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

Percentage Accurate: 85.9% → 99.2%

Time: 11.5s

Alternatives: 11

Speedup: 1.3×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

   1. +-commutative 85.8%

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

   2. remove-double-neg 85.8%

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

   3. distribute-frac-neg 85.8%

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

   4. unsub-neg 85.8%

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

   5. *-commutative 85.8%

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

   6. associate-*r* 85.8%

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

   7. distribute-rgt1-in 85.8%

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

   8. associate-/l* 85.7%

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

   9. fma-neg 85.7%

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

   10. *-commutative 85.7%

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

   11. fma-define 85.7%

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

   12. *-commutative 85.7%

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

   13. distribute-frac-neg 85.7%

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

   14. remove-double-neg 85.7%

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

3. Simplified 85.7%

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

5. Taylor expanded in t around inf 99.1%

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

   1. sub-neg 99.1%

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

   2. +-commutative 99.1%

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

   3. metadata-eval 99.1%

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

   4. associate-+l+ 99.1%

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

   5. associate-*r/ 99.1%

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

   6. distribute-lft-in 99.1%

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

   7. metadata-eval 99.1%

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

   8. associate-*r/ 99.1%

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

   9. metadata-eval 99.1%

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

7. Simplified 99.1%

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

8. Final simplification 99.1%

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

Alternative 2: 50.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.75 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -9.6 \cdot 10^{-191}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 3.8 \cdot 10^{-285}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.75e-11)
   (/ x y)
   (if (<= (/ x y) -9.6e-191)
     -2.0
     (if (<= (/ x y) 3.8e-285)
       (/ 2.0 t)
       (if (<= (/ x y) 6.2e-149)
         -2.0
         (if (<= (/ x y) 2.2e-53)
           (/ 2.0 t)
           (if (<= (/ x y) 2.0) -2.0 (/ x y))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.75e-11) {
		tmp = x / y;
	} else if ((x / y) <= -9.6e-191) {
		tmp = -2.0;
	} else if ((x / y) <= 3.8e-285) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 6.2e-149) {
		tmp = -2.0;
	} else if ((x / y) <= 2.2e-53) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.75d-11)) then
        tmp = x / y
    else if ((x / y) <= (-9.6d-191)) then
        tmp = -2.0d0
    else if ((x / y) <= 3.8d-285) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 6.2d-149) then
        tmp = -2.0d0
    else if ((x / y) <= 2.2d-53) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.75e-11) {
		tmp = x / y;
	} else if ((x / y) <= -9.6e-191) {
		tmp = -2.0;
	} else if ((x / y) <= 3.8e-285) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 6.2e-149) {
		tmp = -2.0;
	} else if ((x / y) <= 2.2e-53) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.75e-11:
		tmp = x / y
	elif (x / y) <= -9.6e-191:
		tmp = -2.0
	elif (x / y) <= 3.8e-285:
		tmp = 2.0 / t
	elif (x / y) <= 6.2e-149:
		tmp = -2.0
	elif (x / y) <= 2.2e-53:
		tmp = 2.0 / t
	elif (x / y) <= 2.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.75e-11)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -9.6e-191)
		tmp = -2.0;
	elseif (Float64(x / y) <= 3.8e-285)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 6.2e-149)
		tmp = -2.0;
	elseif (Float64(x / y) <= 2.2e-53)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.75e-11)
		tmp = x / y;
	elseif ((x / y) <= -9.6e-191)
		tmp = -2.0;
	elseif ((x / y) <= 3.8e-285)
		tmp = 2.0 / t;
	elseif ((x / y) <= 6.2e-149)
		tmp = -2.0;
	elseif ((x / y) <= 2.2e-53)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.75e-11], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -9.6e-191], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 3.8e-285], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 6.2e-149], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 2.2e-53], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.0], -2.0, N[(x / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.7500000000000001e-11 or 2 < (/.f64 x y)

   1. Initial program 79.9%

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

   3. Taylor expanded in x around inf 66.1%

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

   if -1.7500000000000001e-11 < (/.f64 x y) < -9.5999999999999997e-191 or 3.8000000000000002e-285 < (/.f64 x y) < 6.19999999999999974e-149 or 2.20000000000000018e-53 < (/.f64 x y) < 2

