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

Percentage Accurate: 86.3% → 99.3%

Time: 11.9s

Alternatives: 17

Speedup: 0.9×

• 24.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 96.9%

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

4. Final simplification 99.5%

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

Alternative 2: 67.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{2}{t}\\ t_2 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -70:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -3.1 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-179}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.9 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 86000000000000:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ 2.0 t))) (t_2 (+ (/ x y) (/ 2.0 t))))
   (if (<= (/ x y) -70.0)
     t_2
     (if (<= (/ x y) -3.1e-114)
       t_1
       (if (<= (/ x y) -1e-179)
         (/ (/ 2.0 t) z)
         (if (<= (/ x y) 3.9e-83)
           t_1
           (if (<= (/ x y) 86000000000000.0) (/ 2.0 (* t z)) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (2.0 / t);
	double t_2 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -70.0) {
		tmp = t_2;
	} else if ((x / y) <= -3.1e-114) {
		tmp = t_1;
	} else if ((x / y) <= -1e-179) {
		tmp = (2.0 / t) / z;
	} else if ((x / y) <= 3.9e-83) {
		tmp = t_1;
	} else if ((x / y) <= 86000000000000.0) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-2.0d0) + (2.0d0 / t)
    t_2 = (x / y) + (2.0d0 / t)
    if ((x / y) <= (-70.0d0)) then
        tmp = t_2
    else if ((x / y) <= (-3.1d-114)) then
        tmp = t_1
    else if ((x / y) <= (-1d-179)) then
        tmp = (2.0d0 / t) / z
    else if ((x / y) <= 3.9d-83) then
        tmp = t_1
    else if ((x / y) <= 86000000000000.0d0) then
        tmp = 2.0d0 / (t * z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (2.0 / t);
	double t_2 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -70.0) {
		tmp = t_2;
	} else if ((x / y) <= -3.1e-114) {
		tmp = t_1;
	} else if ((x / y) <= -1e-179) {
		tmp = (2.0 / t) / z;
	} else if ((x / y) <= 3.9e-83) {
		tmp = t_1;
	} else if ((x / y) <= 86000000000000.0) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (2.0 / t)
	t_2 = (x / y) + (2.0 / t)
	tmp = 0
	if (x / y) <= -70.0:
		tmp = t_2
	elif (x / y) <= -3.1e-114:
		tmp = t_1
	elif (x / y) <= -1e-179:
		tmp = (2.0 / t) / z
	elif (x / y) <= 3.9e-83:
		tmp = t_1
	elif (x / y) <= 86000000000000.0:
		tmp = 2.0 / (t * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(2.0 / t))
	t_2 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (Float64(x / y) <= -70.0)
		tmp = t_2;
	elseif (Float64(x / y) <= -3.1e-114)
		tmp = t_1;
	elseif (Float64(x / y) <= -1e-179)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (Float64(x / y) <= 3.9e-83)
		tmp = t_1;
	elseif (Float64(x / y) <= 86000000000000.0)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (2.0 / t);
	t_2 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if ((x / y) <= -70.0)
		tmp = t_2;
	elseif ((x / y) <= -3.1e-114)
		tmp = t_1;
	elseif ((x / y) <= -1e-179)
		tmp = (2.0 / t) / z;
	elseif ((x / y) <= 3.9e-83)
		tmp = t_1;
	elseif ((x / y) <= 86000000000000.0)
		tmp = 2.0 / (t * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -70.0], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -3.1e-114], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -1e-179], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3.9e-83], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 86000000000000.0], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -70 or 8.6e13 < (/.f64 x y)

   1. Initial program 85.6%

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

   3. Taylor expanded in t around 0 97.9%

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

   4. Taylor expanded in z around inf 82.6%

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

      1. associate-*r/ 82.6%

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

      2. metadata-eval 82.6%

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

      3. +-commutative 82.6%

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

   6. Simplified 82.6%

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

   if -70 < (/.f64 x y) < -3.1e-114 or -1e-179 < (/.f64 x y) < 3.9e-83

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in x around 0 98.8%

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

      1. associate-*r/ 98.8%

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

      2. metadata-eval 98.8%

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

      3. associate-/r* 98.7%

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

      4. +-commutative 98.7%

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

      5. associate-/l/ 98.8%

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

      6. div-sub 98.8%

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

      7. sub-neg 98.8%

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

      8. *-inverses 98.8%

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

      9. metadata-eval 98.8%

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

      10. distribute-lft-in 98.8%

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

      11. associate-*r/ 98.8%

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

      12. metadata-eval 98.8%

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

      13. metadata-eval 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in z around inf 64.5%

