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

Percentage Accurate: 86.8% → 99.2%

Time: 14.5s

Alternatives: 15

Speedup: 1.3×

• 23.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

3. Taylor expanded in t around 0 98.3%

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

   1. sub-neg 98.3%

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

   2. metadata-eval 98.3%

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

   3. associate-*r/ 98.3%

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

   4. +-commutative 98.3%

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

   5. associate-*r/ 98.3%

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

   6. metadata-eval 98.3%

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

   7. metadata-eval 98.3%

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

   8. +-commutative 98.3%

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

   9. associate-/l/ 98.3%

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

   10. metadata-eval 98.3%

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

   11. associate-*r/ 98.3%

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

   12. *-rgt-identity 98.3%

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

   13. associate-*r/ 98.3%

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

   14. distribute-rgt-out 98.3%

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

   15. associate-*r/ 98.3%

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

   16. metadata-eval 98.3%

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

5. Simplified 98.3%

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

6. Final simplification 98.3%

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

Alternative 2: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -0.00078:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-180}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-159}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+53} \lor \neg \left(t \leq 1.6 \cdot 10^{+63}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (+ (/ x y) -2.0)))
   (if (<= t -0.00078)
     t_2
     (if (<= t -5e-137)
       t_1
       (if (<= t -1.9e-180)
         (/ 2.0 t)
         (if (<= t -1.25e-272)
           t_1
           (if (<= t 2.45e-159)
             (/ 2.0 t)
             (if (or (<= t 1.55e+53) (not (<= t 1.6e+63))) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t <= -0.00078) {
		tmp = t_2;
	} else if (t <= -5e-137) {
		tmp = t_1;
	} else if (t <= -1.9e-180) {
		tmp = 2.0 / t;
	} else if (t <= -1.25e-272) {
		tmp = t_1;
	} else if (t <= 2.45e-159) {
		tmp = 2.0 / t;
	} else if ((t <= 1.55e+53) || !(t <= 1.6e+63)) {
		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 * z)
    t_2 = (x / y) + (-2.0d0)
    if (t <= (-0.00078d0)) then
        tmp = t_2
    else if (t <= (-5d-137)) then
        tmp = t_1
    else if (t <= (-1.9d-180)) then
        tmp = 2.0d0 / t
    else if (t <= (-1.25d-272)) then
        tmp = t_1
    else if (t <= 2.45d-159) then
        tmp = 2.0d0 / t
    else if ((t <= 1.55d+53) .or. (.not. (t <= 1.6d+63))) 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 * z);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t <= -0.00078) {
		tmp = t_2;
	} else if (t <= -5e-137) {
		tmp = t_1;
	} else if (t <= -1.9e-180) {
		tmp = 2.0 / t;
	} else if (t <= -1.25e-272) {
		tmp = t_1;
	} else if (t <= 2.45e-159) {
		tmp = 2.0 / t;
	} else if ((t <= 1.55e+53) || !(t <= 1.6e+63)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) + -2.0
	tmp = 0
	if t <= -0.00078:
		tmp = t_2
	elif t <= -5e-137:
		tmp = t_1
	elif t <= -1.9e-180:
		tmp = 2.0 / t
	elif t <= -1.25e-272:
		tmp = t_1
	elif t <= 2.45e-159:
		tmp = 2.0 / t
	elif (t <= 1.55e+53) or not (t <= 1.6e+63):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -0.00078)
		tmp = t_2;
	elseif (t <= -5e-137)
		tmp = t_1;
	elseif (t <= -1.9e-180)
		tmp = Float64(2.0 / t);
	elseif (t <= -1.25e-272)
		tmp = t_1;
	elseif (t <= 2.45e-159)
		tmp = Float64(2.0 / t);
	elseif ((t <= 1.55e+53) || !(t <= 1.6e+63))
		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 * z);
	t_2 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -0.00078)
		tmp = t_2;
	elseif (t <= -5e-137)
		tmp = t_1;
	elseif (t <= -1.9e-180)
		tmp = 2.0 / t;
	elseif (t <= -1.25e-272)
		tmp = t_1;
	elseif (t <= 2.45e-159)
		tmp = 2.0 / t;
	elseif ((t <= 1.55e+53) || ~((t <= 1.6e+63)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -0.00078], t$95$2, If[LessEqual[t, -5e-137], t$95$1, If[LessEqual[t, -1.9e-180], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, -1.25e-272], t$95$1, If[LessEqual[t, 2.45e-159], N[(2.0 / t), $MachinePrecision], If[Or[LessEqual[t, 1.55e+53], N[Not[LessEqual[t, 1.6e+63]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.79999999999999986e-4 or 2.45000000000000007e-159 < t < 1.5500000000000001e53 or 1.60000000000000006e63 < t

