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

Percentage Accurate: 86.7% → 99.3%

Time: 14.6s

Alternatives: 17

Speedup: 0.7×

• 23.2% 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: 86.7% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(1.0 - t), $MachinePrecision] * N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(z * N[(1.0 - t), $MachinePrecision] + 1.0), $MachinePrecision] * N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], 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 99.4%

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

      1. +-commutative 99.4%

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

      2. remove-double-neg 99.4%

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

      3. distribute-frac-neg 99.4%

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

      4. unsub-neg 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. distribute-rgt1-in 99.4%

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

      8. associate-/l* 99.7%

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

      9. fma-neg 99.7%

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

      10. *-commutative 99.7%

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

      11. fma-define 99.7%

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

      12. *-commutative 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. remove-double-neg 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, 1 - t, 1\right), \frac{2}{z \cdot t}, \frac{x}{y}\right)} \]
   4. Add Preprocessing

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 100.0%

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

4. Final simplification 99.5%

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

Alternative 3: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-54}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-16}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+16)
   (/ x y)
   (if (<= (/ x y) 5e-54)
     (- -2.0 (/ -2.0 t))
     (if (<= (/ x y) 1e-16) (/ (/ 2.0 z) t) (- (/ x y) 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+16) {
		tmp = x / y;
	} else if ((x / y) <= 5e-54) {
		tmp = -2.0 - (-2.0 / t);
	} else if ((x / y) <= 1e-16) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+16)) then
        tmp = x / y
    else if ((x / y) <= 5d-54) then
        tmp = (-2.0d0) - ((-2.0d0) / t)
    else if ((x / y) <= 1d-16) then
        tmp = (2.0d0 / z) / t
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+16) {
		tmp = x / y;
	} else if ((x / y) <= 5e-54) {
		tmp = -2.0 - (-2.0 / t);
	} else if ((x / y) <= 1e-16) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+16:
		tmp = x / y
	elif (x / y) <= 5e-54:
		tmp = -2.0 - (-2.0 / t)
	elif (x / y) <= 1e-16:
		tmp = (2.0 / z) / t
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+16)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e-54)
		tmp = Float64(-2.0 - Float64(-2.0 / t));
	elseif (Float64(x / y) <= 1e-16)
		tmp = Float64(Float64(2.0 / z) / t);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+16)
		tmp = x / y;
	elseif ((x / y) <= 5e-54)
		tmp = -2.0 - (-2.0 / t);
	elseif ((x / y) <= 1e-16)
		tmp = (2.0 / z) / t;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+16], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-54], N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-16], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -5e16

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf 72.3%

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

   if -5e16 < (/.f64 x y) < 5.00000000000000015e-54

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 61.5%

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

      1. div-sub 61.5%

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

      2. sub-neg 61.5%

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

      3. *-inverses 61.5%

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

      4. metadata-eval 61.5%

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

      5. distribute-lft-in 61.5%

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

      6. associate-*r/ 61.5%

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

      7. metadata-eval 61.5%

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

      8. metadata-eval 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in x around 0 60.8%

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

      1. sub-neg 60.8%

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

      2. metadata-eval 60.8%

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

      3. associate-*r/ 60.8%

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

      4. metadata-eval 60.8%

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

      5. +-commutative 60.8%

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

      6. metadata-eval 60.8%

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

      7. distribute-neg-frac 60.8%

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

      8. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if 5.00000000000000015e-54 < (/.f64 x y) < 9.9999999999999998e-17

   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 z around 0 80.0%

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

      1. associate-/l/ 80.2%

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

   5. Simplified 80.2%

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

   if 9.9999999999999998e-17 < (/.f64 x y)

   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 t around inf 77.6%

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

Alternative 4: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-54}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-16}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+16)
   (/ x y)
   (if (<= (/ x y) 5e-54)
     (- -2.0 (/ -2.0 t))
     (if (<= (/ x y) 1e-16) (/ (/ 2.0 t) z) (- (/ x y) 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+16) {
		tmp = x / y;
	} else if ((x / y) <= 5e-54) {
		tmp = -2.0 - (-2.0 / t);
	} else if ((x / y) <= 1e-16) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+16)) then
        tmp = x / y
    else if ((x / y) <= 5d-54) then
        tmp = (-2.0d0) - ((-2.0d0) / t)
    else if ((x / y) <= 1d-16) then
        tmp = (2.0d0 / t) / z
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+16) {
		tmp = x / y;
	} else if ((x / y) <= 5e-54) {
		tmp = -2.0 - (-2.0 / t);
	} else if ((x / y) <= 1e-16) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+16:
		tmp = x / y
	elif (x / y) <= 5e-54:
		tmp = -2.0 - (-2.0 / t)
	elif (x / y) <= 1e-16:
		tmp = (2.0 / t) / z
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+16)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e-54)
		tmp = Float64(-2.0 - Float64(-2.0 / t));
	elseif (Float64(x / y) <= 1e-16)
		tmp = Float64(Float64(2.0 / t) / z);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+16)
		tmp = x / y;
	elseif ((x / y) <= 5e-54)
		tmp = -2.0 - (-2.0 / t);
	elseif ((x / y) <= 1e-16)
		tmp = (2.0 / t) / z;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+16], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-54], N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-16], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -5e16