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

      1. sub-neg 64.5%

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

      2. metadata-eval 64.5%

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

      3. associate-*r/ 64.5%

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

      4. metadata-eval 64.5%

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

      5. +-commutative 64.5%

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

   9. Simplified 64.5%

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

   if -3.1e-114 < (/.f64 x y) < -1e-179

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0 82.8%

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

   4. Taylor expanded in x around 0 82.8%

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

      1. associate-*r/ 82.8%

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

      2. metadata-eval 82.8%

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

      3. associate-+r+ 82.8%

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

      4. associate-*r/ 82.8%

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

      5. metadata-eval 82.8%

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

      6. associate-/r* 82.9%

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

      7. +-commutative 82.9%

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

      8. associate-+r+ 82.9%

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

      9. +-commutative 82.9%

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

      10. +-commutative 82.9%

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

      11. associate-+l+ 82.9%

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

      12. +-commutative 82.9%

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

      13. +-commutative 82.9%

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

      14. metadata-eval 82.9%

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

      15. associate-*r/ 82.9%

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

      16. *-commutative 82.9%

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

      17. *-rgt-identity 82.9%

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

      18. associate-*r/ 82.8%

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

   6. Simplified 82.5%

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

   7. Taylor expanded in z around 0 74.1%

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

      1. associate-/r* 74.3%

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

   9. Simplified 74.3%

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

   if 3.9e-83 < (/.f64 x y) < 8.6e13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in z around 0 69.5%

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

      1. *-commutative 69.5%

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

   6. Simplified 69.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -70:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -3.1 \cdot 10^{-114}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-179}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.9 \cdot 10^{-83}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 86000000000000:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := \frac{2}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -3 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.18 \cdot 10^{+89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1.6 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 1.12 \cdot 10^{-81}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (/ 2.0 (* t z))))
   (if (<= (/ x y) -3e+115)
     (/ x y)
     (if (<= (/ x y) -1.18e+89)
       t_2
       (if (<= (/ x y) -1.6e-15)
         t_1
         (if (<= (/ x y) 1.12e-81)
           (+ -2.0 (/ 2.0 t))
           (if (<= (/ x y) 4.2e+15) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = 2.0 / (t * z);
	double tmp;
	if ((x / y) <= -3e+115) {
		tmp = x / y;
	} else if ((x / y) <= -1.18e+89) {
		tmp = t_2;
	} else if ((x / y) <= -1.6e-15) {
		tmp = t_1;
	} else if ((x / y) <= 1.12e-81) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 4.2e+15) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    t_2 = 2.0d0 / (t * z)
    if ((x / y) <= (-3d+115)) then
        tmp = x / y
    else if ((x / y) <= (-1.18d+89)) then
        tmp = t_2
    else if ((x / y) <= (-1.6d-15)) then
        tmp = t_1
    else if ((x / y) <= 1.12d-81) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if ((x / y) <= 4.2d+15) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = 2.0 / (t * z);
	double tmp;
	if ((x / y) <= -3e+115) {
		tmp = x / y;
	} else if ((x / y) <= -1.18e+89) {
		tmp = t_2;
	} else if ((x / y) <= -1.6e-15) {
		tmp = t_1;
	} else if ((x / y) <= 1.12e-81) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 4.2e+15) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	t_2 = 2.0 / (t * z)
	tmp = 0
	if (x / y) <= -3e+115:
		tmp = x / y
	elif (x / y) <= -1.18e+89:
		tmp = t_2
	elif (x / y) <= -1.6e-15:
		tmp = t_1
	elif (x / y) <= 1.12e-81:
		tmp = -2.0 + (2.0 / t)
	elif (x / y) <= 4.2e+15:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	t_2 = Float64(2.0 / Float64(t * z))
	tmp = 0.0
	if (Float64(x / y) <= -3e+115)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -1.18e+89)
		tmp = t_2;
	elseif (Float64(x / y) <= -1.6e-15)
		tmp = t_1;
	elseif (Float64(x / y) <= 1.12e-81)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (Float64(x / y) <= 4.2e+15)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	t_2 = 2.0 / (t * z);
	tmp = 0.0;
	if ((x / y) <= -3e+115)
		tmp = x / y;
	elseif ((x / y) <= -1.18e+89)
		tmp = t_2;
	elseif ((x / y) <= -1.6e-15)
		tmp = t_1;
	elseif ((x / y) <= 1.12e-81)
		tmp = -2.0 + (2.0 / t);
	elseif ((x / y) <= 4.2e+15)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -3e+115], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1.18e+89], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -1.6e-15], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1.12e-81], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.2e+15], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -3e115

