initial program 85.7%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. div-sub 100.0%

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

      2. sub-neg 100.0%

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

      3. *-inverses 100.0%

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

      4. metadata-eval 100.0%

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

      5. distribute-lft-in 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 82.6%

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

      1. sub-neg 82.6%

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

      2. associate-*r/ 82.6%

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

      3. metadata-eval 82.6%

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

      4. metadata-eval 82.6%

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

   8. Simplified 82.6%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+27} \lor \neg \left(z \leq 4.4 \cdot 10^{+190}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -3.95 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+27} \lor \neg \left(z \leq 4.4 \cdot 10^{+190}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -3.95e-79)
     t_1
     (if (<= z 5.5e-60)
       (/ 2.0 (* z t))
       (if (or (<= z 2.25e+27) (not (<= z 4.4e+190)))
         t_1
         (+ -2.0 (/ 2.0 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -3.95e-79) {
		tmp = t_1;
	} else if (z <= 5.5e-60) {
		tmp = 2.0 / (z * t);
	} else if ((z <= 2.25e+27) || !(z <= 4.4e+190)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-3.95d-79)) then
        tmp = t_1
    else if (z <= 5.5d-60) then
        tmp = 2.0d0 / (z * t)
    else if ((z <= 2.25d+27) .or. (.not. (z <= 4.4d+190))) then
        tmp = t_1
    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 t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -3.95e-79) {
		tmp = t_1;
	} else if (z <= 5.5e-60) {
		tmp = 2.0 / (z * t);
	} else if ((z <= 2.25e+27) || !(z <= 4.4e+190)) {
		tmp = t_1;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -3.95e-79:
		tmp = t_1
	elif z <= 5.5e-60:
		tmp = 2.0 / (z * t)
	elif (z <= 2.25e+27) or not (z <= 4.4e+190):
		tmp = t_1
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -3.95e-79)
		tmp = t_1;
	elseif (z <= 5.5e-60)
		tmp = Float64(2.0 / Float64(z * t));
	elseif ((z <= 2.25e+27) || !(z <= 4.4e+190))
		tmp = t_1;
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -3.95e-79)
		tmp = t_1;
	elseif (z <= 5.5e-60)
		tmp = 2.0 / (z * t);
	elseif ((z <= 2.25e+27) || ~((z <= 4.4e+190)))
		tmp = t_1;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -3.95e-79], t$95$1, If[LessEqual[z, 5.5e-60], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.25e+27], N[Not[LessEqual[z, 4.4e+190]], $MachinePrecision]], t$95$1, N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.94999999999999973e-79 or 5.4999999999999997e-60 < z < 2.25e27 or 4.4e190 < z

   1. Initial program 80.2%

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

   3. Taylor expanded in t around inf 74.5%

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

   if -3.94999999999999973e-79 < z < 5.4999999999999997e-60

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 67.1%

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

   if 2.25e27 < z < 4.4e190

   1. Initial program 85.7%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. div-sub 100.0%

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

      2. sub-neg 100.0%

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

      3. *-inverses 100.0%

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

      4. metadata-eval 100.0%

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

      5. distribute-lft-in 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 82.6%

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

      1. sub-neg 82.6%

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

      2. associate-*r/ 82.6%

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

      3. metadata-eval 82.6%

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

      4. metadata-eval 82.6%

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

   8. Simplified 82.6%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.95 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+27} \lor \neg \left(z \leq 4.4 \cdot 10^{+190}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+34} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+34) (not (<= (/ x y) 2e+15)))
   (+ (/ x y) (/ (/ 2.0 z) t))
   (+ -2.0 (* (/ 1.0 t) (+ 2.0 (/ 2.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+34) || !((x / y) <= 2e+15)) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else {
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d+34)) .or. (.not. ((x / y) <= 2d+15))) then
        tmp = (x / y) + ((2.0d0 / z) / t)
    else
        tmp = (-2.0d0) + ((1.0d0 / t) * (2.0d0 + (2.0d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+34) || !((x / y) <= 2e+15)) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else {
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+34) or not ((x / y) <= 2e+15):
		tmp = (x / y) + ((2.0 / z) / t)
	else:
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+34) || !(Float64(x / y) <= 2e+15))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / z) / t));
	else
		tmp = Float64(-2.0 + Float64(Float64(1.0 / t) * Float64(2.0 + Float64(2.0 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+34) || ~(((x / y) <= 2e+15)))
		tmp = (x / y) + ((2.0 / z) / t);
	else
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+34], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+15]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(1.0 / t), $MachinePrecision] * N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999989e34 or 2e15 < (/.f64 x y)