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf 72.3%

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

   if -5e16 < (/.f64 x y) < 5.00000000000000015e-54

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 61.5%

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

      1. div-sub 61.5%

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

      2. sub-neg 61.5%

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

      3. *-inverses 61.5%

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

      4. metadata-eval 61.5%

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

      5. distribute-lft-in 61.5%

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

      6. associate-*r/ 61.5%

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

      7. metadata-eval 61.5%

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

      8. metadata-eval 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in x around 0 60.8%

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

      1. sub-neg 60.8%

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

      2. metadata-eval 60.8%

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

      3. associate-*r/ 60.8%

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

      4. metadata-eval 60.8%

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

      5. +-commutative 60.8%

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

      6. metadata-eval 60.8%

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

      7. distribute-neg-frac 60.8%

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

      8. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if 5.00000000000000015e-54 < (/.f64 x y) < 9.9999999999999998e-17

   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 z around 0 80.0%

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

      1. associate-/l/ 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in z around 0 80.0%

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

      1. associate-/r* 80.0%

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

   8. Simplified 80.0%

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

   if 9.9999999999999998e-17 < (/.f64 x y)

   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 t around inf 77.6%

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

Alternative 5: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-54}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-16}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+16)
   (/ x y)
   (if (<= (/ x y) 5e-54)
     (- -2.0 (/ -2.0 t))
     (if (<= (/ x y) 1e-16) (/ 2.0 (* z t)) (- (/ x y) 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+16) {
		tmp = x / y;
	} else if ((x / y) <= 5e-54) {
		tmp = -2.0 - (-2.0 / t);
	} else if ((x / y) <= 1e-16) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+16)) then
        tmp = x / y
    else if ((x / y) <= 5d-54) then
        tmp = (-2.0d0) - ((-2.0d0) / t)
    else if ((x / y) <= 1d-16) then
        tmp = 2.0d0 / (z * t)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+16) {
		tmp = x / y;
	} else if ((x / y) <= 5e-54) {
		tmp = -2.0 - (-2.0 / t);
	} else if ((x / y) <= 1e-16) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+16:
		tmp = x / y
	elif (x / y) <= 5e-54:
		tmp = -2.0 - (-2.0 / t)
	elif (x / y) <= 1e-16:
		tmp = 2.0 / (z * t)
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+16)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e-54)
		tmp = Float64(-2.0 - Float64(-2.0 / t));
	elseif (Float64(x / y) <= 1e-16)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+16)
		tmp = x / y;
	elseif ((x / y) <= 5e-54)
		tmp = -2.0 - (-2.0 / t);
	elseif ((x / y) <= 1e-16)
		tmp = 2.0 / (z * t);
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+16], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-54], N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-16], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -5e16

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf 72.3%

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

   if -5e16 < (/.f64 x y) < 5.00000000000000015e-54

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 61.5%

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

      1. div-sub 61.5%

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

      2. sub-neg 61.5%

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

      3. *-inverses 61.5%

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

      4. metadata-eval 61.5%

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

      5. distribute-lft-in 61.5%

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

      6. associate-*r/ 61.5%

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

      7. metadata-eval 61.5%

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

      8. metadata-eval 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in x around 0 60.8%

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

      1. sub-neg 60.8%

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

      2. metadata-eval 60.8%

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

      3. associate-*r/ 60.8%

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

      4. metadata-eval 60.8%

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

      5. +-commutative 60.8%

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

      6. metadata-eval 60.8%

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

      7. distribute-neg-frac 60.8%

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

      8. unsub-neg 60.8%

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

   8. Simplified 60.8%

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

   if 5.00000000000000015e-54 < (/.f64 x y) < 9.9999999999999998e-17

   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 z around 0 80.0%

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

   if 9.9999999999999998e-17 < (/.f64 x y)

