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

Percentage Accurate: 86.8% → 98.4%

Time: 11.1s

Alternatives: 16

Speedup: 0.9×

• 23.9% 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: 86.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(1 - t\right) \cdot \left(2 \cdot z\right)}{z \cdot t}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;t\_1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t} + z \cdot \left(\frac{2}{t} + -2\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (- 1.0 t) (* 2.0 z))) (* z t))))
   (if (<= t_1 5e+297)
     (+ t_1 (/ x y))
     (+ (/ x y) (/ (+ (/ 2.0 t) (* z (+ (/ 2.0 t) -2.0))) z)))))

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 <= 5e+297) {
		tmp = t_1 + (x / y);
	} else {
		tmp = (x / y) + (((2.0 / t) + (z * ((2.0 / t) + -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) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 + ((1.0d0 - t) * (2.0d0 * z))) / (z * t)
    if (t_1 <= 5d+297) then
        tmp = t_1 + (x / y)
    else
        tmp = (x / y) + (((2.0d0 / t) + (z * ((2.0d0 / t) + (-2.0d0)))) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((1.0 - t) * (2.0 * z))) / (z * t);
	double tmp;
	if (t_1 <= 5e+297) {
		tmp = t_1 + (x / y);
	} else {
		tmp = (x / y) + (((2.0 / t) + (z * ((2.0 / t) + -2.0))) / z);
	}
	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 <= 5e+297:
		tmp = t_1 + (x / y)
	else:
		tmp = (x / y) + (((2.0 / t) + (z * ((2.0 / t) + -2.0))) / z)
	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 <= 5e+297)
		tmp = Float64(t_1 + Float64(x / y));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(Float64(2.0 / t) + Float64(z * Float64(Float64(2.0 / t) + -2.0))) / z));
	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 <= 5e+297)
		tmp = t_1 + (x / y);
	else
		tmp = (x / y) + (((2.0 / t) + (z * ((2.0 / t) + -2.0))) / z);
	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, 5e+297], N[(t$95$1 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(N[(2.0 / t), $MachinePrecision] + N[(z * N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $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)) < 4.9999999999999998e297

   1. Initial program 98.9%

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

   if 4.9999999999999998e297 < (/.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 20.0%

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

   3. Taylor expanded in z around 0 27.0%

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

      1. +-commutative 27.0%

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

      2. associate-/l* 100.0%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*r* 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. div-sub 100.0%

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

      9. sub-neg 100.0%

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

      10. *-inverses 100.0%

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

      11. metadata-eval 100.0%

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

      12. distribute-lft-in 100.0%

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

      13. metadata-eval 100.0%

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

      14. associate-*r/ 100.0%

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

      15. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(1 - t\right) \cdot \left(2 \cdot z\right)}{z \cdot t} \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{2 + \left(1 - t\right) \cdot \left(2 \cdot z\right)}{z \cdot t} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t} + z \cdot \left(\frac{2}{t} + -2\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.3% accurate, 0.4× speedup

Math

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

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))))

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;
	}
	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;
	}
	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
	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 / y) - 2.0);
	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;
	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 / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 94.1%