   1. Initial program 79.5%

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

   3. Taylor expanded in t around inf 78.3%

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

   if -7.79999999999999986e-4 < t < -5.00000000000000001e-137 or -1.9e-180 < t < -1.24999999999999995e-272 or 1.5500000000000001e53 < t < 1.60000000000000006e63

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-*r/ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-*r/ 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. +-commutative 99.7%

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

      9. associate-/l/ 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*r/ 99.7%

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

      12. *-rgt-identity 99.7%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.7%

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

      15. associate-*r/ 99.7%

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

      16. metadata-eval 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 66.2%

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

   if -5.00000000000000001e-137 < t < -1.9e-180 or -1.24999999999999995e-272 < t < 2.45000000000000007e-159

   1. Initial program 94.3%

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

   3. Taylor expanded in t around 0 85.4%

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

      1. associate-*r/ 85.4%

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

      2. metadata-eval 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around inf 57.5%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00078:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-137}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-180}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-272}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-159}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+53} \lor \neg \left(t \leq 1.6 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := \frac{2}{t \cdot z}\\ \mathbf{if}\;t \leq -0.135:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-132}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-181}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-159}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+53} \lor \neg \left(t \leq 1.6 \cdot 10^{+63}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)) (t_2 (/ 2.0 (* t z))))
   (if (<= t -0.135)
     t_1
     (if (<= t -1.3e-132)
       (/ (/ 2.0 t) z)
       (if (<= t -8.5e-181)
         (/ 2.0 t)
         (if (<= t -1.2e-272)
           t_2
           (if (<= t 9.2e-159)
             (/ 2.0 t)
             (if (or (<= t 1.55e+53) (not (<= t 1.6e+63))) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double t_2 = 2.0 / (t * z);
	double tmp;
	if (t <= -0.135) {
		tmp = t_1;
	} else if (t <= -1.3e-132) {
		tmp = (2.0 / t) / z;
	} else if (t <= -8.5e-181) {
		tmp = 2.0 / t;
	} else if (t <= -1.2e-272) {
		tmp = t_2;
	} else if (t <= 9.2e-159) {
		tmp = 2.0 / t;
	} else if ((t <= 1.55e+53) || !(t <= 1.6e+63)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    t_2 = 2.0d0 / (t * z)
    if (t <= (-0.135d0)) then
        tmp = t_1
    else if (t <= (-1.3d-132)) then
        tmp = (2.0d0 / t) / z
    else if (t <= (-8.5d-181)) then
        tmp = 2.0d0 / t
    else if (t <= (-1.2d-272)) then
        tmp = t_2
    else if (t <= 9.2d-159) then
        tmp = 2.0d0 / t
    else if ((t <= 1.55d+53) .or. (.not. (t <= 1.6d+63))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double t_2 = 2.0 / (t * z);
	double tmp;
	if (t <= -0.135) {
		tmp = t_1;
	} else if (t <= -1.3e-132) {
		tmp = (2.0 / t) / z;
	} else if (t <= -8.5e-181) {
		tmp = 2.0 / t;
	} else if (t <= -1.2e-272) {
		tmp = t_2;
	} else if (t <= 9.2e-159) {
		tmp = 2.0 / t;
	} else if ((t <= 1.55e+53) || !(t <= 1.6e+63)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	t_2 = 2.0 / (t * z)
	tmp = 0
	if t <= -0.135:
		tmp = t_1
	elif t <= -1.3e-132:
		tmp = (2.0 / t) / z
	elif t <= -8.5e-181:
		tmp = 2.0 / t
	elif t <= -1.2e-272:
		tmp = t_2
	elif t <= 9.2e-159:
		tmp = 2.0 / t
	elif (t <= 1.55e+53) or not (t <= 1.6e+63):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	t_2 = Float64(2.0 / Float64(t * z))
	tmp = 0.0
	if (t <= -0.135)
		tmp = t_1;
	elseif (t <= -1.3e-132)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t <= -8.5e-181)
		tmp = Float64(2.0 / t);
	elseif (t <= -1.2e-272)
		tmp = t_2;
	elseif (t <= 9.2e-159)
		tmp = Float64(2.0 / t);
	elseif ((t <= 1.55e+53) || !(t <= 1.6e+63))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	t_2 = 2.0 / (t * z);
	tmp = 0.0;
	if (t <= -0.135)
		tmp = t_1;
	elseif (t <= -1.3e-132)
		tmp = (2.0 / t) / z;
	elseif (t <= -8.5e-181)
		tmp = 2.0 / t;
	elseif (t <= -1.2e-272)
		tmp = t_2;
	elseif (t <= 9.2e-159)
		tmp = 2.0 / t;
	elseif ((t <= 1.55e+53) || ~((t <= 1.6e+63)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.135], t$95$1, If[LessEqual[t, -1.3e-132], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -8.5e-181], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, -1.2e-272], t$95$2, If[LessEqual[t, 9.2e-159], N[(2.0 / t), $MachinePrecision], If[Or[LessEqual[t, 1.55e+53], N[Not[LessEqual[t, 1.6e+63]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.13500000000000001 or 9.19999999999999914e-159 < t < 1.5500000000000001e53 or 1.60000000000000006e63 < t