   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 t around inf 77.6%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-54}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-16}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -2000000 \lor \neg \left(\frac{x}{y} \leq 0.2\right):\\ \;\;\;\;\frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)))
   (if (or (<= (/ x y) -2000000.0) (not (<= (/ x y) 0.2)))
     (+ (/ x y) t_1)
     (+ -2.0 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) <= -2000000.0) || !((x / y) <= 0.2)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = -2.0 + 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) <= (-2000000.0d0)) .or. (.not. ((x / y) <= 0.2d0))) then
        tmp = (x / y) + t_1
    else
        tmp = (-2.0d0) + 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) <= -2000000.0) || !((x / y) <= 0.2)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = -2.0 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	tmp = 0
	if ((x / y) <= -2000000.0) or not ((x / y) <= 0.2):
		tmp = (x / y) + t_1
	else:
		tmp = -2.0 + 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) <= -2000000.0) || !(Float64(x / y) <= 0.2))
		tmp = Float64(Float64(x / y) + t_1);
	else
		tmp = Float64(-2.0 + 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) <= -2000000.0) || ~(((x / y) <= 0.2)))
		tmp = (x / y) + t_1;
	else
		tmp = -2.0 + 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[Or[LessEqual[N[(x / y), $MachinePrecision], -2000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.2]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(-2.0 + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e6 or 0.20000000000000001 < (/.f64 x y)

   1. Initial program 85.0%

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

   3. Taylor expanded in z around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. associate-/l* 86.3%

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

      3. *-commutative 86.3%

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

      4. div-sub 86.3%

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

      5. *-inverses 86.3%

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

      6. associate-*l* 86.3%

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

      7. associate-*r/ 86.3%

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

      8. metadata-eval 86.3%

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

      9. sub-neg 86.3%

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

      10. metadata-eval 86.3%

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

      11. distribute-lft-in 86.3%

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

      12. associate-*r/ 86.3%

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

      13. metadata-eval 86.3%

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

      14. metadata-eval 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in t around 0 85.8%

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

   7. Taylor expanded in x around 0 98.1%

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

      1. associate-+r+ 98.1%

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

      2. +-commutative 98.1%

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

      3. distribute-lft-out 98.1%

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

      4. associate-/l/ 98.1%

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

      5. *-lft-identity 98.1%

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

      6. associate-*l/ 98.1%

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

      7. distribute-lft-out 98.1%

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

      8. *-commutative 98.1%

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

      9. associate-*r* 98.1%

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

      10. associate-*r/ 98.1%

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

      11. metadata-eval 98.1%

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

      12. distribute-rgt-in 98.1%

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

      13. associate-*l/ 98.1%

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

      14. *-lft-identity 98.1%

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

   9. Simplified 98.1%

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

   if -2e6 < (/.f64 x y) < 0.20000000000000001

   1. Initial program 89.4%

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

   3. Taylor expanded in x around 0 98.1%

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

      1. associate-*r/ 98.1%

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

      2. metadata-eval 98.1%

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

      3. associate-/l/ 98.1%

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

      4. +-commutative 98.1%

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

      5. div-sub 98.1%

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

      6. sub-neg 98.1%

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

      7. *-inverses 98.1%

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

      8. metadata-eval 98.1%

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

      9. distribute-lft-in 98.1%

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

      10. metadata-eval 98.1%

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

      11. associate-+l+ 98.1%

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

      12. +-commutative 98.1%

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

      13. associate-/l/ 98.1%

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

      14. +-commutative 98.1%

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

      15. associate-/l/ 98.1%

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

      16. *-rgt-identity 98.1%

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

      17. associate-*r/ 98.1%

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

      18. distribute-rgt-out 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in t around inf 98.1%