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

4. Final simplification 99.1%

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

Alternative 3: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -5 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-134} \lor \neg \left(z \leq 116\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -5e+121)
     t_1
     (if (<= z -9.8e+23)
       (+ (/ 2.0 t) -2.0)
       (if (or (<= z -4.1e-134) (not (<= z 116.0)))
         t_1
         (+ -2.0 (/ 2.0 (* z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -5e+121) {
		tmp = t_1;
	} else if (z <= -9.8e+23) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -4.1e-134) || !(z <= 116.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-5d+121)) then
        tmp = t_1
    else if (z <= (-9.8d+23)) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if ((z <= (-4.1d-134)) .or. (.not. (z <= 116.0d0))) then
        tmp = t_1
    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 t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -5e+121) {
		tmp = t_1;
	} else if (z <= -9.8e+23) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -4.1e-134) || !(z <= 116.0)) {
		tmp = t_1;
	} else {
		tmp = -2.0 + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -5e+121:
		tmp = t_1
	elif z <= -9.8e+23:
		tmp = (2.0 / t) + -2.0
	elif (z <= -4.1e-134) or not (z <= 116.0):
		tmp = t_1
	else:
		tmp = -2.0 + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -5e+121)
		tmp = t_1;
	elseif (z <= -9.8e+23)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif ((z <= -4.1e-134) || !(z <= 116.0))
		tmp = t_1;
	else
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * 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 <= -5e+121)
		tmp = t_1;
	elseif (z <= -9.8e+23)
		tmp = (2.0 / t) + -2.0;
	elseif ((z <= -4.1e-134) || ~((z <= 116.0)))
		tmp = t_1;
	else
		tmp = -2.0 + (2.0 / (z * 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, -5e+121], t$95$1, If[LessEqual[z, -9.8e+23], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[Or[LessEqual[z, -4.1e-134], N[Not[LessEqual[z, 116.0]], $MachinePrecision]], t$95$1, N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000007e121 or -9.8000000000000006e23 < z < -4.1000000000000002e-134 or 116 < z

   1. Initial program 77.7%

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

   3. Taylor expanded in t around inf 71.3%

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

   if -5.00000000000000007e121 < z < -9.8000000000000006e23

   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 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. metadata-eval 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 83.3%

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

      1. sub-neg 83.3%

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

      2. metadata-eval 83.3%

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

      3. associate-*r/ 83.3%

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

      4. metadata-eval 83.3%

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

      5. +-commutative 83.3%

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

   8. Simplified 83.3%

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

   if -4.1000000000000002e-134 < z < 116

   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 t around inf 97.0%

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

      1. *-commutative 97.0%

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

      2. *-commutative 97.0%

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

      3. associate-*l* 97.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in z around inf 97.0%

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

      1. sub-neg 97.0%

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

      2. associate-*r/ 97.0%

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

      3. metadata-eval 97.0%

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

      4. *-commutative 97.0%

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

      5. associate-/r* 96.8%

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

      6. metadata-eval 96.8%

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

   8. Simplified 96.8%

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

   9. Taylor expanded in x around 0 77.1%

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

       1. sub-neg 77.1%

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

       2. associate-*r/ 77.1%

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

       3. metadata-eval 77.1%

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

       4. *-commutative 77.1%

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

       5. metadata-eval 77.1%

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

       6. +-commutative 77.1%

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

       7. *-commutative 77.1%

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

   11. Simplified 77.1%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-134} \lor \neg \left(z \leq 116\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -5 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+26}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-134} \lor \neg \left(z \leq 116\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -5e+121)
     t_1
     (if (<= z -8e+26)
       (+ (/ 2.0 t) -2.0)
       (if (or (<= z -1.05e-134) (not (<= z 116.0))) t_1 (/ 2.0 (* z t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -5e+121) {
		tmp = t_1;
	} else if (z <= -8e+26) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -1.05e-134) || !(z <= 116.0)) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-5d+121)) then
        tmp = t_1
    else if (z <= (-8d+26)) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if ((z <= (-1.05d-134)) .or. (.not. (z <= 116.0d0))) then
        tmp = t_1
    else
        tmp = 2.0d0 / (z * 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 <= -5e+121) {
		tmp = t_1;
	} else if (z <= -8e+26) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -1.05e-134) || !(z <= 116.0)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -5e+121:
		tmp = t_1
	elif z <= -8e+26:
		tmp = (2.0 / t) + -2.0
	elif (z <= -1.05e-134) or not (z <= 116.0):
		tmp = t_1
	else:
		tmp = 2.0 / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -5e+121)
		tmp = t_1;
	elseif (z <= -8e+26)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif ((z <= -1.05e-134) || !(z <= 116.0))
		tmp = t_1;
	else
		tmp = Float64(2.0 / Float64(z * 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 <= -5e+121)
		tmp = t_1;
	elseif (z <= -8e+26)
		tmp = (2.0 / t) + -2.0;
	elseif ((z <= -1.05e-134) || ~((z <= 116.0)))
		tmp = t_1;
	else
		tmp = 2.0 / (z * 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, -5e+121], t$95$1, If[LessEqual[z, -8e+26], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[Or[LessEqual[z, -1.05e-134], N[Not[LessEqual[z, 116.0]], $MachinePrecision]], t$95$1, N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000007e121 or -8.00000000000000038e26 < z < -1.05e-134 or 116 < z

