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

Percentage Accurate: 85.8% → 99.1%

Time: 13.8s

Alternatives: 15

Speedup: 1.1×

• 23.6% 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: 85.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.1%

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

3. Taylor expanded in t around 0 98.7%

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

   1. associate--l+ 98.7%

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

   2. associate-*r/ 98.7%

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

   3. metadata-eval 98.7%

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

   4. associate-/r* 98.8%

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

5. Simplified 98.8%

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

6. Final simplification 98.8%

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

Alternative 2: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t} + -2\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-108}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+51} \lor \neg \left(z \leq 3.4 \cdot 10^{+123}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 t) -2.0)) (t_2 (- (/ x y) 2.0)))
   (if (<= z -5.1e+157)
     t_2
     (if (<= z -2e+35)
       t_1
       (if (<= z -3.8e-117)
         t_2
         (if (<= z 2.4e-108)
           (/ 2.0 (* t z))
           (if (or (<= z 1.6e+51) (not (<= z 3.4e+123))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + -2.0;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (z <= -5.1e+157) {
		tmp = t_2;
	} else if (z <= -2e+35) {
		tmp = t_1;
	} else if (z <= -3.8e-117) {
		tmp = t_2;
	} else if (z <= 2.4e-108) {
		tmp = 2.0 / (t * z);
	} else if ((z <= 1.6e+51) || !(z <= 3.4e+123)) {
		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 = (2.0d0 / t) + (-2.0d0)
    t_2 = (x / y) - 2.0d0
    if (z <= (-5.1d+157)) then
        tmp = t_2
    else if (z <= (-2d+35)) then
        tmp = t_1
    else if (z <= (-3.8d-117)) then
        tmp = t_2
    else if (z <= 2.4d-108) then
        tmp = 2.0d0 / (t * z)
    else if ((z <= 1.6d+51) .or. (.not. (z <= 3.4d+123))) 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 = (2.0 / t) + -2.0;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (z <= -5.1e+157) {
		tmp = t_2;
	} else if (z <= -2e+35) {
		tmp = t_1;
	} else if (z <= -3.8e-117) {
		tmp = t_2;
	} else if (z <= 2.4e-108) {
		tmp = 2.0 / (t * z);
	} else if ((z <= 1.6e+51) || !(z <= 3.4e+123)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) + -2.0
	t_2 = (x / y) - 2.0
	tmp = 0
	if z <= -5.1e+157:
		tmp = t_2
	elif z <= -2e+35:
		tmp = t_1
	elif z <= -3.8e-117:
		tmp = t_2
	elif z <= 2.4e-108:
		tmp = 2.0 / (t * z)
	elif (z <= 1.6e+51) or not (z <= 3.4e+123):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) + -2.0)
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -5.1e+157)
		tmp = t_2;
	elseif (z <= -2e+35)
		tmp = t_1;
	elseif (z <= -3.8e-117)
		tmp = t_2;
	elseif (z <= 2.4e-108)
		tmp = Float64(2.0 / Float64(t * z));
	elseif ((z <= 1.6e+51) || !(z <= 3.4e+123))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) + -2.0;
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -5.1e+157)
		tmp = t_2;
	elseif (z <= -2e+35)
		tmp = t_1;
	elseif (z <= -3.8e-117)
		tmp = t_2;
	elseif (z <= 2.4e-108)
		tmp = 2.0 / (t * z);
	elseif ((z <= 1.6e+51) || ~((z <= 3.4e+123)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -5.1e+157], t$95$2, If[LessEqual[z, -2e+35], t$95$1, If[LessEqual[z, -3.8e-117], t$95$2, If[LessEqual[z, 2.4e-108], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.6e+51], N[Not[LessEqual[z, 3.4e+123]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.09999999999999999e157 or -1.9999999999999999e35 < z < -3.79999999999999972e-117 or 2.40000000000000017e-108 < z < 1.6000000000000001e51 or 3.40000000000000001e123 < z

   1. Initial program 73.3%

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

   3. Taylor expanded in t around inf 70.4%

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

   if -5.09999999999999999e157 < z < -1.9999999999999999e35 or 1.6000000000000001e51 < z < 3.40000000000000001e123