   1. Initial program 86.8%

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

      1. +-commutative 86.8%

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

      2. remove-double-neg 86.8%

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

      3. distribute-frac-neg 86.8%

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

      4. unsub-neg 86.8%

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

      5. *-commutative 86.8%

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

      6. associate-*r* 86.8%

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

      7. distribute-rgt1-in 86.8%

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

      8. associate-/l* 86.7%

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

      9. fma-neg 86.7%

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

      10. *-commutative 86.7%

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

      11. fma-define 86.7%

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

      12. *-commutative 86.7%

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

      13. distribute-frac-neg 86.7%

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

      14. remove-double-neg 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-+l+ 99.9%

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

      5. associate-*r/ 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. metadata-eval 99.5%

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

      4. associate-+r- 99.5%

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

      5. +-commutative 99.5%

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

      6. sub-neg 99.5%

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

      7. metadata-eval 99.5%

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

      8. +-commutative 99.5%

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

      9. +-commutative 99.5%

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

      10. metadata-eval 99.5%

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

      11. associate-*l/ 99.5%

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

      12. *-commutative 99.5%

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

      13. associate-/r* 99.4%

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

      14. associate-*l/ 99.4%

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

      15. associate-/l* 99.4%

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

      16. distribute-lft-in 99.4%

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

      17. associate-*l/ 99.4%

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

      18. *-lft-identity 99.4%

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

   10. Simplified 99.4%

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

   11. Taylor expanded in z around inf 66.7%

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

   12. Taylor expanded in t around inf 49.3%

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

   if -9.5999999999999997e-191 < (/.f64 x y) < 3.8000000000000002e-285 or 6.19999999999999974e-149 < (/.f64 x y) < 2.20000000000000018e-53

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0 80.0%

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

      1. associate-*r/ 80.0%

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

      2. metadata-eval 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in z around inf 38.7%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.75 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -9.6 \cdot 10^{-191}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 3.8 \cdot 10^{-285}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.2 \cdot 10^{-149}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := -2 + \frac{\frac{2}{z}}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -1580:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -1.6 \cdot 10^{-176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1.55 \cdot 10^{-208}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.7 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (+ -2.0 (/ (/ 2.0 z) t))))
   (if (<= (/ x y) -1580.0)
     t_1
     (if (<= (/ x y) -1.6e-176)
       t_2
       (if (<= (/ x y) -1.55e-208)
         (+ -2.0 (/ 2.0 t))
         (if (<= (/ x y) 1.7e+97) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + ((2.0 / z) / t);
	double tmp;
	if ((x / y) <= -1580.0) {
		tmp = t_1;
	} else if ((x / y) <= -1.6e-176) {
		tmp = t_2;
	} else if ((x / y) <= -1.55e-208) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 1.7e+97) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    t_2 = (-2.0d0) + ((2.0d0 / z) / t)
    if ((x / y) <= (-1580.0d0)) then
        tmp = t_1
    else if ((x / y) <= (-1.6d-176)) then
        tmp = t_2
    else if ((x / y) <= (-1.55d-208)) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if ((x / y) <= 1.7d+97) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + ((2.0 / z) / t);
	double tmp;
	if ((x / y) <= -1580.0) {
		tmp = t_1;
	} else if ((x / y) <= -1.6e-176) {
		tmp = t_2;
	} else if ((x / y) <= -1.55e-208) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 1.7e+97) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	t_2 = -2.0 + ((2.0 / z) / t)
	tmp = 0
	if (x / y) <= -1580.0:
		tmp = t_1
	elif (x / y) <= -1.6e-176:
		tmp = t_2
	elif (x / y) <= -1.55e-208:
		tmp = -2.0 + (2.0 / t)
	elif (x / y) <= 1.7e+97:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	t_2 = Float64(-2.0 + Float64(Float64(2.0 / z) / t))
	tmp = 0.0
	if (Float64(x / y) <= -1580.0)
		tmp = t_1;
	elseif (Float64(x / y) <= -1.6e-176)
		tmp = t_2;
	elseif (Float64(x / y) <= -1.55e-208)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (Float64(x / y) <= 1.7e+97)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	t_2 = -2.0 + ((2.0 / z) / t);
	tmp = 0.0;
	if ((x / y) <= -1580.0)
		tmp = t_1;
	elseif ((x / y) <= -1.6e-176)
		tmp = t_2;
	elseif ((x / y) <= -1.55e-208)
		tmp = -2.0 + (2.0 / t);
	elseif ((x / y) <= 1.7e+97)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1580.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -1.6e-176], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -1.55e-208], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.7e+97], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1580 or 1.70000000000000005e97 < (/.f64 x y)