   1. Initial program 77.7%

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

   3. Taylor expanded in t around inf 71.3%

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

   if -5.00000000000000007e121 < z < -8.00000000000000038e26

   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 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. metadata-eval 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 83.3%

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

      1. sub-neg 83.3%

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

      2. metadata-eval 83.3%

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

      3. associate-*r/ 83.3%

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

      4. metadata-eval 83.3%

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

      5. +-commutative 83.3%

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

   8. Simplified 83.3%

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

   if -1.05e-134 < z < 116

   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 t around inf 97.0%

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

      1. *-commutative 97.0%

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

      2. *-commutative 97.0%

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

      3. associate-*l* 97.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in z around inf 97.0%

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

      1. sub-neg 97.0%

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

      2. associate-*r/ 97.0%

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

      3. metadata-eval 97.0%

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

      4. *-commutative 97.0%

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

      5. associate-/r* 96.8%

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

      6. metadata-eval 96.8%

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

   8. Simplified 96.8%

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

   9. Taylor expanded in z around 0 68.9%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+26}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-134} \lor \neg \left(z \leq 116\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+81} \lor \neg \left(t \leq 5 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{z}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5e+81) (not (<= t 5e+55)))
   (+ (/ x y) (+ -2.0 (/ (/ 2.0 z) t)))
   (/ (+ (+ 2.0 (/ 2.0 z)) (* t (+ (/ x y) -2.0))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e+81) || !(t <= 5e+55)) {
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5d+81)) .or. (.not. (t <= 5d+55))) then
        tmp = (x / y) + ((-2.0d0) + ((2.0d0 / z) / t))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) + (t * ((x / y) + (-2.0d0)))) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e+81) || !(t <= 5e+55)) {
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5e+81) or not (t <= 5e+55):
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t))
	else:
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5e+81) || !(t <= 5e+55))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(Float64(2.0 / z) / t)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) + Float64(t * Float64(Float64(x / y) + -2.0))) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5e+81) || ~((t <= 5e+55)))
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	else
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5e+81], N[Not[LessEqual[t, 5e+55]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.9999999999999998e81 or 5.00000000000000046e55 < t

   1. Initial program 67.3%

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

   3. Taylor expanded in t around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. *-commutative 67.3%

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

      3. associate-*l* 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in z around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   if -4.9999999999999998e81 < t < 5.00000000000000046e55

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0 98.6%

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

      1. associate-+r+ 98.6%

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

      2. associate-*r/ 98.6%

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

      3. metadata-eval 98.6%

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

      4. sub-neg 98.6%

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

      5. metadata-eval 98.6%

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

   5. Simplified 98.6%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+81} \lor \neg \left(t \leq 5 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{z}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.46 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.3 \cdot 10^{-127}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.8 \cdot 10^{-8}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.46e+22)
   (/ x y)
   (if (<= (/ x y) 2.3e-127) (/ 2.0 t) (if (<= (/ x y) 1.8e-8) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.46e+22) {
		tmp = x / y;
	} else if ((x / y) <= 2.3e-127) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 1.8e-8) {
		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) <= (-1.46d+22)) then
        tmp = x / y
    else if ((x / y) <= 2.3d-127) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 1.8d-8) 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) <= -1.46e+22) {
		tmp = x / y;
	} else if ((x / y) <= 2.3e-127) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 1.8e-8) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.46e+22:
		tmp = x / y
	elif (x / y) <= 2.3e-127:
		tmp = 2.0 / t
	elif (x / y) <= 1.8e-8:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.46e+22)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.3e-127)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 1.8e-8)
		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) <= -1.46e+22)
		tmp = x / y;
	elseif ((x / y) <= 2.3e-127)
		tmp = 2.0 / t;
	elseif ((x / y) <= 1.8e-8)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.46e+22], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.3e-127], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.8e-8], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.46e22 or 1.79999999999999991e-8 < (/.f64 x y)