   1. Initial program 90.4%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/r* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 81.0%

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

      1. sub-neg 81.0%

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

      2. associate-*r/ 81.0%

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

      3. metadata-eval 81.0%

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

      4. associate-*r/ 81.0%

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

      5. metadata-eval 81.0%

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

      6. metadata-eval 81.0%

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

      7. +-commutative 81.0%

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

      8. associate-+r+ 81.0%

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

      9. +-commutative 81.0%

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

   8. Simplified 81.0%

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

   9. Taylor expanded in z around inf 81.0%

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

       1. sub-neg 81.0%

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

       2. associate-*r/ 81.0%

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

       3. metadata-eval 81.0%

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

       4. metadata-eval 81.0%

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

   11. Simplified 81.0%

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

   if -3.79999999999999972e-117 < z < 2.40000000000000017e-108

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 97.0%

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

      1. associate--l+ 97.0%

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

      2. associate-*r/ 97.0%

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

      3. metadata-eval 97.0%

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

      4. associate-/r* 97.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in z around 0 70.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-108}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+51} \lor \neg \left(z \leq 3.4 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.05 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.2 \cdot 10^{-192}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.05e-16)
   (/ x y)
   (if (<= (/ x y) 0.0)
     -2.0
     (if (<= (/ x y) 2.2e-192) (/ 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) <= -1.05e-16) {
		tmp = x / y;
	} else if ((x / y) <= 0.0) {
		tmp = -2.0;
	} else if ((x / y) <= 2.2e-192) {
		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) <= (-1.05d-16)) then
        tmp = x / y
    else if ((x / y) <= 0.0d0) then
        tmp = -2.0d0
    else if ((x / y) <= 2.2d-192) 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) <= -1.05e-16) {
		tmp = x / y;
	} else if ((x / y) <= 0.0) {
		tmp = -2.0;
	} else if ((x / y) <= 2.2e-192) {
		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) <= -1.05e-16:
		tmp = x / y
	elif (x / y) <= 0.0:
		tmp = -2.0
	elif (x / y) <= 2.2e-192:
		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) <= -1.05e-16)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 0.0)
		tmp = -2.0;
	elseif (Float64(x / y) <= 2.2e-192)
		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) <= -1.05e-16)
		tmp = x / y;
	elseif ((x / y) <= 0.0)
		tmp = -2.0;
	elseif ((x / y) <= 2.2e-192)
		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], -1.05e-16], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 2.2e-192], 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) < -1.0500000000000001e-16 or 2 < (/.f64 x y)

   1. Initial program 84.5%

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

   3. Taylor expanded in x around inf 66.5%

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

   if -1.0500000000000001e-16 < (/.f64 x y) < -0.0 or 2.20000000000000006e-192 < (/.f64 x y) < 2

   1. Initial program 84.5%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 99.4%

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

      1. sub-neg 99.4%

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

      2. associate-*r/ 99.4%

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

      3. metadata-eval 99.4%

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

      4. associate-*r/ 99.4%

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

      5. metadata-eval 99.4%

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

      6. metadata-eval 99.4%

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

      7. +-commutative 99.4%

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

      8. associate-+r+ 99.4%

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

      9. +-commutative 99.4%

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

   8. Simplified 99.4%

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

   9. Taylor expanded in t around inf 39.4%

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

   if -0.0 < (/.f64 x y) < 2.20000000000000006e-192

   1. Initial program 93.2%

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

   3. Taylor expanded in z around inf 64.1%

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

      1. associate-*r/ 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in t around 0 52.4%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.05 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.2 \cdot 10^{-192}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -400000000000 \lor \neg \left(\frac{x}{y} \leq 2600000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -400000000000.0) (not (<= (/ x y) 2600000000.0)))
   (+ (/ x y) (/ (/ 2.0 t) z))
   (+ (/ 2.0 (* t z)) (+ (/ 2.0 t) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -400000000000.0) || !((x / y) <= 2600000000.0)) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-400000000000.0d0)) .or. (.not. ((x / y) <= 2600000000.0d0))) then
        tmp = (x / y) + ((2.0d0 / t) / z)
    else
        tmp = (2.0d0 / (t * z)) + ((2.0d0 / t) + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -400000000000.0) || !((x / y) <= 2600000000.0)) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -400000000000.0) or not ((x / y) <= 2600000000.0):
		tmp = (x / y) + ((2.0 / t) / z)
	else:
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -400000000000.0) || !(Float64(x / y) <= 2600000000.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(Float64(2.0 / t) + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -400000000000.0) || ~(((x / y) <= 2600000000.0)))
		tmp = (x / y) + ((2.0 / t) / z);
	else
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -400000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2600000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4e11 or 2.6e9 < (/.f64 x y)