   1. Initial program 87.9%

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

   3. Taylor expanded in y around 0 99.2%

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

   4. Taylor expanded in z around 0 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l/ 92.8%

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

      3. associate-*r/ 92.8%

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

      4. associate-/r* 92.9%

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

   6. Simplified 92.9%

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

   7. Taylor expanded in x around 0 91.8%

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

      1. associate-*r/ 91.8%

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

      2. metadata-eval 91.8%

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

      3. associate-/l/ 91.9%

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

   9. Simplified 91.9%

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

   if -1.99999999999999989e34 < (/.f64 x y) < 2e15

   1. Initial program 87.6%

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

   3. Taylor expanded in x around 0 96.7%

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

      1. associate-*r/ 96.7%

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

      2. metadata-eval 96.7%

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

      3. associate-/l/ 96.7%

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

      4. +-commutative 96.7%

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

      5. div-sub 96.7%

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

      6. sub-neg 96.7%

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

      7. *-inverses 96.7%

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

      8. metadata-eval 96.7%

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

      9. distribute-lft-in 96.7%

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

      10. metadata-eval 96.7%

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

      11. associate-+l+ 96.7%

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

      12. +-commutative 96.7%

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

      13. associate-/l/ 96.7%

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

      14. +-commutative 96.7%

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

      15. associate-/l/ 96.7%

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

      16. *-rgt-identity 96.7%

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

      17. associate-*r/ 96.6%

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

      18. distribute-rgt-out 96.6%

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

   5. Simplified 96.6%

      \[\leadsto \color{blue}{-2 + \frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+34} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+34}:\\ \;\;\;\;\frac{x + y \cdot \frac{\frac{2}{t}}{z}}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+15}:\\ \;\;\;\;-2 + \frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+34)
   (/ (+ x (* y (/ (/ 2.0 t) z))) y)
   (if (<= (/ x y) 2e+15)
     (+ -2.0 (* (/ 1.0 t) (+ 2.0 (/ 2.0 z))))
     (+ (/ x y) (/ (/ 2.0 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+34) {
		tmp = (x + (y * ((2.0 / t) / z))) / y;
	} else if ((x / y) <= 2e+15) {
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)));
	} else {
		tmp = (x / y) + ((2.0 / z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2d+34)) then
        tmp = (x + (y * ((2.0d0 / t) / z))) / y
    else if ((x / y) <= 2d+15) then
        tmp = (-2.0d0) + ((1.0d0 / t) * (2.0d0 + (2.0d0 / z)))
    else
        tmp = (x / y) + ((2.0d0 / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+34) {
		tmp = (x + (y * ((2.0 / t) / z))) / y;
	} else if ((x / y) <= 2e+15) {
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)));
	} else {
		tmp = (x / y) + ((2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+34:
		tmp = (x + (y * ((2.0 / t) / z))) / y
	elif (x / y) <= 2e+15:
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)))
	else:
		tmp = (x / y) + ((2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+34)
		tmp = Float64(Float64(x + Float64(y * Float64(Float64(2.0 / t) / z))) / y);
	elseif (Float64(x / y) <= 2e+15)
		tmp = Float64(-2.0 + Float64(Float64(1.0 / t) * Float64(2.0 + Float64(2.0 / z))));
	else
		tmp = Float64(Float64(x / y) + Float64(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+34)
		tmp = (x + (y * ((2.0 / t) / z))) / y;
	elseif ((x / y) <= 2e+15)
		tmp = -2.0 + ((1.0 / t) * (2.0 + (2.0 / z)));
	else
		tmp = (x / y) + ((2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+34], N[(N[(x + N[(y * N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+15], N[(-2.0 + N[(N[(1.0 / t), $MachinePrecision] * N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.99999999999999989e34