   1. Initial program 83.3%

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

   3. Taylor expanded in x around inf 70.2%

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

   if -1.46e22 < (/.f64 x y) < 2.30000000000000019e-127

   1. Initial program 89.4%

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

   3. Taylor expanded in z around inf 59.2%

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

      1. div-sub 59.2%

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

      2. sub-neg 59.2%

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

      3. *-inverses 59.2%

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

      4. metadata-eval 59.2%

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

      5. distribute-lft-in 59.2%

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

      6. metadata-eval 59.2%

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

      7. associate-*r/ 59.2%

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

      8. metadata-eval 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in t around 0 36.2%

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

   if 2.30000000000000019e-127 < (/.f64 x y) < 1.79999999999999991e-8

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 79.9%

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

      1. div-sub 79.9%

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

      2. sub-neg 79.9%

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

      3. *-inverses 79.9%

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

      4. metadata-eval 79.9%

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

      5. distribute-lft-in 79.9%

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

      6. metadata-eval 79.9%

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

      7. associate-*r/ 79.9%

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

      8. metadata-eval 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in x around 0 77.7%

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

      1. sub-neg 77.7%

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

      2. metadata-eval 77.7%

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

      3. associate-*r/ 77.7%

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

      4. metadata-eval 77.7%

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

      5. +-commutative 77.7%

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

   8. Simplified 77.7%

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

   9. Taylor expanded in t around inf 61.9%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.46 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.3 \cdot 10^{-127}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.8 \cdot 10^{-8}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+14} \lor \neg \left(t \leq 0.0002\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{z}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.36e+14) (not (<= t 0.0002)))
   (+ (/ x y) (+ -2.0 (/ (/ 2.0 z) t)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.36e+14) || !(t <= 0.0002)) {
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	} else {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.36d+14)) .or. (.not. (t <= 0.0002d0))) then
        tmp = (x / y) + ((-2.0d0) + ((2.0d0 / z) / t))
    else
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.36e+14) || !(t <= 0.0002)) {
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	} else {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.36e+14) or not (t <= 0.0002):
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t))
	else:
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.36e+14) || !(t <= 0.0002))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(Float64(2.0 / z) / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.36e+14) || ~((t <= 0.0002)))
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	else
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.36e+14], N[Not[LessEqual[t, 0.0002]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.36e14 or 2.0000000000000001e-4 < t

   1. Initial program 73.9%

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

   3. Taylor expanded in t around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*l* 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in z around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   if -1.36e14 < t < 2.0000000000000001e-4

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 98.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+14} \lor \neg \left(t \leq 0.0002\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{z}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+22} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{z}}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e+22) (not (<= z 1.0)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (+ -2.0 (/ (/ 2.0 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+22) || !(z <= 1.0)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d+22)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (x / y) + ((-2.0d0) + ((2.0d0 / z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+22) || !(z <= 1.0)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e+22) or not (z <= 1.0):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e+22) || !(z <= 1.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(Float64(2.0 / z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e+22) || ~((z <= 1.0)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e+22], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e22 or 1 < z

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf 99.4%

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

      1. div-sub 99.4%

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

      2. sub-neg 99.4%

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

      3. *-inverses 99.4%

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

      4. metadata-eval 99.4%

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

      5. distribute-lft-in 99.4%

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

      6. metadata-eval 99.4%

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

      7. associate-*r/ 99.4%

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

      8. metadata-eval 99.4%

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

   5. Simplified 99.4%

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

   if -1.6e22 < z < 1

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 97.1%

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

      1. *-commutative 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*l* 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in z around inf 97.0%