   1. Initial program 82.9%

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

   3. Taylor expanded in z around 0 90.3%

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

      1. associate-/r* 90.3%

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

   5. Simplified 90.3%

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

   if -4e11 < (/.f64 x y) < 2.6e9

   1. Initial program 87.0%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-*r/ 98.7%

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

      3. metadata-eval 98.7%

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

      4. associate-*r/ 98.7%

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

      5. metadata-eval 98.7%

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

      6. metadata-eval 98.7%

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

      7. +-commutative 98.7%

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

      8. associate-+r+ 98.7%

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

      9. +-commutative 98.7%

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

   8. Simplified 98.7%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -400000000000 \lor \neg \left(\frac{x}{y} \leq 2600000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.05 \cdot 10^{-14} \lor \neg \left(\frac{x}{y} \leq 2\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.05e-14) (not (<= (/ x y) 2.0)))
   (+ (/ x y) (/ (+ 2.0 (/ 2.0 z)) t))
   (+ (/ 2.0 (* t z)) (+ (/ 2.0 t) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.05e-14) || !((x / y) <= 2.0)) {
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2.05d-14)) .or. (.not. ((x / y) <= 2.0d0))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (2.0d0 / (t * z)) + ((2.0d0 / t) + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.05e-14) || !((x / y) <= 2.0)) {
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.05e-14) or not ((x / y) <= 2.0):
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.05e-14) || !(Float64(x / y) <= 2.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(Float64(2.0 / t) + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.05e-14) || ~(((x / y) <= 2.0)))
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.05e-14], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.0500000000000001e-14 or 2 < (/.f64 x y)

   1. Initial program 84.3%

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

   3. Taylor expanded in t around 0 96.1%

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

   4. Taylor expanded in z around 0 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*r/ 96.8%

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

      3. metadata-eval 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-/l/ 96.8%

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

      6. *-rgt-identity 96.8%

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

      7. associate-*r/ 96.7%

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

      8. metadata-eval 96.7%

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

      9. associate-*l/ 96.7%

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

      10. associate-*l* 96.7%

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

      11. associate-*r/ 96.7%

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

      12. metadata-eval 96.7%

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

      13. distribute-lft-in 96.7%

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

      14. associate-*l/ 96.7%

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

      15. *-lft-identity 96.7%

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

   6. Simplified 96.7%

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

   if -2.0500000000000001e-14 < (/.f64 x y) < 2

   1. Initial program 85.9%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 99.5%

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

      1. sub-neg 99.5%

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

      2. associate-*r/ 99.5%

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

      3. metadata-eval 99.5%

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

      4. associate-*r/ 99.5%

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

      5. metadata-eval 99.5%

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

      6. metadata-eval 99.5%

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

      7. +-commutative 99.5%

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

      8. associate-+r+ 99.5%

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

      9. +-commutative 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.05 \cdot 10^{-14} \lor \neg \left(\frac{x}{y} \leq 2\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e-14)
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* t z)))
   (if (<= (/ x y) 5e-6)
     (+ (/ 2.0 (* t z)) (+ (/ 2.0 t) -2.0))
     (+ (/ x y) (/ (+ 2.0 (/ 2.0 z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-14) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	} else if ((x / y) <= 5e-6) {
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d-14)) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (t * z))
    else if ((x / y) <= 5d-6) then
        tmp = (2.0d0 / (t * z)) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (x / y) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-14) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	} else if ((x / y) <= 5e-6) {
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e-14:
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z))
	elif (x / y) <= 5e-6:
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e-14)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(t * z)));
	elseif (Float64(x / y) <= 5e-6)
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e-14)
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	elseif ((x / y) <= 5e-6)
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e-14], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-6], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.0000000000000002e-14