   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 y around 0 99.9%

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

   4. Taylor expanded in z around 0 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-*l/ 95.3%

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

      3. associate-*r/ 95.3%

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

      4. associate-/r* 95.4%

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

   6. Simplified 95.4%

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

   if -1.99999999999999989e34 < (/.f64 x y) < 2e15

   1. Initial program 87.6%

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

   3. Taylor expanded in x around 0 96.7%

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

      1. associate-*r/ 96.7%

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

      2. metadata-eval 96.7%

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

      3. associate-/l/ 96.7%

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

      4. +-commutative 96.7%

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

      5. div-sub 96.7%

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

      6. sub-neg 96.7%

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

      7. *-inverses 96.7%

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

      8. metadata-eval 96.7%

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

      9. distribute-lft-in 96.7%

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

      10. metadata-eval 96.7%

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

      11. associate-+l+ 96.7%

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

      12. +-commutative 96.7%

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

      13. associate-/l/ 96.7%

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

      14. +-commutative 96.7%

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

      15. associate-/l/ 96.7%

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

      16. *-rgt-identity 96.7%

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

      17. associate-*r/ 96.6%

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

      18. distribute-rgt-out 96.6%

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

   5. Simplified 96.6%

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

   if 2e15 < (/.f64 x y)

   1. Initial program 86.6%

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

   3. Taylor expanded in y around 0 98.6%

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

   4. Taylor expanded in z around 0 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-*l/ 90.5%

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

      3. associate-*r/ 90.5%

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

      4. associate-/r* 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in x around 0 91.9%

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

      1. associate-*r/ 91.9%

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

      2. metadata-eval 91.9%

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

      3. associate-/l/ 91.9%

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

   9. Simplified 91.9%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+34}:\\ \;\;\;\;\frac{x + y \cdot \frac{\frac{2}{t}}{z}}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+15}:\\ \;\;\;\;-2 + \frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.1 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.02 \cdot 10^{-79}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -3.1e+29)
   (/ x y)
   (if (<= (/ x y) -1.02e-79) (/ 2.0 t) (if (<= (/ x y) 2.0) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -3.1e+29) {
		tmp = x / y;
	} else if ((x / y) <= -1.02e-79) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} 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) <= (-3.1d+29)) then
        tmp = x / y
    else if ((x / y) <= (-1.02d-79)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2.0d0) then
        tmp = -2.0d0
    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) <= -3.1e+29) {
		tmp = x / y;
	} else if ((x / y) <= -1.02e-79) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -3.1e+29:
		tmp = x / y
	elif (x / y) <= -1.02e-79:
		tmp = 2.0 / t
	elif (x / y) <= 2.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -3.1e+29)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -1.02e-79)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -3.1e+29)
		tmp = x / y;
	elseif ((x / y) <= -1.02e-79)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -3.1e+29], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1.02e-79], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.0], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -3.0999999999999999e29 or 2 < (/.f64 x y)

   1. Initial program 88.2%

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

   3. Taylor expanded in x around inf 69.8%

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

   if -3.0999999999999999e29 < (/.f64 x y) < -1.02000000000000002e-79

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 68.1%

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

      1. associate-*r/ 68.1%

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

      2. metadata-eval 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in z around inf 44.3%

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

   if -1.02000000000000002e-79 < (/.f64 x y) < 2

   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 t around inf 46.1%

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

   4. Taylor expanded in x around 0 44.7%

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

Alternative 9: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+157} \lor \neg \left(\frac{x}{y} \leq 1.45 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+157) (not (<= (/ x y) 1.45e+26)))
   (/ x y)
   (+ -2.0 (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+157) || !((x / y) <= 1.45e+26)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d+157)) .or. (.not. ((x / y) <= 1.45d+26))) then
        tmp = x / y
    else
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+157) || !((x / y) <= 1.45e+26)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+157) or not ((x / y) <= 1.45e+26):
		tmp = x / y
	else:
		tmp = -2.0 + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+157) || !(Float64(x / y) <= 1.45e+26))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+157) || ~(((x / y) <= 1.45e+26)))
		tmp = x / y;
	else
		tmp = -2.0 + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+157], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.45e+26]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999997e157 or 1.45e26 < (/.f64 x y)