   1. Initial program 77.5%

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

   3. Taylor expanded in t around inf 75.7%

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

   if -1580 < (/.f64 x y) < -1.59999999999999992e-176 or -1.5499999999999999e-208 < (/.f64 x y) < 1.70000000000000005e97

   1. Initial program 91.3%

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

      1. +-commutative 91.3%

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

      2. remove-double-neg 91.3%

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

      3. distribute-frac-neg 91.3%

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

      4. unsub-neg 91.3%

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

      5. *-commutative 91.3%

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

      6. associate-*r* 91.3%

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

      7. distribute-rgt1-in 91.3%

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

      8. associate-/l* 91.2%

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

      9. fma-neg 91.2%

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

      10. *-commutative 91.2%

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

      11. fma-define 91.2%

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

      12. *-commutative 91.2%

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

      13. distribute-frac-neg 91.2%

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

      14. remove-double-neg 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-+l+ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 97.6%

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

      1. associate--l+ 97.6%

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

      2. associate-*r/ 97.6%

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

      3. metadata-eval 97.6%

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

      4. associate-+r- 97.6%

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

      5. +-commutative 97.6%

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

      6. sub-neg 97.6%

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

      7. metadata-eval 97.6%

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

      8. +-commutative 97.6%

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

      9. +-commutative 97.6%

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

      10. metadata-eval 97.6%

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

      11. associate-*l/ 97.6%

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

      12. *-commutative 97.6%

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

      13. associate-/r* 97.5%

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

      14. associate-*l/ 97.5%

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

      15. associate-/l* 97.5%

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

      16. distribute-lft-in 97.5%

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

      17. associate-*l/ 97.5%

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

      18. *-lft-identity 97.5%

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

   10. Simplified 97.5%

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

   11. Taylor expanded in z around 0 70.9%

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

   if -1.59999999999999992e-176 < (/.f64 x y) < -1.5499999999999999e-208

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. remove-double-neg 99.8%

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

      3. distribute-frac-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r* 99.8%

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

      7. distribute-rgt1-in 99.8%

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

      8. associate-/l* 99.6%

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

      9. fma-neg 99.6%

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

      10. *-commutative 99.6%

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

      11. fma-define 99.6%

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

      12. *-commutative 99.6%

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

      13. distribute-frac-neg 99.6%

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

      14. remove-double-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-+l+ 100.0%

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

      5. associate-*r/ 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-+r- 100.0%

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

      5. +-commutative 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. +-commutative 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*l/ 100.0%

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

      12. *-commutative 100.0%

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

      13. associate-/r* 100.0%

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

      14. associate-*l/ 100.0%

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

      15. associate-/l* 100.0%

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

      16. distribute-lft-in 100.0%

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

      17. associate-*l/ 100.0%

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

      18. *-lft-identity 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in z around inf 100.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1580:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq -1.6 \cdot 10^{-176}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.55 \cdot 10^{-208}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.7 \cdot 10^{+97}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000 \lor \neg \left(\frac{x}{y} \leq 4.8 \cdot 10^{+97}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -10000.0) (not (<= (/ x y) 4.8e+97)))
   (- (/ x y) 2.0)
   (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10000.0) || !((x / y) <= 4.8e+97)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-10000.0d0)) .or. (.not. ((x / y) <= 4.8d+97))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10000.0) || !((x / y) <= 4.8e+97)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -10000.0) or not ((x / y) <= 4.8e+97):
		tmp = (x / y) - 2.0
	else:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -10000.0) || !(Float64(x / y) <= 4.8e+97))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -10000.0) || ~(((x / y) <= 4.8e+97)))
		tmp = (x / y) - 2.0;
	else
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -10000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.8e+97]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e4 or 4.8e97 < (/.f64 x y)