   1. Initial program 83.7%

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

   3. Taylor expanded in x around inf 78.0%

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

   if -3e115 < (/.f64 x y) < -1.17999999999999993e89 or 1.1200000000000001e-81 < (/.f64 x y) < 4.2e15

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in z around 0 68.0%

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

      1. *-commutative 68.0%

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

   6. Simplified 68.0%

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

   if -1.17999999999999993e89 < (/.f64 x y) < -1.6e-15 or 4.2e15 < (/.f64 x y)

   1. Initial program 84.8%

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

   3. Taylor expanded in t around inf 74.6%

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

   if -1.6e-15 < (/.f64 x y) < 1.1200000000000001e-81

   1. Initial program 87.4%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in x around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-/r* 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-/l/ 99.9%

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

      6. div-sub 99.9%

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

      7. sub-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

      10. distribute-lft-in 99.9%

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

      11. associate-*r/ 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in z around inf 61.1%

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

      1. sub-neg 61.1%

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

      2. metadata-eval 61.1%

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

      3. associate-*r/ 61.1%

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

      4. metadata-eval 61.1%

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

      5. +-commutative 61.1%

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

   9. Simplified 61.1%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.18 \cdot 10^{+89}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.12 \cdot 10^{-81}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;\frac{x}{y} \leq -2.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.8 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq -8 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 1.02 \cdot 10^{-81}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= (/ x y) -2.8e+115)
     (/ x y)
     (if (<= (/ x y) -2.8e+83)
       (/ (/ 2.0 t) z)
       (if (<= (/ x y) -8e-16)
         t_1
         (if (<= (/ x y) 1.02e-81)
           (+ -2.0 (/ 2.0 t))
           (if (<= (/ x y) 2.7e+14) (/ 2.0 (* t z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if ((x / y) <= -2.8e+115) {
		tmp = x / y;
	} else if ((x / y) <= -2.8e+83) {
		tmp = (2.0 / t) / z;
	} else if ((x / y) <= -8e-16) {
		tmp = t_1;
	} else if ((x / y) <= 1.02e-81) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 2.7e+14) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	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 ((x / y) <= (-2.8d+115)) then
        tmp = x / y
    else if ((x / y) <= (-2.8d+83)) then
        tmp = (2.0d0 / t) / z
    else if ((x / y) <= (-8d-16)) then
        tmp = t_1
    else if ((x / y) <= 1.02d-81) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if ((x / y) <= 2.7d+14) then
        tmp = 2.0d0 / (t * z)
    else
        tmp = t_1
    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 ((x / y) <= -2.8e+115) {
		tmp = x / y;
	} else if ((x / y) <= -2.8e+83) {
		tmp = (2.0 / t) / z;
	} else if ((x / y) <= -8e-16) {
		tmp = t_1;
	} else if ((x / y) <= 1.02e-81) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 2.7e+14) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if (x / y) <= -2.8e+115:
		tmp = x / y
	elif (x / y) <= -2.8e+83:
		tmp = (2.0 / t) / z
	elif (x / y) <= -8e-16:
		tmp = t_1
	elif (x / y) <= 1.02e-81:
		tmp = -2.0 + (2.0 / t)
	elif (x / y) <= 2.7e+14:
		tmp = 2.0 / (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (Float64(x / y) <= -2.8e+115)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -2.8e+83)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (Float64(x / y) <= -8e-16)
		tmp = t_1;
	elseif (Float64(x / y) <= 1.02e-81)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (Float64(x / y) <= 2.7e+14)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if ((x / y) <= -2.8e+115)
		tmp = x / y;
	elseif ((x / y) <= -2.8e+83)
		tmp = (2.0 / t) / z;
	elseif ((x / y) <= -8e-16)
		tmp = t_1;
	elseif ((x / y) <= 1.02e-81)
		tmp = -2.0 + (2.0 / t);
	elseif ((x / y) <= 2.7e+14)
		tmp = 2.0 / (t * z);
	else
		tmp = t_1;
	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[N[(x / y), $MachinePrecision], -2.8e+115], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2.8e+83], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -8e-16], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1.02e-81], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.7e+14], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 x y) < -2.8e115

   1. Initial program 83.7%

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

   3. Taylor expanded in x around inf 78.0%

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

   if -2.8e115 < (/.f64 x y) < -2.8e83

   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

   3. Taylor expanded in t around 0 99.8%

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

   4. Taylor expanded in x around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-+r+ 99.8%

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

      4. associate-*r/ 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-/r* 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. +-commutative 100.0%