   1. Initial program 87.6%

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

   3. Taylor expanded in x around inf 79.6%

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

   if -1.99999999999999997e157 < (/.f64 x y) < 1.45e26

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0 94.1%

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

      1. associate-*r/ 94.1%

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

      2. metadata-eval 94.1%

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

      3. associate-/l/ 94.1%

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

      4. +-commutative 94.1%

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

      5. div-sub 94.1%

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

      6. sub-neg 94.1%

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

      7. *-inverses 94.1%

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

      8. metadata-eval 94.1%

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

      9. distribute-lft-in 94.1%

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

      10. metadata-eval 94.1%

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

      11. associate-+l+ 94.1%

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

      12. +-commutative 94.1%

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

      13. associate-/l/ 94.1%

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

      14. +-commutative 94.1%

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

      15. associate-/l/ 94.1%

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

      16. *-rgt-identity 94.1%

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

      17. associate-*r/ 94.1%

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

      18. distribute-rgt-out 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in z around 0 72.1%

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

   7. Taylor expanded in t around inf 72.2%

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

      1. sub-neg 72.2%

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

      2. metadata-eval 72.2%

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

      3. associate-*r/ 72.2%

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

      4. metadata-eval 72.2%

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

      5. +-commutative 72.2%

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

      6. associate-/r* 72.2%

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

   9. Simplified 72.2%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+157} \lor \neg \left(\frac{x}{y} \leq 1.45 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 90.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-41} \lor \neg \left(z \leq 3.1 \cdot 10^{-59}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.02e-41) (not (<= z 3.1e-59)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ (/ 2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e-41) || !(z <= 3.1e-59)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.02d-41)) .or. (.not. (z <= 3.1d-59))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + ((2.0d0 / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e-41) || !(z <= 3.1e-59)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.02e-41) or not (z <= 3.1e-59):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + ((2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.02e-41) || !(z <= 3.1e-59))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.02e-41) || ~((z <= 3.1e-59)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + ((2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.02e-41], N[Not[LessEqual[z, 3.1e-59]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e-41 or 3.09999999999999999e-59 < z

   1. Initial program 79.4%

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

   3. Taylor expanded in z around inf 98.1%

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

      1. div-sub 98.1%

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

      2. sub-neg 98.1%

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

      3. *-inverses 98.1%

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

      4. metadata-eval 98.1%

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

      5. distribute-lft-in 98.1%

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

      6. associate-*r/ 98.1%

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

      7. metadata-eval 98.1%

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

      8. metadata-eval 98.1%

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

   5. Simplified 98.1%

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

   if -1.02e-41 < z < 3.09999999999999999e-59

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 93.4%

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

   4. Taylor expanded in z around 0 80.6%

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

      1. *-commutative 80.6%

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

      2. associate-*l/ 80.6%

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

      3. associate-*r/ 80.6%

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

      4. associate-/r* 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in x around 0 85.2%

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

      1. associate-*r/ 85.2%

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

      2. metadata-eval 85.2%

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

      3. associate-/l/ 85.3%

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

   9. Simplified 85.3%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-41} \lor \neg \left(z \leq 3.1 \cdot 10^{-59}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-57} \lor \neg \left(z \leq 3.2 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e-57) (not (<= z 3.2e-60)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ -2.0 (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e-57) || !(z <= 3.2e-60)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6d-57)) .or. (.not. (z <= 3.2d-60))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e-57) || !(z <= 3.2e-60)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e-57) or not (z <= 3.2e-60):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = -2.0 + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e-57) || !(z <= 3.2e-60))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6e-57) || ~((z <= 3.2e-60)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = -2.0 + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e-57], N[Not[LessEqual[z, 3.2e-60]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000001e-57 or 3.2000000000000001e-60 < z