   1. Initial program 79.5%

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

   3. Taylor expanded in t around inf 78.3%

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

   if -0.13500000000000001 < t < -1.3e-132

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-*r/ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-*r/ 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. +-commutative 99.7%

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

      9. associate-/l/ 99.6%

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

      10. metadata-eval 99.6%

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

      11. associate-*r/ 99.6%

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

      12. *-rgt-identity 99.6%

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

      13. associate-*r/ 99.7%

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

      14. distribute-rgt-out 99.7%

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

      15. associate-*r/ 99.7%

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

      16. metadata-eval 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0 99.7%

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

      1. associate-+r+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. metadata-eval 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/r* 99.6%

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

      6. *-rgt-identity 99.6%

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

      7. associate-*r/ 99.7%

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

      8. distribute-rgt-in 99.7%

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

      9. associate-*l/ 99.6%

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

      10. *-lft-identity 99.6%

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

      11. associate--l+ 99.6%

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

      12. sub-neg 99.6%

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

      13. metadata-eval 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in z around 0 65.1%

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

       1. associate-/r* 65.3%

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

   11. Simplified 65.3%

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

   if -1.3e-132 < t < -8.49999999999999953e-181 or -1.19999999999999995e-272 < t < 9.19999999999999914e-159

   1. Initial program 94.3%

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

   3. Taylor expanded in t around 0 85.4%

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

      1. associate-*r/ 85.4%

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

      2. metadata-eval 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around inf 57.5%

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

   if -8.49999999999999953e-181 < t < -1.19999999999999995e-272 or 1.5500000000000001e53 < t < 1.60000000000000006e63

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-*r/ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-*r/ 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. +-commutative 99.7%