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

      1. sub-neg 97.0%

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

      2. associate-*r/ 97.0%

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

      3. metadata-eval 97.0%

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

      4. *-commutative 97.0%

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

      5. associate-/r* 96.9%

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

      6. metadata-eval 96.9%

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

   8. Simplified 96.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+22} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{z}}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.65 \cdot 10^{+19} \lor \neg \left(\frac{x}{y} \leq 14000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3.65e+19) (not (<= (/ x y) 14000.0)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3.65e+19) || !((x / y) <= 14000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-3.65d+19)) .or. (.not. ((x / y) <= 14000.0d0))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3.65e+19) || !((x / y) <= 14000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3.65e+19) or not ((x / y) <= 14000.0):
		tmp = x / y
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -3.65e+19) || !(Float64(x / y) <= 14000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -3.65e+19) || ~(((x / y) <= 14000.0)))
		tmp = x / y;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -3.65e+19], N[Not[LessEqual[N[(x / y), $MachinePrecision], 14000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.65e19 or 14000 < (/.f64 x y)

   1. Initial program 83.1%

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

   3. Taylor expanded in x around inf 70.7%

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

   if -3.65e19 < (/.f64 x y) < 14000

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 62.5%

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

      1. div-sub 62.5%

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

      2. sub-neg 62.5%

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

      3. *-inverses 62.5%

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

      4. metadata-eval 62.5%

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

      5. distribute-lft-in 62.5%

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

      6. metadata-eval 62.5%

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

      7. associate-*r/ 62.5%

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

      8. metadata-eval 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in x around 0 61.4%

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

      1. sub-neg 61.4%

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

      2. metadata-eval 61.4%

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

      3. associate-*r/ 61.4%

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

      4. metadata-eval 61.4%

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

      5. +-commutative 61.4%

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

   8. Simplified 61.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.65 \cdot 10^{+19} \lor \neg \left(\frac{x}{y} \leq 14000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-132} \lor \neg \left(z \leq 6.4 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.8e-132) (not (<= z 6.4e-28)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ -2.0 (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.8e-132) || !(z <= 6.4e-28)) {
		tmp = (x / y) + ((2.0 / t) + -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 ((z <= (-9.8d-132)) .or. (.not. (z <= 6.4d-28))) then
        tmp = (x / y) + ((2.0d0 / t) + (-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 ((z <= -9.8e-132) || !(z <= 6.4e-28)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = -2.0 + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.8e-132) or not (z <= 6.4e-28):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = -2.0 + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.8e-132) || !(z <= 6.4e-28))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.8e-132) || ~((z <= 6.4e-28)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = -2.0 + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.8e-132], N[Not[LessEqual[z, 6.4e-28]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999961e-132 or 6.39999999999999964e-28 < z

   1. Initial program 79.5%

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

   3. Taylor expanded in z around inf 95.3%

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

      1. div-sub 95.3%

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

      2. sub-neg 95.3%

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

      3. *-inverses 95.3%

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

      4. metadata-eval 95.3%

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

      5. distribute-lft-in 95.3%

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

      6. metadata-eval 95.3%

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

      7. associate-*r/ 95.3%

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

      8. metadata-eval 95.3%

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

   5. Simplified 95.3%

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

   if -9.79999999999999961e-132 < z < 6.39999999999999964e-28

   1. Initial program 97.8%

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

   3. Taylor expanded in t around inf 97.8%

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

      1. *-commutative 97.8%

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

      2. *-commutative 97.8%

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

      3. associate-*l* 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in z around inf 97.8%

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

      1. sub-neg 97.8%

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

      2. associate-*r/ 97.8%

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

      3. metadata-eval 97.8%

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

      4. *-commutative 97.8%

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

      5. associate-/r* 97.6%

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

      6. metadata-eval 97.6%

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

   8. Simplified 97.6%

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

   9. Taylor expanded in x around 0 77.7%

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

       1. sub-neg 77.7%

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

       2. associate-*r/ 77.7%

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

       3. metadata-eval 77.7%

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

       4. *-commutative 77.7%

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

       5. metadata-eval 77.7%

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

       6. +-commutative 77.7%

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

       7. *-commutative 77.7%

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

   11. Simplified 77.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-132} \lor \neg \left(z \leq 6.4 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-29} \lor \neg \left(z \leq 9 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.05e-29) (not (<= z 9e-9)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-29) || !(z <= 9e-9)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} 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 <= (-1.05d-29)) .or. (.not. (z <= 9d-9))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    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 <= -1.05e-29) || !(z <= 9e-9)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.05e-29) or not (z <= 9e-9):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.05e-29) || !(z <= 9e-9))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05e-29) || ~((z <= 9e-9)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05e-29], N[Not[LessEqual[z, 9e-9]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999995e-29 or 8.99999999999999953e-9 < z