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

      1. sub-neg 98.1%

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

      2. associate-/r* 98.1%

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

      3. metadata-eval 98.1%

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

      4. associate-*r/ 98.1%

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

      5. associate-*l/ 98.1%

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

      6. distribute-rgt-in 98.1%

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

      7. metadata-eval 98.1%

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

      8. associate-*l/ 98.1%

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

      9. *-lft-identity 98.1%

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

      10. +-commutative 98.1%

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

   8. Simplified 98.1%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000 \lor \neg \left(\frac{x}{y} \leq 0.2\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.2:\\ \;\;\;\;-2 + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)))
   (if (<= (/ x y) -2e-11)
     (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))
     (if (<= (/ x y) 0.2) (+ -2.0 t_1) (+ (/ 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) <= -2e-11) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else if ((x / y) <= 0.2) {
		tmp = -2.0 + t_1;
	} 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) <= (-2d-11)) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    else if ((x / y) <= 0.2d0) then
        tmp = (-2.0d0) + t_1
    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) <= -2e-11) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else if ((x / y) <= 0.2) {
		tmp = -2.0 + t_1;
	} 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) <= -2e-11:
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	elif (x / y) <= 0.2:
		tmp = -2.0 + t_1
	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) <= -2e-11)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	elseif (Float64(x / y) <= 0.2)
		tmp = Float64(-2.0 + t_1);
	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) <= -2e-11)
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	elseif ((x / y) <= 0.2)
		tmp = -2.0 + t_1;
	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], -2e-11], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.2], N[(-2.0 + t$95$1), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.99999999999999988e-11

   1. Initial program 83.8%

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

   3. Taylor expanded in t around 0 96.3%

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

   if -1.99999999999999988e-11 < (/.f64 x y) < 0.20000000000000001

   1. Initial program 89.0%

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

   3. Taylor expanded in x around 0 98.0%

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

      1. associate-*r/ 98.0%

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

      2. metadata-eval 98.0%

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

      3. associate-/l/ 98.1%

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

      4. +-commutative 98.1%

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

      5. div-sub 98.1%

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

      6. sub-neg 98.1%

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

      7. *-inverses 98.1%

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

      8. metadata-eval 98.1%

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

      9. distribute-lft-in 98.1%

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

      10. metadata-eval 98.1%

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

      11. associate-+l+ 98.1%

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

      12. +-commutative 98.1%

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

      13. associate-/l/ 98.0%

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

      14. +-commutative 98.0%

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

      15. associate-/l/ 98.1%

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

      16. *-rgt-identity 98.1%

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

      17. associate-*r/ 98.0%

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

      18. distribute-rgt-out 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in t around inf 98.0%

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

      1. sub-neg 98.0%

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

      2. associate-/r* 98.1%

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

      3. metadata-eval 98.1%

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

      4. associate-*r/ 98.1%

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

      5. associate-*l/ 98.0%

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

      6. distribute-rgt-in 98.0%

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

      7. metadata-eval 98.0%

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

      8. associate-*l/ 98.1%

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

      9. *-lft-identity 98.1%

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

      10. +-commutative 98.1%

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

   8. Simplified 98.1%

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

   if 0.20000000000000001 < (/.f64 x y)

   1. Initial program 86.8%

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

   3. Taylor expanded in z around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 92.3%

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

      3. *-commutative 92.3%

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

      4. div-sub 92.3%

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

      5. *-inverses 92.3%

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

      6. associate-*l* 92.3%

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

      7. associate-*r/ 92.3%

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

      8. metadata-eval 92.3%

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

      9. sub-neg 92.3%

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

      10. metadata-eval 92.3%

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

      11. distribute-lft-in 92.3%

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

      12. associate-*r/ 92.3%

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

      13. metadata-eval 92.3%

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

      14. metadata-eval 92.3%

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

   5. Simplified 92.3%

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

   6. Taylor expanded in t around 0 92.0%

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

   7. Taylor expanded in x around 0 99.7%

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

      1. associate-+r+ 99.7%

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

      2. +-commutative 99.7%

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

      3. distribute-lft-out 99.7%

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

      4. associate-/l/ 99.8%

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

      5. *-lft-identity 99.8%

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

      6. associate-*l/ 99.7%

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

      7. distribute-lft-out 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-*r* 99.7%

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

      10. associate-*r/ 99.7%

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

      11. metadata-eval 99.7%

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

      12. distribute-rgt-in 99.7%

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

      13. associate-*l/ 99.8%

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

      14. *-lft-identity 99.8%

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

   9. Simplified 99.8%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.2:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16} \lor \neg \left(\frac{x}{y} \leq 40000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+16) (not (<= (/ x y) 40000000000.0)))
   (+ (/ x y) (/ 2.0 t))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+16) || !((x / y) <= 40000000000.0)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d+16)) .or. (.not. ((x / y) <= 40000000000.0d0))) then
        tmp = (x / y) + (2.0d0 / t)
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+16) || !((x / y) <= 40000000000.0)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+16) or not ((x / y) <= 40000000000.0):
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+16) || !(Float64(x / y) <= 40000000000.0))
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e+16) || ~(((x / y) <= 40000000000.0)))
		tmp = (x / y) + (2.0 / t);
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+16], N[Not[LessEqual[N[(x / y), $MachinePrecision], 40000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e16 or 4e10 < (/.f64 x y)