   1. Initial program 81.1%

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

   3. Taylor expanded in t around 0 95.6%

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

   if -5.0000000000000002e-14 < (/.f64 x y) < 5.00000000000000041e-6

   1. Initial program 86.0%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 99.5%

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

      1. sub-neg 99.5%

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

      2. associate-*r/ 99.5%

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

      3. metadata-eval 99.5%

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

      4. associate-*r/ 99.5%

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

      5. metadata-eval 99.5%

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

      6. metadata-eval 99.5%

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

      7. +-commutative 99.5%

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

      8. associate-+r+ 99.5%

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

      9. +-commutative 99.5%

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

   8. Simplified 99.5%

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

   if 5.00000000000000041e-6 < (/.f64 x y)

   1. Initial program 87.5%

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

   3. Taylor expanded in t around 0 96.6%

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

   4. Taylor expanded in z around 0 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-*r/ 98.0%

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

      3. metadata-eval 98.0%

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

      4. *-commutative 98.0%

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

      5. associate-/l/ 98.0%

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

      6. *-rgt-identity 98.0%

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

      7. associate-*r/ 97.9%

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

      8. metadata-eval 97.9%

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

      9. associate-*l/ 97.9%

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

      10. associate-*l* 97.9%

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

      11. associate-*r/ 97.9%

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

      12. metadata-eval 97.9%

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

      13. distribute-lft-in 97.9%

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

      14. associate-*l/ 97.9%

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

      15. *-lft-identity 97.9%

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

   6. Simplified 97.9%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -43 \lor \neg \left(\frac{x}{y} \leq 1.45 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -43.0) (not (<= (/ x y) 1.45e+87)))
   (+ (/ x y) (/ 2.0 t))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -43.0) || !((x / y) <= 1.45e+87)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-43.0d0)) .or. (.not. ((x / y) <= 1.45d+87))) then
        tmp = (x / y) + (2.0d0 / t)
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -43.0) || !((x / y) <= 1.45e+87)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -43.0) or not ((x / y) <= 1.45e+87):
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -43.0) || !(Float64(x / y) <= 1.45e+87))
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -43.0) || ~(((x / y) <= 1.45e+87)))
		tmp = (x / y) + (2.0 / t);
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -43.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.45e+87]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -43 or 1.4499999999999999e87 < (/.f64 x y)

   1. Initial program 82.6%

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

   3. Taylor expanded in t around 0 95.7%

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

      1. associate-/r* 88.3%

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

      2. +-commutative 88.3%

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

      3. fma-def 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in z around inf 82.4%