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

      9. associate-/l/ 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*r/ 99.7%

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

      12. *-rgt-identity 99.7%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.8%

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

      15. associate-*r/ 99.8%

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

      16. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 66.8%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.135:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-132}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-181}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-272}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-159}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+53} \lor \neg \left(t \leq 1.6 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := 2 \cdot \left(\frac{1}{t} + -1\right)\\ \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 9.2 \cdot 10^{-181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 7.8 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 6.8 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (* 2.0 (+ (/ 1.0 t) -1.0))))
   (if (<= (/ x y) -4e+58)
     (/ x y)
     (if (<= (/ x y) 9.2e-181)
       t_2
       (if (<= (/ x y) 7.8e-71)
         t_1
         (if (<= (/ x y) 2.9e-5)
           t_2
           (if (<= (/ x y) 6.8e+16) t_1 (/ x y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = 2.0 * ((1.0 / t) + -1.0);
	double tmp;
	if ((x / y) <= -4e+58) {
		tmp = x / y;
	} else if ((x / y) <= 9.2e-181) {
		tmp = t_2;
	} else if ((x / y) <= 7.8e-71) {
		tmp = t_1;
	} else if ((x / y) <= 2.9e-5) {
		tmp = t_2;
	} else if ((x / y) <= 6.8e+16) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 / (t * z)
    t_2 = 2.0d0 * ((1.0d0 / t) + (-1.0d0))
    if ((x / y) <= (-4d+58)) then
        tmp = x / y
    else if ((x / y) <= 9.2d-181) then
        tmp = t_2
    else if ((x / y) <= 7.8d-71) then
        tmp = t_1
    else if ((x / y) <= 2.9d-5) then
        tmp = t_2
    else if ((x / y) <= 6.8d+16) then
        tmp = t_1
    else
        tmp = x / y
    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 * z);
	double t_2 = 2.0 * ((1.0 / t) + -1.0);
	double tmp;
	if ((x / y) <= -4e+58) {
		tmp = x / y;
	} else if ((x / y) <= 9.2e-181) {
		tmp = t_2;
	} else if ((x / y) <= 7.8e-71) {
		tmp = t_1;
	} else if ((x / y) <= 2.9e-5) {
		tmp = t_2;
	} else if ((x / y) <= 6.8e+16) {
		tmp = t_1;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = 2.0 * ((1.0 / t) + -1.0)
	tmp = 0
	if (x / y) <= -4e+58:
		tmp = x / y
	elif (x / y) <= 9.2e-181:
		tmp = t_2
	elif (x / y) <= 7.8e-71:
		tmp = t_1
	elif (x / y) <= 2.9e-5:
		tmp = t_2
	elif (x / y) <= 6.8e+16:
		tmp = t_1
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(2.0 * Float64(Float64(1.0 / t) + -1.0))
	tmp = 0.0
	if (Float64(x / y) <= -4e+58)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 9.2e-181)
		tmp = t_2;
	elseif (Float64(x / y) <= 7.8e-71)
		tmp = t_1;
	elseif (Float64(x / y) <= 2.9e-5)
		tmp = t_2;
	elseif (Float64(x / y) <= 6.8e+16)
		tmp = t_1;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = 2.0 * ((1.0 / t) + -1.0);
	tmp = 0.0;
	if ((x / y) <= -4e+58)
		tmp = x / y;
	elseif ((x / y) <= 9.2e-181)
		tmp = t_2;
	elseif ((x / y) <= 7.8e-71)
		tmp = t_1;
	elseif ((x / y) <= 2.9e-5)
		tmp = t_2;
	elseif ((x / y) <= 6.8e+16)
		tmp = t_1;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(1.0 / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -4e+58], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 9.2e-181], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 7.8e-71], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2.9e-5], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 6.8e+16], t$95$1, N[(x / y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -3.99999999999999978e58 or 6.8e16 < (/.f64 x y)

   1. Initial program 83.4%

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

   3. Taylor expanded in x around inf 75.6%

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

   if -3.99999999999999978e58 < (/.f64 x y) < 9.19999999999999963e-181 or 7.8000000000000004e-71 < (/.f64 x y) < 2.9e-5

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. remove-double-neg 85.5%

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

      3. distribute-frac-neg 85.5%

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

      4. unsub-neg 85.5%

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

      5. *-commutative 85.5%

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

      6. associate-*r* 85.5%

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

      7. distribute-rgt1-in 85.5%

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

      8. associate-*r/ 85.4%

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

      9. /-rgt-identity 85.4%

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

      10. fma-neg 85.4%

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

      11. /-rgt-identity 85.4%

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

      12. *-commutative 85.4%

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

      13. fma-def 85.4%

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

      14. *-commutative 85.4%

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

      15. distribute-frac-neg 85.4%

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

      16. remove-double-neg 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in x around 0 81.7%

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

   6. Taylor expanded in z around inf 65.3%

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

      1. div-sub 65.3%

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

      2. sub-neg 65.3%

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

      3. *-inverses 65.3%

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

      4. metadata-eval 65.3%

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

   8. Simplified 65.3%

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

   if 9.19999999999999963e-181 < (/.f64 x y) < 7.8000000000000004e-71 or 2.9e-5 < (/.f64 x y) < 6.8e16

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-*r/ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-*r/ 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. +-commutative 99.7%