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

      11. associate-+l+ 100.0%

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

      12. +-commutative 100.0%

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

      13. +-commutative 100.0%

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

      14. metadata-eval 100.0%

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

      15. associate-*r/ 100.0%

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

      16. *-commutative 100.0%

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

      17. *-rgt-identity 100.0%

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

      18. associate-*r/ 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 63.8%

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

      1. associate-/r* 64.0%

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

   9. Simplified 64.0%

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

   if -2.8e83 < (/.f64 x y) < -7.9999999999999998e-16 or 2.7e14 < (/.f64 x y)

   1. Initial program 84.8%

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

   3. Taylor expanded in t around inf 74.6%

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

   if -7.9999999999999998e-16 < (/.f64 x y) < 1.01999999999999998e-81

   1. Initial program 87.4%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in x around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-/r* 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-/l/ 99.9%

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

      6. div-sub 99.9%

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

      7. sub-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

      10. distribute-lft-in 99.9%

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

      11. associate-*r/ 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in z around inf 61.1%

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

      1. sub-neg 61.1%

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

      2. metadata-eval 61.1%

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

      3. associate-*r/ 61.1%

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

      4. metadata-eval 61.1%

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

      5. +-commutative 61.1%

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

   9. Simplified 61.1%

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

   if 1.01999999999999998e-81 < (/.f64 x y) < 2.7e14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in z around 0 69.5%

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

      1. *-commutative 69.5%

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

   6. Simplified 69.5%

      \[\leadsto \color{blue}{\frac{2}{z \cdot t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.8 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq -8 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.02 \cdot 10^{-81}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 + \frac{2}{z}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+30} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{t\_1}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 2.0 (/ 2.0 z))))
   (if (or (<= (/ x y) -2e+30) (not (<= (/ x y) 5e+76)))
     (/ (+ x (* y (/ t_1 t))) y)
     (/ (+ t_1 (* t (+ (/ x y) -2.0))) t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 + (2.0 / z);
	double tmp;
	if (((x / y) <= -2e+30) || !((x / y) <= 5e+76)) {
		tmp = (x + (y * (t_1 / t))) / y;
	} else {
		tmp = (t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 + (2.0d0 / z)
    if (((x / y) <= (-2d+30)) .or. (.not. ((x / y) <= 5d+76))) then
        tmp = (x + (y * (t_1 / t))) / y
    else
        tmp = (t_1 + (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 t_1 = 2.0 + (2.0 / z);
	double tmp;
	if (((x / y) <= -2e+30) || !((x / y) <= 5e+76)) {
		tmp = (x + (y * (t_1 / t))) / y;
	} else {
		tmp = (t_1 + (t * ((x / y) + -2.0))) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 + (2.0 / z)
	tmp = 0
	if ((x / y) <= -2e+30) or not ((x / y) <= 5e+76):
		tmp = (x + (y * (t_1 / t))) / y
	else:
		tmp = (t_1 + (t * ((x / y) + -2.0))) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 + Float64(2.0 / z))
	tmp = 0.0
	if ((Float64(x / y) <= -2e+30) || !(Float64(x / y) <= 5e+76))
		tmp = Float64(Float64(x + Float64(y * Float64(t_1 / t))) / y);
	else
		tmp = Float64(Float64(t_1 + Float64(t * Float64(Float64(x / y) + -2.0))) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 + (2.0 / z);
	tmp = 0.0;
	if (((x / y) <= -2e+30) || ~(((x / y) <= 5e+76)))
		tmp = (x + (y * (t_1 / t))) / y;
	else
		tmp = (t_1 + (t * ((x / y) + -2.0))) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+30], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+76]], $MachinePrecision]], N[(N[(x + N[(y * N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(t$95$1 + N[(t * N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e30 or 4.99999999999999991e76 < (/.f64 x y)