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

      1. associate-*r/ 82.4%

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

      2. metadata-eval 82.4%

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

      3. +-commutative 82.4%

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

   8. Simplified 82.4%

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

   if -43 < (/.f64 x y) < 1.4499999999999999e87

   1. Initial program 87.0%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 97.4%

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

      1. sub-neg 97.4%

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

      2. associate-*r/ 97.4%

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

      3. metadata-eval 97.4%

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

      4. associate-*r/ 97.4%

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

      5. metadata-eval 97.4%

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

      6. metadata-eval 97.4%

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

      7. +-commutative 97.4%

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

      8. associate-+r+ 97.4%

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

      9. +-commutative 97.4%

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

   8. Simplified 97.4%

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

   9. Taylor expanded in t around 0 97.4%

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

       1. sub-neg 97.4%

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

       2. metadata-eval 97.4%

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

       3. +-commutative 97.4%

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

       4. metadata-eval 97.4%

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

       5. *-commutative 97.4%

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

       6. associate-*r/ 97.4%

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

       7. associate-/r* 97.3%

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

       8. associate-*r/ 97.3%

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

       9. associate-*l/ 97.3%

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

       10. *-commutative 97.3%

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

       11. metadata-eval 97.3%

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

       12. associate-*r/ 97.3%

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

       13. associate-*r* 97.3%

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

       14. associate-*l/ 97.3%

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

       15. metadata-eval 97.3%

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

       16. distribute-rgt-in 97.3%

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

       17. associate-*l/ 97.3%

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

       18. *-lft-identity 97.3%

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

   11. Simplified 97.3%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -43 \lor \neg \left(\frac{x}{y} \leq 1.45 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1350000000000 \lor \neg \left(\frac{x}{y} \leq 2200000\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1350000000000.0) (not (<= (/ x y) 2200000.0)))
   (+ (/ x y) (/ (/ 2.0 t) z))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1350000000000.0) || !((x / y) <= 2200000.0)) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1350000000000.0d0)) .or. (.not. ((x / y) <= 2200000.0d0))) then
        tmp = (x / y) + ((2.0d0 / t) / z)
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1350000000000.0) || !((x / y) <= 2200000.0)) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1350000000000.0) or not ((x / y) <= 2200000.0):
		tmp = (x / y) + ((2.0 / t) / z)
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1350000000000.0) || !(Float64(x / y) <= 2200000.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1350000000000.0) || ~(((x / y) <= 2200000.0)))
		tmp = (x / y) + ((2.0 / t) / z);
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1350000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2200000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.35e12 or 2.2e6 < (/.f64 x y)

   1. Initial program 82.9%

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

   3. Taylor expanded in z around 0 90.3%

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

      1. associate-/r* 90.3%

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

   5. Simplified 90.3%

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

   if -1.35e12 < (/.f64 x y) < 2.2e6

   1. Initial program 87.0%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-*r/ 98.7%

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

      3. metadata-eval 98.7%

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

      4. associate-*r/ 98.7%

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

      5. metadata-eval 98.7%

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

      6. metadata-eval 98.7%

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

      7. +-commutative 98.7%

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

      8. associate-+r+ 98.7%

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

      9. +-commutative 98.7%

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

   8. Simplified 98.7%

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

   9. Taylor expanded in t around 0 98.7%

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

       1. sub-neg 98.7%

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

       2. metadata-eval 98.7%

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

       3. +-commutative 98.7%

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

       4. metadata-eval 98.7%

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

       5. *-commutative 98.7%

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

       6. associate-*r/ 98.7%

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

       7. associate-/r* 98.7%

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

       8. associate-*r/ 98.7%

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

       9. associate-*l/ 98.6%

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

       10. *-commutative 98.6%

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

       11. metadata-eval 98.6%

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

       12. associate-*r/ 98.6%

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

       13. associate-*r* 98.6%

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

       14. associate-*l/ 98.6%

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

       15. metadata-eval 98.6%

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

       16. distribute-rgt-in 98.6%

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

       17. associate-*l/ 98.6%

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

       18. *-lft-identity 98.6%

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

   11. Simplified 98.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1350000000000 \lor \neg \left(\frac{x}{y} \leq 2200000\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 4800000:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= z -1.65e-39)
     t_1
     (if (<= z 1.8e-108)
       (/ 2.0 (* t z))
       (if (<= z 4800000.0) (- (/ x y) 2.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if (z <= -1.65e-39) {
		tmp = t_1;
	} else if (z <= 1.8e-108) {
		tmp = 2.0 / (t * z);
	} else if (z <= 4800000.0) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (2.0d0 / t)
    if (z <= (-1.65d-39)) then
        tmp = t_1
    else if (z <= 1.8d-108) then
        tmp = 2.0d0 / (t * z)
    else if (z <= 4800000.0d0) then
        tmp = (x / y) - 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if (z <= -1.65e-39) {
		tmp = t_1;
	} else if (z <= 1.8e-108) {
		tmp = 2.0 / (t * z);
	} else if (z <= 4800000.0) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / t)
	tmp = 0
	if z <= -1.65e-39:
		tmp = t_1
	elif z <= 1.8e-108:
		tmp = 2.0 / (t * z)
	elif z <= 4800000.0:
		tmp = (x / y) - 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -1.65e-39)
		tmp = t_1;
	elseif (z <= 1.8e-108)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (z <= 4800000.0)
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if (z <= -1.65e-39)
		tmp = t_1;
	elseif (z <= 1.8e-108)
		tmp = 2.0 / (t * z);
	elseif (z <= 4800000.0)
		tmp = (x / y) - 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e-39], t$95$1, If[LessEqual[z, 1.8e-108], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4800000.0], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999992e-39 or 4.8e6 < z