   1. Initial program 84.6%

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

   3. Taylor expanded in z around inf 85.2%

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

      1. div-sub 85.2%

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

      2. sub-neg 85.2%

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

      3. *-inverses 85.2%

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

      4. metadata-eval 85.2%

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

      5. distribute-lft-in 85.2%

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

      6. associate-*r/ 85.2%

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

      7. metadata-eval 85.2%

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

      8. metadata-eval 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in t around 0 85.0%

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

   if -5e16 < (/.f64 x y) < 4e10

   1. Initial program 89.7%

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

   3. Taylor expanded in x around 0 97.5%

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

      1. associate-*r/ 97.5%

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

      2. metadata-eval 97.5%

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

      3. associate-/l/ 97.5%

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

      4. +-commutative 97.5%

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

      5. div-sub 97.5%

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

      6. sub-neg 97.5%

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

      7. *-inverses 97.5%

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

      8. metadata-eval 97.5%

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

      9. distribute-lft-in 97.5%

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

      10. metadata-eval 97.5%

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

      11. associate-+l+ 97.5%

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

      12. +-commutative 97.5%

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

      13. associate-/l/ 97.5%

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

      14. +-commutative 97.5%

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

      15. associate-/l/ 97.5%

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

      16. *-rgt-identity 97.5%

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

      17. associate-*r/ 97.5%

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

      18. distribute-rgt-out 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in t around inf 97.5%

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

      1. sub-neg 97.5%

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

      2. associate-/r* 97.5%

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

      3. metadata-eval 97.5%

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

      4. associate-*r/ 97.5%

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

      5. associate-*l/ 97.5%

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

      6. distribute-rgt-in 97.5%

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

      7. metadata-eval 97.5%

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

      8. associate-*l/ 97.5%

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

      9. *-lft-identity 97.5%

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

      10. +-commutative 97.5%

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

   8. Simplified 97.5%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16} \lor \neg \left(\frac{x}{y} \leq 40000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 40000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+16)
   (+ (/ x y) (/ 2.0 t))
   (if (<= (/ x y) 40000000000.0)
     (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
     (+ (/ x y) (+ -2.0 (/ 2.0 t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+16) {
		tmp = (x / y) + (2.0 / t);
	} else if ((x / y) <= 40000000000.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + (-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) <= (-5d+16)) then
        tmp = (x / y) + (2.0d0 / t)
    else if ((x / y) <= 40000000000.0d0) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (x / y) + ((-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) <= -5e+16) {
		tmp = (x / y) + (2.0 / t);
	} else if ((x / y) <= 40000000000.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+16:
		tmp = (x / y) + (2.0 / t)
	elif (x / y) <= 40000000000.0:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (x / y) + (-2.0 + (2.0 / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+16)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (Float64(x / y) <= 40000000000.0)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(x / y) + 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) <= -5e+16)
		tmp = (x / y) + (2.0 / t);
	elseif ((x / y) <= 40000000000.0)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (x / y) + (-2.0 + (2.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+16], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 40000000000.0], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5e16

   1. Initial program 82.2%

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

   3. Taylor expanded in z around inf 84.3%

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

      1. div-sub 84.3%

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

      2. sub-neg 84.3%

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

      3. *-inverses 84.3%

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

      4. metadata-eval 84.3%

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

      5. distribute-lft-in 84.3%

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

      6. associate-*r/ 84.3%

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

      7. metadata-eval 84.3%

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

      8. metadata-eval 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in t around 0 84.3%

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

   if -5e16 < (/.f64 x y) < 4e10

   1. Initial program 89.7%

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

   3. Taylor expanded in x around 0 97.5%

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

      1. associate-*r/ 97.5%

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

      2. metadata-eval 97.5%

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

      3. associate-/l/ 97.5%

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

      4. +-commutative 97.5%

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

      5. div-sub 97.5%

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

      6. sub-neg 97.5%

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

      7. *-inverses 97.5%

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

      8. metadata-eval 97.5%

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

      9. distribute-lft-in 97.5%

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

      10. metadata-eval 97.5%

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

      11. associate-+l+ 97.5%

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

      12. +-commutative 97.5%

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

      13. associate-/l/ 97.5%

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

      14. +-commutative 97.5%

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

      15. associate-/l/ 97.5%

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

      16. *-rgt-identity 97.5%

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

      17. associate-*r/ 97.5%

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

      18. distribute-rgt-out 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in t around inf 97.5%