   1. Initial program 86.2%

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

   3. Taylor expanded in t around 0 98.2%

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

   4. Taylor expanded in y around 0 98.3%

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

      1. associate-*r/ 98.3%

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

      2. metadata-eval 98.3%

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

      3. associate-*r/ 98.3%

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

      4. metadata-eval 98.3%

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

      5. associate-/r* 98.3%

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

      6. +-commutative 98.3%

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

      7. +-commutative 98.3%

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

      8. associate-/l/ 98.3%

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

   6. Simplified 98.3%

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

   7. Taylor expanded in t around 0 99.2%

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

      1. associate-/l* 98.3%

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

      2. associate-*r/ 98.3%

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

      3. metadata-eval 98.3%

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

   9. Simplified 98.3%

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

   if -2e30 < (/.f64 x y) < 4.99999999999999991e76

   1. Initial program 88.3%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. associate-+r+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+30} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{2 + \frac{2}{z}}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000 \lor \neg \left(\frac{x}{y} \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5000.0) (not (<= (/ x y) 1.0)))
   (+ (/ x y) (/ (+ 2.0 (/ 2.0 z)) t))
   (+ (/ 2.0 (* t z)) (+ -2.0 (/ 2.0 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5000.0) || !((x / y) <= 1.0)) {
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (2.0 / (t * z)) + (-2.0 + (2.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5000.0d0)) .or. (.not. ((x / y) <= 1.0d0))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (2.0d0 / (t * z)) + ((-2.0d0) + (2.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5000.0) || !((x / y) <= 1.0)) {
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (2.0 / (t * z)) + (-2.0 + (2.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5000.0) or not ((x / y) <= 1.0):
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (2.0 / (t * z)) + (-2.0 + (2.0 / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5000.0) || !(Float64(x / y) <= 1.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(-2.0 + Float64(2.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5000.0) || ~(((x / y) <= 1.0)))
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (2.0 / (t * z)) + (-2.0 + (2.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e3 or 1 < (/.f64 x y)

   1. Initial program 86.0%

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

   3. Taylor expanded in t around 0 97.8%

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

   4. Taylor expanded in x around 0 97.8%

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

      1. associate-*r/ 97.8%

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

      2. metadata-eval 97.8%

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

      3. associate-+r+ 97.8%

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

      4. associate-*r/ 97.8%

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

      5. metadata-eval 97.8%

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

      6. associate-/r* 97.8%

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

      7. +-commutative 97.8%

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

      8. associate-+r+ 97.8%

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

      9. +-commutative 97.8%

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

      10. +-commutative 97.8%

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

      11. associate-+l+ 97.8%

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

      12. +-commutative 97.8%

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

      13. +-commutative 97.8%

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

      14. metadata-eval 97.8%

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

      15. associate-*r/ 97.8%

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

      16. *-commutative 97.8%

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

      17. *-rgt-identity 97.8%

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

      18. associate-*r/ 97.8%

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

   6. Simplified 97.8%

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

   if -5e3 < (/.f64 x y) < 1

   1. Initial program 88.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in x around 0 99.0%

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

      1. associate-*r/ 99.0%

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

      2. metadata-eval 99.0%

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

      3. associate-/r* 99.0%

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

      4. +-commutative 99.0%

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

      5. associate-/l/ 99.0%

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

      6. div-sub 99.0%

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

      7. sub-neg 99.0%

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

      8. *-inverses 99.0%

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

      9. metadata-eval 99.0%

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

      10. distribute-lft-in 99.0%

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

      11. associate-*r/ 99.0%

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

      12. metadata-eval 99.0%

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

      13. metadata-eval 99.0%

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

   6. Simplified 99.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000 \lor \neg \left(\frac{x}{y} \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+33} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + z \cdot \left(t \cdot -2\right)}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e+33) (not (<= z 1.0)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ (+ 2.0 (* z (* t -2.0))) (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+33) || !(z <= 1.0)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 + (z * (t * -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 <= (-1.7d+33)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + ((2.0d0 + (z * (t * (-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 <= -1.7e+33) || !(z <= 1.0)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 + (z * (t * -2.0))) / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e+33) or not (z <= 1.0):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + ((2.0 + (z * (t * -2.0))) / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e+33) || !(z <= 1.0))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(z * Float64(t * -2.0))) / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e+33) || ~((z <= 1.0)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + ((2.0 + (z * (t * -2.0))) / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e+33], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(z * N[(t * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e33 or 1 < z

   1. Initial program 75.5%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. *-inverses 100.0%

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

      5. metadata-eval 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   if -1.7e33 < z < 1