   1. Initial program 77.5%

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

   3. Taylor expanded in t around inf 75.7%

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

   if -1e4 < (/.f64 x y) < 4.8e97

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. remove-double-neg 91.8%

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

      3. distribute-frac-neg 91.8%

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

      4. unsub-neg 91.8%

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

      5. *-commutative 91.8%

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

      6. associate-*r* 91.8%

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

      7. distribute-rgt1-in 91.8%

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

      8. associate-/l* 91.7%

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

      9. fma-neg 91.7%

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

      10. *-commutative 91.7%

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

      11. fma-define 91.7%

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

      12. *-commutative 91.7%

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

      13. distribute-frac-neg 91.7%

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

      14. remove-double-neg 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-+l+ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 97.8%

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

      1. associate--l+ 97.8%

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

      2. associate-*r/ 97.8%

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

      3. metadata-eval 97.8%

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

      4. associate-+r- 97.8%

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

      5. +-commutative 97.8%

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

      6. sub-neg 97.8%

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

      7. metadata-eval 97.8%

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

      8. +-commutative 97.8%

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

      9. +-commutative 97.8%

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

      10. metadata-eval 97.8%

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

      11. associate-*l/ 97.8%

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

      12. *-commutative 97.8%

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

      13. associate-/r* 97.7%

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

      14. associate-*l/ 97.7%

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

      15. associate-/l* 97.6%

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

      16. distribute-lft-in 97.6%

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

      17. associate-*l/ 97.7%

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

      18. *-lft-identity 97.7%

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

   10. Simplified 97.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000 \lor \neg \left(\frac{x}{y} \leq 4.8 \cdot 10^{+97}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -810 \lor \neg \left(\frac{x}{y} \leq 1.12 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -810.0) (not (<= (/ x y) 1.12e+98)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -810.0) || !((x / y) <= 1.12e+98)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-810.0d0)) .or. (.not. ((x / y) <= 1.12d+98))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -810.0) || !((x / y) <= 1.12e+98)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -810.0) or not ((x / y) <= 1.12e+98):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -810.0) || !(Float64(x / y) <= 1.12e+98))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -810.0) || ~(((x / y) <= 1.12e+98)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -810.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.12e+98]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -810 or 1.12e98 < (/.f64 x y)

   1. Initial program 77.5%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. div-sub 83.3%

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

      2. sub-neg 83.3%

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

      3. *-inverses 83.3%

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

      4. metadata-eval 83.3%

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

      5. distribute-lft-in 83.3%

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

      6. associate-*r/ 83.3%

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

      7. metadata-eval 83.3%

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

      8. metadata-eval 83.3%

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

   5. Simplified 83.3%

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

   if -810 < (/.f64 x y) < 1.12e98

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. remove-double-neg 91.8%

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

      3. distribute-frac-neg 91.8%

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

      4. unsub-neg 91.8%

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

      5. *-commutative 91.8%

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

      6. associate-*r* 91.8%

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

      7. distribute-rgt1-in 91.8%

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

      8. associate-/l* 91.7%

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

      9. fma-neg 91.7%

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

      10. *-commutative 91.7%

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

      11. fma-define 91.7%

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

      12. *-commutative 91.7%

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

      13. distribute-frac-neg 91.7%

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

      14. remove-double-neg 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-+l+ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 97.8%

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

      1. associate--l+ 97.8%

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

      2. associate-*r/ 97.8%

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

      3. metadata-eval 97.8%

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

      4. associate-+r- 97.8%

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

      5. +-commutative 97.8%

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

      6. sub-neg 97.8%

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

      7. metadata-eval 97.8%

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

      8. +-commutative 97.8%

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

      9. +-commutative 97.8%

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

      10. metadata-eval 97.8%

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

      11. associate-*l/ 97.8%

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

      12. *-commutative 97.8%

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

      13. associate-/r* 97.7%

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

      14. associate-*l/ 97.7%

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

      15. associate-/l* 97.6%

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

      16. distribute-lft-in 97.6%

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

      17. associate-*l/ 97.7%

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

      18. *-lft-identity 97.7%

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

   10. Simplified 97.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -810 \lor \neg \left(\frac{x}{y} \leq 1.12 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000 \lor \neg \left(\frac{x}{y} \leq 3.5 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -10000.0) (not (<= (/ x y) 3.5e+90)))
   (+ (/ x y) (/ 2.0 (* z t)))
   (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10000.0) || !((x / y) <= 3.5e+90)) {
		tmp = (x / y) + (2.0 / (z * t));
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-10000.0d0)) .or. (.not. ((x / y) <= 3.5d+90))) then
        tmp = (x / y) + (2.0d0 / (z * t))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10000.0) || !((x / y) <= 3.5e+90)) {
		tmp = (x / y) + (2.0 / (z * t));
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -10000.0) or not ((x / y) <= 3.5e+90):
		tmp = (x / y) + (2.0 / (z * t))
	else:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -10000.0) || !(Float64(x / y) <= 3.5e+90))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -10000.0) || ~(((x / y) <= 3.5e+90)))
		tmp = (x / y) + (2.0 / (z * t));
	else
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -10000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.5e+90]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e4 or 3.4999999999999998e90 < (/.f64 x y)