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

      1. sub-neg 97.5%

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

      2. associate-/r* 97.5%

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

      3. metadata-eval 97.5%

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

      4. associate-*r/ 97.5%

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

      5. associate-*l/ 97.5%

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

      6. distribute-rgt-in 97.5%

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

      7. metadata-eval 97.5%

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

      8. associate-*l/ 97.5%

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

      9. *-lft-identity 97.5%

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

      10. +-commutative 97.5%

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

   8. Simplified 97.5%

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

   if 4e10 < (/.f64 x y)

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 85.9%

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

      1. div-sub 85.9%

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

      2. sub-neg 85.9%

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

      3. *-inverses 85.9%

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

      4. metadata-eval 85.9%

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

      5. distribute-lft-in 85.9%

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

      6. associate-*r/ 85.9%

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

      7. metadata-eval 85.9%

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

      8. metadata-eval 85.9%

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

   5. Simplified 85.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 40000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= z -1.1e-64)
     t_1
     (if (<= z 4e-153) (/ (/ 2.0 t) z) (if (<= z 4e-9) (- (/ x y) 2.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if (z <= -1.1e-64) {
		tmp = t_1;
	} else if (z <= 4e-153) {
		tmp = (2.0 / t) / z;
	} else if (z <= 4e-9) {
		tmp = (x / y) - 2.0;
	} 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 / t)
    if (z <= (-1.1d-64)) then
        tmp = t_1
    else if (z <= 4d-153) then
        tmp = (2.0d0 / t) / z
    else if (z <= 4d-9) then
        tmp = (x / y) - 2.0d0
    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 / t);
	double tmp;
	if (z <= -1.1e-64) {
		tmp = t_1;
	} else if (z <= 4e-153) {
		tmp = (2.0 / t) / z;
	} else if (z <= 4e-9) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / t)
	tmp = 0
	if z <= -1.1e-64:
		tmp = t_1
	elif z <= 4e-153:
		tmp = (2.0 / t) / z
	elif z <= 4e-9:
		tmp = (x / y) - 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -1.1e-64)
		tmp = t_1;
	elseif (z <= 4e-153)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (z <= 4e-9)
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if (z <= -1.1e-64)
		tmp = t_1;
	elseif (z <= 4e-153)
		tmp = (2.0 / t) / z;
	elseif (z <= 4e-9)
		tmp = (x / y) - 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e-64], t$95$1, If[LessEqual[z, 4e-153], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4e-9], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e-64 or 4.00000000000000025e-9 < z

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf 97.2%

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

      1. div-sub 97.2%

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

      2. sub-neg 97.2%

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

      3. *-inverses 97.2%

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

      4. metadata-eval 97.2%

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

      5. distribute-lft-in 97.2%

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

      6. associate-*r/ 97.2%

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

      7. metadata-eval 97.2%

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

      8. metadata-eval 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in t around 0 81.4%

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

   if -1.1e-64 < z < 4.00000000000000016e-153

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0 69.9%

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

      1. associate-/l/ 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in z around 0 69.9%

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

      1. associate-/r* 69.9%

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

   8. Simplified 69.9%

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

   if 4.00000000000000016e-153 < z < 4.00000000000000025e-9

   1. Initial program 96.3%

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

   3. Taylor expanded in t around inf 65.9%

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

Alternative 11: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -185 \lor \neg \left(t \leq 3.7 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -185.0) (not (<= t 3.7e-26)))
   (- (/ x y) 2.0)
   (* (+ 2.0 (/ 2.0 z)) (/ 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -185.0) || !(t <= 3.7e-26)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-185.0d0)) .or. (.not. (t <= 3.7d-26))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) * (1.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -185.0) || !(t <= 3.7e-26)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -185.0) or not (t <= 3.7e-26):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) * (1.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -185.0) || !(t <= 3.7e-26))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) * Float64(1.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -185.0) || ~((t <= 3.7e-26)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -185.0], N[Not[LessEqual[t, 3.7e-26]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -185 or 3.6999999999999999e-26 < t