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

      9. associate-/l/ 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*r/ 99.7%

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

      12. *-rgt-identity 99.7%

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

      13. associate-*r/ 99.6%

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

      14. distribute-rgt-out 99.5%

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

      15. associate-*r/ 99.5%

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

      16. metadata-eval 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in z around 0 74.3%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 9.2 \cdot 10^{-181}:\\ \;\;\;\;2 \cdot \left(\frac{1}{t} + -1\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 7.8 \cdot 10^{-71}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;2 \cdot \left(\frac{1}{t} + -1\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 6.8 \cdot 10^{+16}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;\frac{x}{y} \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.6 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{1}{t} \cdot \frac{2}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= (/ x y) -1.35e-5)
     t_1
     (if (<= (/ x y) 1.8e+17)
       (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
       (if (<= (/ x y) 3.6e+70) t_1 (+ (/ x y) (* (/ 1.0 t) (/ 2.0 z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if ((x / y) <= -1.35e-5) {
		tmp = t_1;
	} else if ((x / y) <= 1.8e+17) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else if ((x / y) <= 3.6e+70) {
		tmp = t_1;
	} else {
		tmp = (x / y) + ((1.0 / t) * (2.0 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + ((-2.0d0) + (2.0d0 / t))
    if ((x / y) <= (-1.35d-5)) then
        tmp = t_1
    else if ((x / y) <= 1.8d+17) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else if ((x / y) <= 3.6d+70) then
        tmp = t_1
    else
        tmp = (x / y) + ((1.0d0 / t) * (2.0d0 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if ((x / y) <= -1.35e-5) {
		tmp = t_1;
	} else if ((x / y) <= 1.8e+17) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else if ((x / y) <= 3.6e+70) {
		tmp = t_1;
	} else {
		tmp = (x / y) + ((1.0 / t) * (2.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (-2.0 + (2.0 / t))
	tmp = 0
	if (x / y) <= -1.35e-5:
		tmp = t_1
	elif (x / y) <= 1.8e+17:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	elif (x / y) <= 3.6e+70:
		tmp = t_1
	else:
		tmp = (x / y) + ((1.0 / t) * (2.0 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)))
	tmp = 0.0
	if (Float64(x / y) <= -1.35e-5)
		tmp = t_1;
	elseif (Float64(x / y) <= 1.8e+17)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	elseif (Float64(x / y) <= 3.6e+70)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(1.0 / t) * Float64(2.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if ((x / y) <= -1.35e-5)
		tmp = t_1;
	elseif ((x / y) <= 1.8e+17)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	elseif ((x / y) <= 3.6e+70)
		tmp = t_1;
	else
		tmp = (x / y) + ((1.0 / t) * (2.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1.35e-5], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1.8e+17], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3.6e+70], t$95$1, N[(N[(x / y), $MachinePrecision] + N[(N[(1.0 / t), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.3499999999999999e-5 or 1.8e17 < (/.f64 x y) < 3.6e70

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0 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. sub-neg 98.7%

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

      2. metadata-eval 98.7%

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

      3. associate-*r/ 98.7%

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

      4. +-commutative 98.7%

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

      5. associate-*r/ 98.7%

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

      6. metadata-eval 98.7%

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

      7. metadata-eval 98.7%

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

      8. +-commutative 98.7%

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

      9. associate-/l/ 98.7%

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

      10. metadata-eval 98.7%

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

      11. associate-*r/ 98.7%

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

      12. *-rgt-identity 98.7%

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

      13. associate-*r/ 98.7%

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

      14. distribute-rgt-out 98.7%

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

      15. associate-*r/ 98.7%

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

      16. metadata-eval 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in z around inf 85.9%

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

      1. sub-neg 85.9%

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

      2. associate-*r/ 85.9%

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

      3. metadata-eval 85.9%

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

      4. +-commutative 85.9%

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

      5. metadata-eval 85.9%

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

      6. associate-+l+ 85.9%

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

   8. Simplified 85.9%

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

   if -1.3499999999999999e-5 < (/.f64 x y) < 1.8e17

   1. Initial program 87.4%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

      9. associate-/l/ 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*r/ 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.8%

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

      15. associate-*r/ 99.8%

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

      16. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. *-rgt-identity 99.8%

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

      7. associate-*r/ 99.8%

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

      8. distribute-rgt-in 99.8%

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

      9. associate-*l/ 99.8%

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

      10. *-lft-identity 99.8%

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

      11. metadata-eval 99.8%

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

      12. +-commutative 99.8%

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

   8. Simplified 99.8%

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

   if 3.6e70 < (/.f64 x y)