   1. Initial program 98.4%

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

   3. Taylor expanded in t around inf 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. associate-*r* 97.1%

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

      2. *-commutative 97.1%

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

   5. Simplified 97.1%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+33} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + z \cdot \left(t \cdot -2\right)}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -50:\\ \;\;\;\;\frac{x + y \cdot t\_1}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)))
   (if (<= (/ x y) -50.0)
     (/ (+ x (* y t_1)) y)
     (if (<= (/ x y) 1.0)
       (+ (/ 2.0 (* t z)) (+ -2.0 (/ 2.0 t)))
       (+ (/ x y) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double tmp;
	if ((x / y) <= -50.0) {
		tmp = (x + (y * t_1)) / y;
	} else if ((x / y) <= 1.0) {
		tmp = (2.0 / (t * z)) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + t_1;
	}
	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 + (2.0d0 / z)) / t
    if ((x / y) <= (-50.0d0)) then
        tmp = (x + (y * t_1)) / y
    else if ((x / y) <= 1.0d0) then
        tmp = (2.0d0 / (t * z)) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double tmp;
	if ((x / y) <= -50.0) {
		tmp = (x + (y * t_1)) / y;
	} else if ((x / y) <= 1.0) {
		tmp = (2.0 / (t * z)) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	tmp = 0
	if (x / y) <= -50.0:
		tmp = (x + (y * t_1)) / y
	elif (x / y) <= 1.0:
		tmp = (2.0 / (t * z)) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	tmp = 0.0
	if (Float64(x / y) <= -50.0)
		tmp = Float64(Float64(x + Float64(y * t_1)) / y);
	elseif (Float64(x / y) <= 1.0)
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	tmp = 0.0;
	if ((x / y) <= -50.0)
		tmp = (x + (y * t_1)) / y;
	elseif ((x / y) <= 1.0)
		tmp = (2.0 / (t * z)) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -50.0], N[(N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.0], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -50

   1. Initial program 83.5%

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

   3. Taylor expanded in t around 0 95.9%

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

   4. Taylor expanded in y around 0 96.1%

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

      1. associate-*r/ 96.1%

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

      2. metadata-eval 96.1%

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

      3. associate-*r/ 96.1%

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

      4. metadata-eval 96.1%

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

      5. associate-/r* 96.1%

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

      6. +-commutative 96.1%

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

      7. +-commutative 96.1%

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

      8. associate-/l/ 96.1%

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

   6. Simplified 96.1%

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

   7. Taylor expanded in t around 0 97.5%

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

      1. associate-/l* 96.1%

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

      2. associate-*r/ 96.1%

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

      3. metadata-eval 96.1%

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

   9. Simplified 96.1%

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

   if -50 < (/.f64 x y) < 1

   1. Initial program 88.8%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in x around 0 99.0%

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

      1. associate-*r/ 99.0%

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

      2. metadata-eval 99.0%

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

      3. associate-/r* 98.9%

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

      4. +-commutative 98.9%

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

      5. associate-/l/ 99.0%

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

      6. div-sub 99.0%

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

      7. sub-neg 99.0%

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

      8. *-inverses 99.0%

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

      9. metadata-eval 99.0%

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

      10. distribute-lft-in 99.0%

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

      11. associate-*r/ 99.0%

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

      12. metadata-eval 99.0%

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

      13. metadata-eval 99.0%

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

   6. Simplified 99.0%

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

   if 1 < (/.f64 x y)

   1. Initial program 88.6%

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

   3. Taylor expanded in t around 0 99.5%

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

   4. Taylor expanded in x around 0 99.5%

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

      1. associate-*r/ 99.5%

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

      2. metadata-eval 99.5%

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

      3. associate-+r+ 99.5%

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

      4. associate-*r/ 99.5%

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

      5. metadata-eval 99.5%

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

      6. associate-/r* 99.5%

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

      7. +-commutative 99.5%

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

      8. associate-+r+ 99.5%

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

      9. +-commutative 99.5%

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

      10. +-commutative 99.5%

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

      11. associate-+l+ 99.5%

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

      12. +-commutative 99.5%

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

      13. +-commutative 99.5%

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

      14. metadata-eval 99.5%

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

      15. associate-*r/ 99.5%

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

      16. *-commutative 99.5%

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

      17. *-rgt-identity 99.5%

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

      18. associate-*r/ 99.5%

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

   6. Simplified 99.5%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50:\\ \;\;\;\;\frac{x + y \cdot \frac{2 + \frac{2}{z}}{t}}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7600 \lor \neg \left(\frac{x}{y} \leq 10000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -7600.0) (not (<= (/ x y) 10000000000.0)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -7600.0) || !((x / y) <= 10000000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-7600.0d0)) .or. (.not. ((x / y) <= 10000000000.0d0))) then
        tmp = x / y
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -7600.0) || !((x / y) <= 10000000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -7600.0) or not ((x / y) <= 10000000000.0):
		tmp = x / y
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -7600.0) || !(Float64(x / y) <= 10000000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -7600.0) || ~(((x / y) <= 10000000000.0)))
		tmp = x / y;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -7600.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 10000000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -7600 or 1e10 < (/.f64 x y)