   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 t around inf 83.9%

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

   if -185 < t < 3.6999999999999999e-26

   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 78.7%

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

      1. associate-*r/ 78.7%

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

      2. metadata-eval 78.7%

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

   5. Simplified 78.7%

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

      1. clear-num 78.7%

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

      2. associate-/r/ 78.7%

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

   7. Applied egg-rr 78.7%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -185 \lor \neg \left(t \leq 3.7 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+16) (not (<= (/ x y) 2e+20)))
   (/ x y)
   (- -2.0 (/ -2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+16) || !((x / y) <= 2e+20)) {
		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) <= (-5d+16)) .or. (.not. ((x / y) <= 2d+20))) 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) <= -5e+16) || !((x / y) <= 2e+20)) {
		tmp = x / y;
	} else {
		tmp = -2.0 - (-2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+16) or not ((x / y) <= 2e+20):
		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) <= -5e+16) || !(Float64(x / y) <= 2e+20))
		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) <= -5e+16) || ~(((x / y) <= 2e+20)))
		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], -5e+16], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+20]], $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) < -5e16 or 2e20 < (/.f64 x y)

   1. Initial program 84.3%

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

   3. Taylor expanded in x around inf 77.1%

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

   if -5e16 < (/.f64 x y) < 2e20

   1. Initial program 89.9%

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

   3. Taylor expanded in z around inf 59.8%

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

      1. div-sub 59.8%

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

      2. sub-neg 59.8%

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

      3. *-inverses 59.8%

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

      4. metadata-eval 59.8%

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

      5. distribute-lft-in 59.8%

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

      6. associate-*r/ 59.8%

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

      7. metadata-eval 59.8%

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

      8. metadata-eval 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in x around 0 56.8%

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

      1. sub-neg 56.8%

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

      2. metadata-eval 56.8%

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

      3. associate-*r/ 56.8%

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

      4. metadata-eval 56.8%

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

      5. +-commutative 56.8%

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

      6. metadata-eval 56.8%

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

      7. distribute-neg-frac 56.8%

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

      8. unsub-neg 56.8%

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

   8. Simplified 56.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-25}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+16)
   (/ x y)
   (if (<= (/ x y) 5e-25) (- -2.0 (/ -2.0 t)) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+16) {
		tmp = x / y;
	} else if ((x / y) <= 5e-25) {
		tmp = -2.0 - (-2.0 / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+16)) then
        tmp = x / y
    else if ((x / y) <= 5d-25) then
        tmp = (-2.0d0) - ((-2.0d0) / t)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+16) {
		tmp = x / y;
	} else if ((x / y) <= 5e-25) {
		tmp = -2.0 - (-2.0 / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+16:
		tmp = x / y
	elif (x / y) <= 5e-25:
		tmp = -2.0 - (-2.0 / t)
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+16)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e-25)
		tmp = Float64(-2.0 - Float64(-2.0 / t));
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+16)
		tmp = x / y;
	elseif ((x / y) <= 5e-25)
		tmp = -2.0 - (-2.0 / t);
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+16], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-25], N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5e16

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf 72.3%

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

   if -5e16 < (/.f64 x y) < 4.99999999999999962e-25

   1. Initial program 90.5%

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

   3. Taylor expanded in z around inf 60.3%

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

      1. div-sub 60.3%

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

      2. sub-neg 60.3%

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

      3. *-inverses 60.3%

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

      4. metadata-eval 60.3%

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

      5. distribute-lft-in 60.3%

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

      6. associate-*r/ 60.3%

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

      7. metadata-eval 60.3%

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

      8. metadata-eval 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in x around 0 59.6%

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

      1. sub-neg 59.6%

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

      2. metadata-eval 59.6%

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

      3. associate-*r/ 59.6%

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

      4. metadata-eval 59.6%

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

      5. +-commutative 59.6%

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

      6. metadata-eval 59.6%

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

      7. distribute-neg-frac 59.6%

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

      8. unsub-neg 59.6%

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

   8. Simplified 59.6%

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

   if 4.99999999999999962e-25 < (/.f64 x y)

   1. Initial program 85.9%

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

   3. Taylor expanded in t around inf 74.9%

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

Alternative 14: 80.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -750 \lor \neg \left(t \leq 3.8 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -750.0) (not (<= t 3.8e-26)))
   (- (/ 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 <= -750.0) || !(t <= 3.8e-26)) {
		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 <= (-750.0d0)) .or. (.not. (t <= 3.8d-26))) 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 <= -750.0) || !(t <= 3.8e-26)) {
		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 <= -750.0) or not (t <= 3.8e-26):
		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 <= -750.0) || !(t <= 3.8e-26))
		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 <= -750.0) || ~((t <= 3.8e-26)))
		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, -750.0], N[Not[LessEqual[t, 3.8e-26]], $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 < -750 or 3.80000000000000015e-26 < t