   1. Initial program 76.7%

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

   3. Taylor expanded in z around 0 90.7%

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

      1. associate-/r* 90.8%

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

   5. Simplified 90.8%

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

      1. associate-/l/ 90.7%

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

      2. metadata-eval 90.7%

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

      3. frac-times 90.8%

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

   7. Applied egg-rr 90.8%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.6 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{1}{t} \cdot \frac{2}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;\frac{x}{y} \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5.1 \cdot 10^{+16}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.1 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= (/ x y) -8.8e-10)
     t_1
     (if (<= (/ x y) 5.1e+16)
       (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
       (if (<= (/ x y) 2.1e+71) t_1 (+ (/ x y) (/ (/ 2.0 t) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if ((x / y) <= -8.8e-10) {
		tmp = t_1;
	} else if ((x / y) <= 5.1e+16) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else if ((x / y) <= 2.1e+71) {
		tmp = t_1;
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + ((-2.0d0) + (2.0d0 / t))
    if ((x / y) <= (-8.8d-10)) then
        tmp = t_1
    else if ((x / y) <= 5.1d+16) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else if ((x / y) <= 2.1d+71) then
        tmp = t_1
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if ((x / y) <= -8.8e-10) {
		tmp = t_1;
	} else if ((x / y) <= 5.1e+16) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else if ((x / y) <= 2.1e+71) {
		tmp = t_1;
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (-2.0 + (2.0 / t))
	tmp = 0
	if (x / y) <= -8.8e-10:
		tmp = t_1
	elif (x / y) <= 5.1e+16:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	elif (x / y) <= 2.1e+71:
		tmp = t_1
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)))
	tmp = 0.0
	if (Float64(x / y) <= -8.8e-10)
		tmp = t_1;
	elseif (Float64(x / y) <= 5.1e+16)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	elseif (Float64(x / y) <= 2.1e+71)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if ((x / y) <= -8.8e-10)
		tmp = t_1;
	elseif ((x / y) <= 5.1e+16)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	elseif ((x / y) <= 2.1e+71)
		tmp = t_1;
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -8.8e-10], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5.1e+16], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.1e+71], t$95$1, N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -8.7999999999999996e-10 or 5.1e16 < (/.f64 x y) < 2.09999999999999989e71

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0 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. sub-neg 98.7%

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

      2. metadata-eval 98.7%

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

      3. associate-*r/ 98.7%

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

      4. +-commutative 98.7%

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

      5. associate-*r/ 98.7%

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

      6. metadata-eval 98.7%

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

      7. metadata-eval 98.7%

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

      8. +-commutative 98.7%

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

      9. associate-/l/ 98.7%

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

      10. metadata-eval 98.7%

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

      11. associate-*r/ 98.7%

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

      12. *-rgt-identity 98.7%

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

      13. associate-*r/ 98.7%

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

      14. distribute-rgt-out 98.7%

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

      15. associate-*r/ 98.7%

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

      16. metadata-eval 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in z around inf 85.9%

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

      1. sub-neg 85.9%

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

      2. associate-*r/ 85.9%

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

      3. metadata-eval 85.9%

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

      4. +-commutative 85.9%

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

      5. metadata-eval 85.9%

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

      6. associate-+l+ 85.9%

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

   8. Simplified 85.9%

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

   if -8.7999999999999996e-10 < (/.f64 x y) < 5.1e16

   1. Initial program 87.4%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

      9. associate-/l/ 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*r/ 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.8%

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

      15. associate-*r/ 99.8%

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

      16. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. *-rgt-identity 99.8%

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

      7. associate-*r/ 99.8%

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

      8. distribute-rgt-in 99.8%

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

      9. associate-*l/ 99.8%

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

      10. *-lft-identity 99.8%

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

      11. metadata-eval 99.8%

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

      12. +-commutative 99.8%

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

   8. Simplified 99.8%

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

   if 2.09999999999999989e71 < (/.f64 x y)