   1. Initial program 85.8%

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

   3. Taylor expanded in x around inf 71.0%

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

   if -7600 < (/.f64 x y) < 1e10

   1. Initial program 89.1%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in x around 0 99.0%

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

      1. associate-*r/ 99.0%

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

      2. metadata-eval 99.0%

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

      3. associate-/r* 99.0%

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

      4. +-commutative 99.0%

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

      5. associate-/l/ 99.0%

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

      6. div-sub 99.0%

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

      7. sub-neg 99.0%

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

      8. *-inverses 99.0%

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

      9. metadata-eval 99.0%

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

      10. distribute-lft-in 99.0%

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

      11. associate-*r/ 99.0%

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

      12. metadata-eval 99.0%

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

      13. metadata-eval 99.0%

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

   6. Simplified 99.0%

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

   7. Taylor expanded in z around inf 55.9%

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

      1. sub-neg 55.9%

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

      2. metadata-eval 55.9%

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

      3. associate-*r/ 55.9%

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

      4. metadata-eval 55.9%

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

      5. +-commutative 55.9%

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

   9. Simplified 55.9%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7600 \lor \neg \left(\frac{x}{y} \leq 10000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.6 \cdot 10^{-15} \lor \neg \left(\frac{x}{y} \leq 11500000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.6e-15) (not (<= (/ x y) 11500000000.0)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.6e-15) || !((x / y) <= 11500000000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1.6d-15)) .or. (.not. ((x / y) <= 11500000000.0d0))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.6e-15) || !((x / y) <= 11500000000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.6e-15) or not ((x / y) <= 11500000000.0):
		tmp = (x / y) - 2.0
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.6e-15) || !(Float64(x / y) <= 11500000000.0))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.6e-15) || ~(((x / y) <= 11500000000.0)))
		tmp = (x / y) - 2.0;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.6e-15], N[Not[LessEqual[N[(x / y), $MachinePrecision], 11500000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.6e-15 or 1.15e10 < (/.f64 x y)

   1. Initial program 85.5%

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

   3. Taylor expanded in t around inf 71.8%

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

   if -1.6e-15 < (/.f64 x y) < 1.15e10

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in x around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-/r* 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-/l/ 99.9%

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

      6. div-sub 99.9%

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

      7. sub-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

      10. distribute-lft-in 99.9%

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

      11. associate-*r/ 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in z around inf 56.1%

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

      1. sub-neg 56.1%

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

      2. metadata-eval 56.1%

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

      3. associate-*r/ 56.1%

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

      4. metadata-eval 56.1%

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

      5. +-commutative 56.1%

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

   9. Simplified 56.1%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.6 \cdot 10^{-15} \lor \neg \left(\frac{x}{y} \leq 11500000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-44} \lor \neg \left(z \leq 7.5 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-44) (not (<= z 7.5e-91)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (/ 2.0 (* t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-44) || !(z <= 7.5e-91)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = 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 <= (-1.7d-44)) .or. (.not. (z <= 7.5d-91))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = 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 <= -1.7e-44) || !(z <= 7.5e-91)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e-44) or not (z <= 7.5e-91):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = 2.0 / (t * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e-44) || !(z <= 7.5e-91))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(2.0 / Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e-44) || ~((z <= 7.5e-91)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = 2.0 / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e-44], N[Not[LessEqual[z, 7.5e-91]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000008e-44 or 7.50000000000000051e-91 < z

   1. Initial program 80.7%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in z around inf 92.7%

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

      1. +-commutative 92.7%

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

      2. div-sub 92.7%

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

      3. sub-neg 92.7%

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

      4. *-inverses 92.7%

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

      5. metadata-eval 92.7%

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

      6. distribute-lft-in 92.7%

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

      7. associate-*r/ 92.7%

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

      8. metadata-eval 92.7%

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

      9. metadata-eval 92.7%

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

   6. Simplified 92.7%

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

   if -1.70000000000000008e-44 < z < 7.50000000000000051e-91

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0 97.9%

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

   4. Taylor expanded in z around 0 67.9%

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

      1. *-commutative 67.9%

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

   6. Simplified 67.9%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-44} \lor \neg \left(z \leq 7.5 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 92.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-14} \lor \neg \left(z \leq 0.00205\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-14) (not (<= z 0.00205)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-14) || !(z <= 0.00205)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.7d-14)) .or. (.not. (z <= 0.00205d0))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + (2.0d0 / (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-14) || !(z <= 0.00205)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e-14) or not (z <= 0.00205):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e-14) || !(z <= 0.00205))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e-14) || ~((z <= 0.00205)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e-14], N[Not[LessEqual[z, 0.00205]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000001e-14 or 0.00205000000000000017 < z