   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 t around inf 83.9%

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

   if -750 < t < 3.80000000000000015e-26

   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 78.7%

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

      1. associate-*r/ 78.7%

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

      2. metadata-eval 78.7%

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

   5. Simplified 78.7%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -750 \lor \neg \left(t \leq 3.8 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16} \lor \neg \left(\frac{x}{y} \leq 0.2\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+16) (not (<= (/ x y) 0.2))) (/ x y) -2.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+16) || !((x / y) <= 0.2)) {
		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) <= (-5d+16)) .or. (.not. ((x / y) <= 0.2d0))) 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) <= -5e+16) || !((x / y) <= 0.2)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+16) or not ((x / y) <= 0.2):
		tmp = x / y
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+16) || !(Float64(x / y) <= 0.2))
		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) <= -5e+16) || ~(((x / y) <= 0.2)))
		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], -5e+16], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.2]], $MachinePrecision]], N[(x / y), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e16 or 0.20000000000000001 < (/.f64 x y)

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf 75.5%

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

   if -5e16 < (/.f64 x y) < 0.20000000000000001

   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 97.5%

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

      1. associate-*r/ 97.5%

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

      2. metadata-eval 97.5%

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

      3. associate-/l/ 97.5%

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

      4. +-commutative 97.5%

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

      5. div-sub 97.5%

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

      6. sub-neg 97.5%

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

      7. *-inverses 97.5%

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

      8. metadata-eval 97.5%

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

      9. distribute-lft-in 97.5%

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

      10. metadata-eval 97.5%

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

      11. associate-+l+ 97.5%

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

      12. +-commutative 97.5%

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

      13. associate-/l/ 97.5%

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

      14. +-commutative 97.5%

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

      15. associate-/l/ 97.5%

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

      16. *-rgt-identity 97.5%

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

      17. associate-*r/ 97.5%

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

      18. distribute-rgt-out 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around inf 56.9%

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

   7. Taylor expanded in t around inf 30.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+16} \lor \neg \left(\frac{x}{y} \leq 0.2\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.5% accurate, 1.3× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 2.0) (/ 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 <= 2.0) {
		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 <= 2.0d0) 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 <= 2.0) {
		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 <= 2.0:
		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 <= 2.0)
		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 <= 2.0)
		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, 2.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 2 < t

   1. Initial program 75.3%

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

   3. Taylor expanded in x around 0 42.8%

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

      1. associate-*r/ 42.8%

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

      2. metadata-eval 42.8%

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

      3. associate-/l/ 42.9%

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

      4. +-commutative 42.9%

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

      5. div-sub 42.9%

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

      6. sub-neg 42.9%

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

      7. *-inverses 42.9%

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

      8. metadata-eval 42.9%

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

      9. distribute-lft-in 42.9%

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

      10. metadata-eval 42.9%

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

      11. associate-+l+ 42.9%

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

      12. +-commutative 42.9%

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

      13. associate-/l/ 42.8%

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

      14. +-commutative 42.8%

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

      15. associate-/l/ 42.9%

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

      16. *-rgt-identity 42.9%

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

      17. associate-*r/ 42.9%

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

      18. distribute-rgt-out 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in z around inf 29.2%

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

   7. Taylor expanded in t around inf 28.7%

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

   if -1 < t < 2

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 60.4%

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

      1. div-sub 60.4%

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

      2. sub-neg 60.4%

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

      3. *-inverses 60.4%

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

      4. metadata-eval 60.4%

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

      5. distribute-lft-in 60.4%

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

      6. associate-*r/ 60.4%

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

      7. metadata-eval 60.4%

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

      8. metadata-eval 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in t around 0 35.1%

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

Alternative 17: 20.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 0 59.4%

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

   1. associate-*r/ 59.4%

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

   2. metadata-eval 59.4%

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

   3. associate-/l/ 59.4%

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

   4. +-commutative 59.4%

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

   5. div-sub 59.4%

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

   6. sub-neg 59.4%

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

   7. *-inverses 59.4%

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

   8. metadata-eval 59.4%

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

   9. distribute-lft-in 59.4%

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

   10. metadata-eval 59.4%

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

   11. associate-+l+ 59.4%

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

   12. +-commutative 59.4%

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

   13. associate-/l/ 59.4%

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

   14. +-commutative 59.4%

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

   15. associate-/l/ 59.4%

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

   16. *-rgt-identity 59.4%

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

   17. associate-*r/ 59.4%

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

   18. distribute-rgt-out 59.4%

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

5. Simplified 59.4%

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

6. Taylor expanded in z around inf 32.3%

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

7. Taylor expanded in t around inf 15.4%

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

Developer Target 1: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024139 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

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