   1. Initial program 80.7%

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

   3. Taylor expanded in z around inf 96.3%

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

      1. div-sub 96.3%

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

      2. sub-neg 96.3%

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

      3. *-inverses 96.3%

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

      4. metadata-eval 96.3%

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

      5. distribute-lft-in 96.3%

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

      6. associate-*r/ 96.3%

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

      7. metadata-eval 96.3%

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

      8. metadata-eval 96.3%

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

   5. Simplified 96.3%

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

   if -6.00000000000000001e-57 < z < 3.2000000000000001e-60

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0 76.5%

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

      1. associate-*r/ 76.5%

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

      2. metadata-eval 76.5%

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

      3. associate-/l/ 76.6%

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

      4. +-commutative 76.6%

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

      5. div-sub 76.6%

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

      6. sub-neg 76.6%

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

      7. *-inverses 76.6%

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

      8. metadata-eval 76.6%

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

      9. distribute-lft-in 76.6%

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

      10. metadata-eval 76.6%

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

      11. associate-+l+ 76.6%

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

      12. +-commutative 76.6%

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

      13. associate-/l/ 76.5%

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

      14. +-commutative 76.5%

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

      15. associate-/l/ 76.6%

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

      16. *-rgt-identity 76.6%

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

      17. associate-*r/ 76.5%

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

      18. distribute-rgt-out 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in z around 0 76.5%

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

   7. Taylor expanded in t around inf 76.5%

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

      1. sub-neg 76.5%

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

      2. metadata-eval 76.5%

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

      3. associate-*r/ 76.5%

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

      4. metadata-eval 76.5%

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

      5. +-commutative 76.5%

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

      6. associate-/r* 76.6%

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

   9. Simplified 76.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-57} \lor \neg \left(z \leq 3.2 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{+28} \lor \neg \left(\frac{x}{y} \leq 2.1 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6.6e+28) (not (<= (/ x y) 2.1e+15)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.6e+28) || !((x / y) <= 2.1e+15)) {
		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) <= (-6.6d+28)) .or. (.not. ((x / y) <= 2.1d+15))) 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) <= -6.6e+28) || !((x / y) <= 2.1e+15)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -6.6e+28) or not ((x / y) <= 2.1e+15):
		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) <= -6.6e+28) || !(Float64(x / y) <= 2.1e+15))
		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) <= -6.6e+28) || ~(((x / y) <= 2.1e+15)))
		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], -6.6e+28], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2.1e+15]], $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) < -6.6e28 or 2.1e15 < (/.f64 x y)

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf 71.3%

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

   if -6.6e28 < (/.f64 x y) < 2.1e15

   1. Initial program 87.6%

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

   3. Taylor expanded in z around inf 67.2%

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

      1. div-sub 67.2%

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

      2. sub-neg 67.2%

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

      3. *-inverses 67.2%

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

      4. metadata-eval 67.2%

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

      5. distribute-lft-in 67.2%

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

      6. associate-*r/ 67.2%

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

      7. metadata-eval 67.2%

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

      8. metadata-eval 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in x around 0 64.0%

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

      1. sub-neg 64.0%

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

      2. associate-*r/ 64.0%

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

      3. metadata-eval 64.0%

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

      4. metadata-eval 64.0%

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

   8. Simplified 64.0%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{+28} \lor \neg \left(\frac{x}{y} \leq 2.1 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.000108:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -9e+28)
   (/ x y)
   (if (<= (/ x y) 0.000108) (+ -2.0 (/ 2.0 t)) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -9e+28) {
		tmp = x / y;
	} else if ((x / y) <= 0.000108) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-9d+28)) then
        tmp = x / y
    else if ((x / y) <= 0.000108d0) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -9e+28) {
		tmp = x / y;
	} else if ((x / y) <= 0.000108) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -9e+28:
		tmp = x / y
	elif (x / y) <= 0.000108:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -9e+28)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 0.000108)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -9e+28)
		tmp = x / y;
	elseif ((x / y) <= 0.000108)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -9e+28], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.000108], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -8.9999999999999994e28

   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 x around inf 71.2%

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

   if -8.9999999999999994e28 < (/.f64 x y) < 1.08e-4

   1. Initial program 87.9%

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

   3. Taylor expanded in z around inf 66.7%

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

      1. div-sub 66.7%

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

      2. sub-neg 66.7%

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

      3. *-inverses 66.7%

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

      4. metadata-eval 66.7%

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

      5. distribute-lft-in 66.7%

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

      6. associate-*r/ 66.7%

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

      7. metadata-eval 66.7%

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

      8. metadata-eval 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around 0 65.3%