   1. Initial program 77.7%

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

   3. Taylor expanded in z around 0 87.6%

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

   if -1e4 < (/.f64 x y) < 3.4999999999999998e90

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. remove-double-neg 91.7%

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

      3. distribute-frac-neg 91.7%

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

      4. unsub-neg 91.7%

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

      5. *-commutative 91.7%

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

      6. associate-*r* 91.7%

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

      7. distribute-rgt1-in 91.7%

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

      8. associate-/l* 91.6%

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

      9. fma-neg 91.6%

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

      10. *-commutative 91.6%

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

      11. fma-define 91.6%

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

      12. *-commutative 91.6%

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

      13. distribute-frac-neg 91.6%

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

      14. remove-double-neg 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-+l+ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 97.7%

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

      1. associate--l+ 97.7%

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

      2. associate-*r/ 97.7%

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

      3. metadata-eval 97.7%

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

      4. associate-+r- 97.7%

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

      5. +-commutative 97.7%

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

      6. sub-neg 97.7%

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

      7. metadata-eval 97.7%

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

      8. +-commutative 97.7%

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

      9. +-commutative 97.7%

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

      10. metadata-eval 97.7%

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

      11. associate-*l/ 97.7%

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

      12. *-commutative 97.7%

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

      13. associate-/r* 97.6%

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

      14. associate-*l/ 97.6%

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

      15. associate-/l* 97.6%

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

      16. distribute-lft-in 97.6%

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

      17. associate-*l/ 97.6%

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

      18. *-lft-identity 97.6%

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

   10. Simplified 97.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000 \lor \neg \left(\frac{x}{y} \leq 3.5 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.75 \cdot 10^{-11} \lor \neg \left(\frac{x}{y} \leq 2.45 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.75e-11) (not (<= (/ x y) 2.45e+91)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.75e-11) || !((x / y) <= 2.45e+91)) {
		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) <= (-1.75d-11)) .or. (.not. ((x / y) <= 2.45d+91))) 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) <= -1.75e-11) || !((x / y) <= 2.45e+91)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.75e-11) or not ((x / y) <= 2.45e+91):
		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) <= -1.75e-11) || !(Float64(x / y) <= 2.45e+91))
		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) <= -1.75e-11) || ~(((x / y) <= 2.45e+91)))
		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], -1.75e-11], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2.45e+91]], $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) < -1.7500000000000001e-11 or 2.45000000000000015e91 < (/.f64 x y)

   1. Initial program 78.1%

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

   3. Taylor expanded in x around inf 72.2%

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

   if -1.7500000000000001e-11 < (/.f64 x y) < 2.45000000000000015e91

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. remove-double-neg 91.6%

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

      3. distribute-frac-neg 91.6%

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

      4. unsub-neg 91.6%

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

      5. *-commutative 91.6%

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

      6. associate-*r* 91.6%

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

      7. distribute-rgt1-in 91.6%

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

      8. associate-/l* 91.5%

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

      9. fma-neg 91.5%

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

      10. *-commutative 91.5%

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

      11. fma-define 91.5%

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

      12. *-commutative 91.5%

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

      13. distribute-frac-neg 91.5%

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

      14. remove-double-neg 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-+l+ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 97.7%