   1. Initial program 69.8%

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

   3. Taylor expanded in t around 0 77.0%

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

      1. associate-/r* 56.8%

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

      2. +-commutative 56.8%

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

      3. fma-def 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in z around inf 73.8%

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

      1. associate-*r/ 73.8%

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

      2. metadata-eval 73.8%

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

      3. +-commutative 73.8%

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

   8. Simplified 73.8%

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

   if -1.64999999999999992e-39 < z < 1.8e-108

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 97.4%

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

      1. associate--l+ 97.4%

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

      2. associate-*r/ 97.4%

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

      3. metadata-eval 97.4%

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

      4. associate-/r* 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in z around 0 67.6%

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

   if 1.8e-108 < z < 4.8e6

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 79.1%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 4800000:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -104000000000 \lor \neg \left(\frac{x}{y} \leq 260000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -104000000000.0) (not (<= (/ x y) 260000000.0)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -104000000000.0) || !((x / y) <= 260000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-104000000000.0d0)) .or. (.not. ((x / y) <= 260000000.0d0))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -104000000000.0) || !((x / y) <= 260000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -104000000000.0) or not ((x / y) <= 260000000.0):
		tmp = x / y
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -104000000000.0) || !(Float64(x / y) <= 260000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -104000000000.0) || ~(((x / y) <= 260000000.0)))
		tmp = x / y;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -104000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 260000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.04e11 or 2.6e8 < (/.f64 x y)

   1. Initial program 82.9%

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

   3. Taylor expanded in x around inf 73.1%

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

   if -1.04e11 < (/.f64 x y) < 2.6e8

   1. Initial program 87.0%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-*r/ 98.7%

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

      3. metadata-eval 98.7%

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

      4. associate-*r/ 98.7%

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

      5. metadata-eval 98.7%

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

      6. metadata-eval 98.7%

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

      7. +-commutative 98.7%

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

      8. associate-+r+ 98.7%

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

      9. +-commutative 98.7%

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

   8. Simplified 98.7%

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

   9. Taylor expanded in z around inf 54.8%

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

       1. sub-neg 54.8%

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

       2. associate-*r/ 54.8%

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

       3. metadata-eval 54.8%

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

       4. metadata-eval 54.8%

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

   11. Simplified 54.8%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -104000000000 \lor \neg \left(\frac{x}{y} \leq 260000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -380000000000 \lor \neg \left(\frac{x}{y} \leq 7800000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -380000000000.0) (not (<= (/ x y) 7800000.0)))
   (- (/ x y) 2.0)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -380000000000.0) || !((x / y) <= 7800000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-380000000000.0d0)) .or. (.not. ((x / y) <= 7800000.0d0))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -380000000000.0) || !((x / y) <= 7800000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -380000000000.0) or not ((x / y) <= 7800000.0):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -380000000000.0) || !(Float64(x / y) <= 7800000.0))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -380000000000.0) || ~(((x / y) <= 7800000.0)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -380000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 7800000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.8e11 or 7.8e6 < (/.f64 x y)

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 73.5%

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

   if -3.8e11 < (/.f64 x y) < 7.8e6

   1. Initial program 87.0%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-*r/ 98.7%

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

      3. metadata-eval 98.7%

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

      4. associate-*r/ 98.7%

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

      5. metadata-eval 98.7%

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

      6. metadata-eval 98.7%

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

      7. +-commutative 98.7%

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

      8. associate-+r+ 98.7%

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

      9. +-commutative 98.7%

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

   8. Simplified 98.7%

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

   9. Taylor expanded in z around inf 54.8%

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

       1. sub-neg 54.8%

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

       2. associate-*r/ 54.8%

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

       3. metadata-eval 54.8%

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

       4. metadata-eval 54.8%

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

   11. Simplified 54.8%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -380000000000 \lor \neg \left(\frac{x}{y} \leq 7800000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-12} \lor \neg \left(t \leq 10000000000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{z + 1}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.5e-12) (not (<= t 10000000000000.0)))
   (- (/ x y) 2.0)
   (* 2.0 (/ (+ z 1.0) (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-12) || !(t <= 10000000000000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 * ((z + 1.0) / (t * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.5d-12)) .or. (.not. (t <= 10000000000000.0d0))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 * ((z + 1.0d0) / (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-12) || !(t <= 10000000000000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 * ((z + 1.0) / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.5e-12) or not (t <= 10000000000000.0):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 * ((z + 1.0) / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.5e-12) || !(t <= 10000000000000.0))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z + 1.0) / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.5e-12) || ~((t <= 10000000000000.0)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 * ((z + 1.0) / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.5e-12], N[Not[LessEqual[t, 10000000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 * N[(N[(z + 1.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5e-12 or 1e13 < t