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

      1. sub-neg 65.3%

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

      2. associate-*r/ 65.3%

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

      3. metadata-eval 65.3%

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

      4. metadata-eval 65.3%

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

   8. Simplified 65.3%

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

   if 1.08e-4 < (/.f64 x y)

   1. Initial program 86.1%

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

   3. Taylor expanded in t around inf 70.5%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.000108:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.7 \lor \neg \left(t \leq 3000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.7) (not (<= t 3000.0)))
   (- (/ 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 <= -6.7) || !(t <= 3000.0)) {
		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 <= (-6.7d0)) .or. (.not. (t <= 3000.0d0))) 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 <= -6.7) || !(t <= 3000.0)) {
		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 <= -6.7) or not (t <= 3000.0):
		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 <= -6.7) || !(t <= 3000.0))
		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 <= -6.7) || ~((t <= 3000.0)))
		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, -6.7], N[Not[LessEqual[t, 3000.0]], $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 < -6.70000000000000018 or 3e3 < t

   1. Initial program 77.5%

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

   3. Taylor expanded in t around inf 85.8%

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

   if -6.70000000000000018 < t < 3e3

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 77.2%

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

      1. associate-*r/ 77.2%

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

      2. metadata-eval 77.2%

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

   5. Simplified 77.2%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.7 \lor \neg \left(t \leq 3000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 80.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -400:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \mathbf{elif}\;t \leq 80000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -400.0)
   (/ (+ x (* y -2.0)) y)
   (if (<= t 80000.0) (/ (+ 2.0 (/ 2.0 z)) t) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -400.0) {
		tmp = (x + (y * -2.0)) / y;
	} else if (t <= 80000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-400.0d0)) then
        tmp = (x + (y * (-2.0d0))) / y
    else if (t <= 80000.0d0) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -400.0) {
		tmp = (x + (y * -2.0)) / y;
	} else if (t <= 80000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -400.0:
		tmp = (x + (y * -2.0)) / y
	elif t <= 80000.0:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -400.0)
		tmp = Float64(Float64(x + Float64(y * -2.0)) / y);
	elseif (t <= 80000.0)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -400.0)
		tmp = (x + (y * -2.0)) / y;
	elseif (t <= 80000.0)
		tmp = (2.0 + (2.0 / z)) / t;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -400.0], N[(N[(x + N[(y * -2.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 80000.0], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -400

   1. Initial program 71.5%

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

   3. Taylor expanded in y around 0 98.5%

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

   4. Taylor expanded in t around inf 81.5%

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

      1. +-commutative 81.5%

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

      2. *-commutative 81.5%

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

   6. Simplified 81.5%

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

   if -400 < t < 8e4

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 77.2%

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

      1. associate-*r/ 77.2%

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

      2. metadata-eval 77.2%

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

   5. Simplified 77.2%

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

   if 8e4 < t

   1. Initial program 83.8%

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

   3. Taylor expanded in t around inf 90.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -400:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \mathbf{elif}\;t \leq 80000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+26}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 1.15e+26) (/ 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 <= 1.15e+26) {
		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 <= 1.15d+26) 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 <= 1.15e+26) {
		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 <= 1.15e+26:
		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 <= 1.15e+26)
		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 <= 1.15e+26)
		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, 1.15e+26], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 1.15e26 < t

   1. Initial program 77.3%

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

   3. Taylor expanded in t around inf 85.7%

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

   4. Taylor expanded in x around 0 43.7%

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

   if -1 < t < 1.15e26

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 76.6%

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

      1. associate-*r/ 76.6%

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

      2. metadata-eval 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in z around inf 32.9%

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

Alternative 17: 19.9% 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 87.7%

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

3. Taylor expanded in t around inf 56.0%

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

4. Taylor expanded in x around 0 23.0%

   \[\leadsto \color{blue}{-2} \]
5. 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 2024145 
(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))))