   1. Initial program 77.2%

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

   3. Taylor expanded in z around inf 97.6%

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

      1. div-sub 97.6%

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

      2. sub-neg 97.6%

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

      3. *-inverses 97.6%

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

      4. metadata-eval 97.6%

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

      5. distribute-lft-in 97.6%

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

      6. metadata-eval 97.6%

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

      7. associate-*r/ 97.6%

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

      8. metadata-eval 97.6%

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

   5. Simplified 97.6%

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

   if -1.04999999999999995e-29 < z < 8.99999999999999953e-9

   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 z around 0 89.5%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-29} \lor \neg \left(z \leq 9 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 91.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-30} \lor \neg \left(z \leq 1.3 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.2e-30) (not (<= z 1.3e-5)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e-30) || !(z <= 1.3e-5)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9.2d-30)) .or. (.not. (z <= 1.3d-5))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e-30) || !(z <= 1.3e-5)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.2e-30) or not (z <= 1.3e-5):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.2e-30) || !(z <= 1.3e-5))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.2e-30) || ~((z <= 1.3e-5)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.2e-30], N[Not[LessEqual[z, 1.3e-5]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999937e-30 or 1.29999999999999992e-5 < z

   1. Initial program 77.2%

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

   3. Taylor expanded in z around inf 97.6%

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

      1. div-sub 97.6%

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

      2. sub-neg 97.6%

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

      3. *-inverses 97.6%

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

      4. metadata-eval 97.6%

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

      5. distribute-lft-in 97.6%

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

      6. metadata-eval 97.6%

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

      7. associate-*r/ 97.6%

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

      8. metadata-eval 97.6%

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

   5. Simplified 97.6%

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

   if -9.19999999999999937e-30 < z < 1.29999999999999992e-5

   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 z around 0 89.5%

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

   4. Taylor expanded in x around 0 89.5%

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

      1. associate-*r/ 89.5%

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

      2. metadata-eval 89.5%

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

      3. associate-/r* 89.5%

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

   6. Simplified 89.5%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-30} \lor \neg \left(z \leq 1.3 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.3 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0145:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6.3e+19)
   (/ x y)
   (if (<= (/ x y) 0.0145) (+ (/ 2.0 t) -2.0) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6.3e+19) {
		tmp = x / y;
	} else if ((x / y) <= 0.0145) {
		tmp = (2.0 / t) + -2.0;
	} 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) <= (-6.3d+19)) then
        tmp = x / y
    else if ((x / y) <= 0.0145d0) then
        tmp = (2.0d0 / t) + (-2.0d0)
    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) <= -6.3e+19) {
		tmp = x / y;
	} else if ((x / y) <= 0.0145) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -6.3e+19:
		tmp = x / y
	elif (x / y) <= 0.0145:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -6.3e+19)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 0.0145)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	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) <= -6.3e+19)
		tmp = x / y;
	elseif ((x / y) <= 0.0145)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -6.3e+19], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0145], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -6.3e19

   1. Initial program 82.3%

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

   3. Taylor expanded in x around inf 71.4%

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

   if -6.3e19 < (/.f64 x y) < 0.0145000000000000007

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 62.5%

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

      1. div-sub 62.5%

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

      2. sub-neg 62.5%

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

      3. *-inverses 62.5%

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

      4. metadata-eval 62.5%

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

      5. distribute-lft-in 62.5%

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

      6. metadata-eval 62.5%

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

      7. associate-*r/ 62.5%

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

      8. metadata-eval 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in x around 0 61.4%

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

      1. sub-neg 61.4%

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

      2. metadata-eval 61.4%

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

      3. associate-*r/ 61.4%

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

      4. metadata-eval 61.4%

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

      5. +-commutative 61.4%

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

   8. Simplified 61.4%

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

   if 0.0145000000000000007 < (/.f64 x y)