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

      1. associate--l+ 97.7%

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

      2. associate-*r/ 97.7%

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

      3. metadata-eval 97.7%

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

      4. associate-+r- 97.7%

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

      5. +-commutative 97.7%

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

      6. sub-neg 97.7%

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

      7. metadata-eval 97.7%

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

      8. +-commutative 97.7%

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

      9. +-commutative 97.7%

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

      10. metadata-eval 97.7%

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

      11. associate-*l/ 97.7%

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

      12. *-commutative 97.7%

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

      13. associate-/r* 97.6%

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

      14. associate-*l/ 97.6%

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

      15. associate-/l* 97.6%

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

      16. distribute-lft-in 97.6%

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

      17. associate-*l/ 97.6%

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

      18. *-lft-identity 97.6%

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

   10. Simplified 97.6%

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

   11. Taylor expanded in z around inf 59.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.75 \cdot 10^{-11} \lor \neg \left(\frac{x}{y} \leq 2.45 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.75 \cdot 10^{-11} \lor \neg \left(\frac{x}{y} \leq 3.5 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.75e-11) (not (<= (/ x y) 3.5e+90)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.75e-11) || !((x / y) <= 3.5e+90)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1.75d-11)) .or. (.not. ((x / y) <= 3.5d+90))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.75e-11) || !((x / y) <= 3.5e+90)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.75e-11) or not ((x / y) <= 3.5e+90):
		tmp = (x / y) - 2.0
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.75e-11) || !(Float64(x / y) <= 3.5e+90))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.75e-11) || ~(((x / y) <= 3.5e+90)))
		tmp = (x / y) - 2.0;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.75e-11], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.5e+90]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.7500000000000001e-11 or 3.4999999999999998e90 < (/.f64 x y)

   1. Initial program 78.1%

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

   3. Taylor expanded in t around inf 73.7%

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

   if -1.7500000000000001e-11 < (/.f64 x y) < 3.4999999999999998e90

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. remove-double-neg 91.6%

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

      3. distribute-frac-neg 91.6%

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

      4. unsub-neg 91.6%

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

      5. *-commutative 91.6%

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

      6. associate-*r* 91.6%

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

      7. distribute-rgt1-in 91.6%

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

      8. associate-/l* 91.5%

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

      9. fma-neg 91.5%

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

      10. *-commutative 91.5%

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

      11. fma-define 91.5%

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

      12. *-commutative 91.5%

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

      13. distribute-frac-neg 91.5%

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

      14. remove-double-neg 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-+l+ 99.8%

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

      5. associate-*r/ 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 97.7%

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

      1. associate--l+ 97.7%

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

      2. associate-*r/ 97.7%

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

      3. metadata-eval 97.7%

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

      4. associate-+r- 97.7%

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

      5. +-commutative 97.7%

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

      6. sub-neg 97.7%

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

      7. metadata-eval 97.7%

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

      8. +-commutative 97.7%

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

      9. +-commutative 97.7%

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

      10. metadata-eval 97.7%

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

      11. associate-*l/ 97.7%

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

      12. *-commutative 97.7%

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

      13. associate-/r* 97.6%

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

      14. associate-*l/ 97.6%

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

      15. associate-/l* 97.6%

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

      16. distribute-lft-in 97.6%

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

      17. associate-*l/ 97.6%

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

      18. *-lft-identity 97.6%

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

   10. Simplified 97.6%

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

   11. Taylor expanded in z around inf 59.8%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.75 \cdot 10^{-11} \lor \neg \left(\frac{x}{y} \leq 3.5 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -320 \lor \neg \left(t \leq 0.00125\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -320.0) (not (<= t 0.00125)))
   (- (/ 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 <= -320.0) || !(t <= 0.00125)) {
		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 <= (-320.0d0)) .or. (.not. (t <= 0.00125d0))) 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 <= -320.0) || !(t <= 0.00125)) {
		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 <= -320.0) or not (t <= 0.00125):
		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 <= -320.0) || !(t <= 0.00125))
		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 <= -320.0) || ~((t <= 0.00125)))
		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, -320.0], N[Not[LessEqual[t, 0.00125]], $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 < -320 or 0.00125000000000000003 < t

   1. Initial program 74.4%

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

   3. Taylor expanded in t around inf 82.6%

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

   if -320 < t < 0.00125000000000000003

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. metadata-eval 83.9%

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

   5. Simplified 83.9%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -320 \lor \neg \left(t \leq 0.00125\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -82000:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 900:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -82000.0) -2.0 (if (<= t 900.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -82000.0) {
		tmp = -2.0;
	} else if (t <= 900.0) {
		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 <= (-82000.0d0)) then
        tmp = -2.0d0
    else if (t <= 900.0d0) 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 <= -82000.0) {
		tmp = -2.0;
	} else if (t <= 900.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -82000.0:
		tmp = -2.0
	elif t <= 900.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -82000.0)
		tmp = -2.0;
	elseif (t <= 900.0)
		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 <= -82000.0)
		tmp = -2.0;
	elseif (t <= 900.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -82000.0], -2.0, If[LessEqual[t, 900.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -82000 or 900 < t