   1. Initial program 74.1%

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

   3. Taylor expanded in t around inf 83.2%

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

   if -3.5e-12 < t < 1e13

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. remove-double-neg 96.7%

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

      3. distribute-frac-neg 96.7%

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

      4. unsub-neg 96.7%

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

      5. *-commutative 96.7%

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

      6. associate-*r* 96.7%

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

      7. distribute-rgt1-in 96.7%

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

      8. associate-*r/ 97.4%

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

      9. /-rgt-identity 97.4%

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

      10. fma-neg 97.4%

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

      11. /-rgt-identity 97.4%

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

      12. *-commutative 97.4%

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

      13. fma-def 97.4%

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

      14. *-commutative 97.4%

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

      15. distribute-frac-neg 97.4%

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

      16. remove-double-neg 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around 0 83.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-12} \lor \neg \left(t \leq 10000000000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{z + 1}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-12} \lor \neg \left(t \leq 10000000000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.4e-12) (not (<= t 10000000000000.0)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.4e-12) || !(t <= 10000000000000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.4d-12)) .or. (.not. (t <= 10000000000000.0d0))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.4e-12) || !(t <= 10000000000000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.4e-12) or not (t <= 10000000000000.0):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.4e-12) || !(t <= 10000000000000.0))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.4e-12) || ~((t <= 10000000000000.0)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.4e-12], N[Not[LessEqual[t, 10000000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999987e-12 or 1e13 < t

   1. Initial program 74.1%

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

   3. Taylor expanded in t around inf 83.2%

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

   if -2.39999999999999987e-12 < t < 1e13

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 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 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-12} \lor \neg \left(t \leq 10000000000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+46}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 8e+46) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 8e+46) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.0d0)) then
        tmp = -2.0d0
    else if (t <= 8d+46) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 8e+46) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.0:
		tmp = -2.0
	elif t <= 8e+46:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 8e+46)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 8e+46)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.0], -2.0, If[LessEqual[t, 8e+46], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 7.9999999999999999e46 < t

   1. Initial program 72.0%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 50.3%

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

      1. sub-neg 50.3%

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

      2. associate-*r/ 50.3%

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

      3. metadata-eval 50.3%

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

      4. associate-*r/ 50.3%

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

      5. metadata-eval 50.3%

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

      6. metadata-eval 50.3%

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

      7. +-commutative 50.3%

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

      8. associate-+r+ 50.3%

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

      9. +-commutative 50.3%

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

   8. Simplified 50.3%

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

   9. Taylor expanded in t around inf 35.9%

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

   if -1 < t < 7.9999999999999999e46

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 50.1%

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

      1. associate-*r/ 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in t around 0 29.2%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+46}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 20.4% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.1%

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

3. Taylor expanded in t around 0 98.7%

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

   1. associate--l+ 98.7%

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

   2. associate-*r/ 98.7%

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

   3. metadata-eval 98.7%

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

   4. associate-/r* 98.8%

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

5. Simplified 98.8%

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

6. Taylor expanded in x around 0 66.4%

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

   1. sub-neg 66.4%

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

   2. associate-*r/ 66.4%

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

   3. metadata-eval 66.4%

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

   4. associate-*r/ 66.4%

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

   5. metadata-eval 66.4%

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

   6. metadata-eval 66.4%

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

   7. +-commutative 66.4%

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

   8. associate-+r+ 66.4%

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

   9. +-commutative 66.4%

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

8. Simplified 66.4%

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

9. Taylor expanded in t around inf 18.3%

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

10. Final simplification 18.3%

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

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024020 
(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))))