   1. Initial program 77.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in z around inf 99.2%

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

      1. +-commutative 99.2%

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

      2. div-sub 99.2%

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

      3. sub-neg 99.2%

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

      4. *-inverses 99.2%

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

      5. metadata-eval 99.2%

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

      6. distribute-lft-in 99.2%

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

      7. associate-*r/ 99.2%

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

      8. metadata-eval 99.2%

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

      9. metadata-eval 99.2%

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

   6. Simplified 99.2%

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

   if -1.70000000000000001e-14 < z < 0.00205000000000000017

   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 z around 0 88.7%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-14} \lor \neg \left(z \leq 0.00205\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.0% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (2.0 * (1.0 / (t * z))) + ((2.0 * ((1.0 - t) / t)) + (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 * (1.0d0 / (t * z))) + ((2.0d0 * ((1.0d0 - t) / t)) + (x / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

3. Taylor expanded in x around 0 99.2%

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

4. Final simplification 99.2%

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

Alternative 14: 52.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -70 \lor \neg \left(\frac{x}{y} \leq 1.85 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -70.0) (not (<= (/ x y) 1.85e-31))) (/ x y) -2.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -70.0) || !((x / y) <= 1.85e-31)) {
		tmp = x / y;
	} 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 (((x / y) <= (-70.0d0)) .or. (.not. ((x / y) <= 1.85d-31))) then
        tmp = x / y
    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 (((x / y) <= -70.0) || !((x / y) <= 1.85e-31)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -70.0) or not ((x / y) <= 1.85e-31):
		tmp = x / y
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -70.0) || !(Float64(x / y) <= 1.85e-31))
		tmp = Float64(x / y);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -70.0) || ~(((x / y) <= 1.85e-31)))
		tmp = x / y;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -70.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.85e-31]], $MachinePrecision]], N[(x / y), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -70 or 1.8499999999999999e-31 < (/.f64 x y)

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf 65.5%

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

   if -70 < (/.f64 x y) < 1.8499999999999999e-31

   1. Initial program 87.9%

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

   3. Taylor expanded in t around inf 34.0%

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

   4. Taylor expanded in x around 0 33.0%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -70 \lor \neg \left(\frac{x}{y} \leq 1.85 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-35} \lor \neg \left(t \leq 2.85 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.45e-35) (not (<= t 2.85e-15)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e-35) || !(t <= 2.85e-15)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.45d-35)) .or. (.not. (t <= 2.85d-15))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e-35) || !(t <= 2.85e-15)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.45e-35) or not (t <= 2.85e-15):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.45e-35) || !(t <= 2.85e-15))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.45e-35) || ~((t <= 2.85e-15)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.45e-35], N[Not[LessEqual[t, 2.85e-15]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4500000000000001e-35 or 2.8500000000000002e-15 < t

   1. Initial program 78.0%

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

   3. Taylor expanded in t around inf 79.6%

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

   if -1.4500000000000001e-35 < t < 2.8500000000000002e-15

   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 82.0%

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

      1. associate-*r/ 82.0%

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

      2. metadata-eval 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-35} \lor \neg \left(t \leq 2.85 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1050000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 1050000000.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 1050000000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.0d0)) then
        tmp = -2.0d0
    else if (t <= 1050000000.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 1050000000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.0:
		tmp = -2.0
	elif t <= 1050000000.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 1050000000.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 1050000000.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.0], -2.0, If[LessEqual[t, 1050000000.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 1.05e9 < t

   1. Initial program 76.7%

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

   3. Taylor expanded in t around inf 79.8%

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

   4. Taylor expanded in x around 0 28.4%

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

   if -1 < t < 1.05e9

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 98.2%

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

   4. Taylor expanded in z around inf 60.0%

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

      1. associate-*r/ 60.0%

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

      2. metadata-eval 60.0%

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

      3. +-commutative 60.0%

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

   6. Simplified 60.0%

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

   7. Taylor expanded in x around 0 36.9%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1050000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 19.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

3. Taylor expanded in t around inf 52.4%

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

4. Taylor expanded in x around 0 15.4%

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

5. Final simplification 15.4%

   \[\leadsto -2 \]
6. 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 2024095 
(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))))