   1. Initial program 73.4%

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

      1. +-commutative 73.4%

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

      2. remove-double-neg 73.4%

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

      3. distribute-frac-neg 73.4%

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

      4. unsub-neg 73.4%

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

      5. *-commutative 73.4%

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

      6. associate-*r* 73.4%

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

      7. distribute-rgt1-in 73.4%

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

      8. associate-/l* 73.3%

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

      9. fma-neg 73.3%

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

      10. *-commutative 73.3%

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

      11. fma-define 73.3%

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

      12. *-commutative 73.3%

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

      13. distribute-frac-neg 73.3%

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

      14. remove-double-neg 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-+l+ 99.9%

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

      5. associate-*r/ 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 52.9%

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

      1. associate--l+ 52.9%

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

      2. associate-*r/ 52.9%

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

      3. metadata-eval 52.9%

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

      4. associate-+r- 52.9%

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

      5. +-commutative 52.9%

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

      6. sub-neg 52.9%

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

      7. metadata-eval 52.9%

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

      8. +-commutative 52.9%

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

      9. +-commutative 52.9%

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

      10. metadata-eval 52.9%

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

      11. associate-*l/ 52.9%

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

      12. *-commutative 52.9%

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

      13. associate-/r* 52.9%

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

      14. associate-*l/ 52.9%

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

      15. associate-/l* 52.8%

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

      16. distribute-lft-in 52.8%

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

      17. associate-*l/ 52.8%

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

      18. *-lft-identity 52.8%

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

   10. Simplified 52.8%

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

   11. Taylor expanded in z around inf 36.1%

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

   12. Taylor expanded in t around inf 36.0%

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

   if -82000 < t < 900

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 80.8%

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

      1. associate-*r/ 80.8%

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

      2. metadata-eval 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in z around inf 40.2%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -82000:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 900:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 19.9% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

   1. +-commutative 85.8%

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

   2. remove-double-neg 85.8%

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

   3. distribute-frac-neg 85.8%

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

   4. unsub-neg 85.8%

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

   5. *-commutative 85.8%

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

   6. associate-*r* 85.8%

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

   7. distribute-rgt1-in 85.8%

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

   8. associate-/l* 85.7%

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

   9. fma-neg 85.7%

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

   10. *-commutative 85.7%

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

   11. fma-define 85.7%

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

   12. *-commutative 85.7%

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

   13. distribute-frac-neg 85.7%

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

   14. remove-double-neg 85.7%

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

3. Simplified 85.7%

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

5. Taylor expanded in t around inf 99.1%

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

   1. sub-neg 99.1%

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

   2. +-commutative 99.1%

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

   3. metadata-eval 99.1%

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

   4. associate-+l+ 99.1%

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

   5. associate-*r/ 99.1%

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

   6. distribute-lft-in 99.1%

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

   7. metadata-eval 99.1%

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

   8. associate-*r/ 99.1%

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

   9. metadata-eval 99.1%

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

7. Simplified 99.1%

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

8. Taylor expanded in x around 0 66.9%

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

   1. associate--l+ 66.9%

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

   2. associate-*r/ 66.9%

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

   3. metadata-eval 66.9%

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

   4. associate-+r- 66.9%

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

   5. +-commutative 66.9%

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

   6. sub-neg 66.9%

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

   7. metadata-eval 66.9%

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

   8. +-commutative 66.9%

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

   9. +-commutative 66.9%

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

   10. metadata-eval 66.9%

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

   11. associate-*l/ 66.9%

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

   12. *-commutative 66.9%

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

   13. associate-/r* 66.9%

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

   14. associate-*l/ 66.9%

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

   15. associate-/l* 66.9%

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

   16. distribute-lft-in 66.9%

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

   17. associate-*l/ 66.9%

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

   18. *-lft-identity 66.9%

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

10. Simplified 66.9%

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

11. Taylor expanded in z around inf 38.3%

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

12. Taylor expanded in t around inf 19.2%

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

13. Final simplification 19.2%

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

Developer target: 99.2% 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 2024039 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

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