   1. Initial program 84.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.3 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0145:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -620000000000 \lor \neg \left(t \leq 8 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -620000000000.0) (not (<= t 8e-50)))
   (- (/ 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 <= -620000000000.0) || !(t <= 8e-50)) {
		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 <= (-620000000000.0d0)) .or. (.not. (t <= 8d-50))) 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 <= -620000000000.0) || !(t <= 8e-50)) {
		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 <= -620000000000.0) or not (t <= 8e-50):
		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 <= -620000000000.0) || !(t <= 8e-50))
		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 <= -620000000000.0) || ~((t <= 8e-50)))
		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, -620000000000.0], N[Not[LessEqual[t, 8e-50]], $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 < -6.2e11 or 8.00000000000000006e-50 < t

   1. Initial program 76.6%

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

   3. Taylor expanded in t around inf 79.8%

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

   if -6.2e11 < t < 8.00000000000000006e-50

   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 t around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. metadata-eval 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -620000000000 \lor \neg \left(t \leq 8 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.7e-9) -2.0 (if (<= t 3.8e-24) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-9) {
		tmp = -2.0;
	} else if (t <= 3.8e-24) {
		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 <= (-1.7d-9)) then
        tmp = -2.0d0
    else if (t <= 3.8d-24) 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 <= -1.7e-9) {
		tmp = -2.0;
	} else if (t <= 3.8e-24) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.7e-9:
		tmp = -2.0
	elif t <= 3.8e-24:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.7e-9)
		tmp = -2.0;
	elseif (t <= 3.8e-24)
		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 <= -1.7e-9)
		tmp = -2.0;
	elseif (t <= 3.8e-24)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.7e-9], -2.0, If[LessEqual[t, 3.8e-24], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e-9 or 3.80000000000000026e-24 < t

   1. Initial program 75.7%

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

   3. Taylor expanded in z around inf 79.7%

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

      1. div-sub 79.7%

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

      2. sub-neg 79.7%

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

      3. *-inverses 79.7%

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

      4. metadata-eval 79.7%

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

      5. distribute-lft-in 79.7%

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

      6. metadata-eval 79.7%

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

      7. associate-*r/ 79.7%

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

      8. metadata-eval 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in x around 0 28.6%

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

      1. sub-neg 28.6%

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

      2. metadata-eval 28.6%

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

      3. associate-*r/ 28.6%

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

      4. metadata-eval 28.6%

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

      5. +-commutative 28.6%

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

   8. Simplified 28.6%

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

   9. Taylor expanded in t around inf 28.7%

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

   if -1.6999999999999999e-9 < t < 3.80000000000000026e-24

   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 z around inf 60.3%

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

      1. div-sub 60.3%

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

      2. sub-neg 60.3%

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

      3. *-inverses 60.3%

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

      4. metadata-eval 60.3%

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

      5. distribute-lft-in 60.3%

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

      6. metadata-eval 60.3%

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

      7. associate-*r/ 60.3%

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

      8. metadata-eval 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in t around 0 41.5%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 19.4% 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 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 z around inf 70.3%

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

   1. div-sub 70.3%

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

   2. sub-neg 70.3%

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

   3. *-inverses 70.3%

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

   4. metadata-eval 70.3%

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

   5. distribute-lft-in 70.3%

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

   6. metadata-eval 70.3%

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

   7. associate-*r/ 70.3%

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

   8. metadata-eval 70.3%

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

5. Simplified 70.3%

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

6. Taylor expanded in x around 0 35.0%

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

   1. sub-neg 35.0%

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

   2. metadata-eval 35.0%

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

   3. associate-*r/ 35.0%

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

   4. metadata-eval 35.0%

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

   5. +-commutative 35.0%

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

8. Simplified 35.0%

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

9. Taylor expanded in t around inf 16.1%

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

10. Final simplification 16.1%

    \[\leadsto -2 \]
11. Add Preprocessing

Developer target: 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 2024130 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

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