   1. Initial program 76.7%

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

   3. Taylor expanded in z around 0 90.7%

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

      1. associate-/r* 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 5.1 \cdot 10^{+16}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.1 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-32}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+53} \lor \neg \left(t \leq 1.6 \cdot 10^{+63}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= t -7.5e-5)
     t_1
     (if (<= t 6e-32)
       (/ (+ 2.0 (/ 2.0 z)) t)
       (if (or (<= t 1.55e+53) (not (<= t 1.6e+63))) t_1 (/ 2.0 (* t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -7.5e-5) {
		tmp = t_1;
	} else if (t <= 6e-32) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if ((t <= 1.55e+53) || !(t <= 1.6e+63)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (t <= (-7.5d-5)) then
        tmp = t_1
    else if (t <= 6d-32) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else if ((t <= 1.55d+53) .or. (.not. (t <= 1.6d+63))) then
        tmp = t_1
    else
        tmp = 2.0d0 / (t * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -7.5e-5) {
		tmp = t_1;
	} else if (t <= 6e-32) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if ((t <= 1.55e+53) || !(t <= 1.6e+63)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if t <= -7.5e-5:
		tmp = t_1
	elif t <= 6e-32:
		tmp = (2.0 + (2.0 / z)) / t
	elif (t <= 1.55e+53) or not (t <= 1.6e+63):
		tmp = t_1
	else:
		tmp = 2.0 / (t * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -7.5e-5)
		tmp = t_1;
	elseif (t <= 6e-32)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	elseif ((t <= 1.55e+53) || !(t <= 1.6e+63))
		tmp = t_1;
	else
		tmp = Float64(2.0 / Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -7.5e-5)
		tmp = t_1;
	elseif (t <= 6e-32)
		tmp = (2.0 + (2.0 / z)) / t;
	elseif ((t <= 1.55e+53) || ~((t <= 1.6e+63)))
		tmp = t_1;
	else
		tmp = 2.0 / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -7.5e-5], t$95$1, If[LessEqual[t, 6e-32], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[t, 1.55e+53], N[Not[LessEqual[t, 1.6e+63]], $MachinePrecision]], t$95$1, N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.49999999999999934e-5 or 6.0000000000000001e-32 < t < 1.5500000000000001e53 or 1.60000000000000006e63 < t

   1. Initial program 77.1%

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

   3. Taylor expanded in t around inf 85.3%

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

   if -7.49999999999999934e-5 < t < 6.0000000000000001e-32

   1. Initial program 96.2%

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

   3. Taylor expanded in t around 0 82.8%

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

      1. associate-*r/ 82.8%

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

      2. metadata-eval 82.8%

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

   5. Simplified 82.8%

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

   if 1.5500000000000001e53 < t < 1.60000000000000006e63

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-*r/ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-*r/ 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. +-commutative 99.7%

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

      9. associate-/l/ 99.4%

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

      10. metadata-eval 99.4%

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

      11. associate-*r/ 99.4%

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

      12. *-rgt-identity 99.4%

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

      13. associate-*r/ 99.7%

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

      14. distribute-rgt-out 99.7%

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

      15. associate-*r/ 99.7%

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

      16. metadata-eval 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 99.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-32}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+53} \lor \neg \left(t \leq 1.6 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -13500:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.1 \cdot 10^{-276}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -13500.0)
   (/ x y)
   (if (<= (/ x y) 2.1e-276)
     -2.0
     (if (<= (/ x y) 2.9e+17) (/ 2.0 t) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -13500.0) {
		tmp = x / y;
	} else if ((x / y) <= 2.1e-276) {
		tmp = -2.0;
	} else if ((x / y) <= 2.9e+17) {
		tmp = 2.0 / t;
	} 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) <= (-13500.0d0)) then
        tmp = x / y
    else if ((x / y) <= 2.1d-276) then
        tmp = -2.0d0
    else if ((x / y) <= 2.9d+17) then
        tmp = 2.0d0 / t
    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) <= -13500.0) {
		tmp = x / y;
	} else if ((x / y) <= 2.1e-276) {
		tmp = -2.0;
	} else if ((x / y) <= 2.9e+17) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -13500.0:
		tmp = x / y
	elif (x / y) <= 2.1e-276:
		tmp = -2.0
	elif (x / y) <= 2.9e+17:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -13500.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.1e-276)
		tmp = -2.0;
	elseif (Float64(x / y) <= 2.9e+17)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -13500.0)
		tmp = x / y;
	elseif ((x / y) <= 2.1e-276)
		tmp = -2.0;
	elseif ((x / y) <= 2.9e+17)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -13500.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.1e-276], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 2.9e+17], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -13500 or 2.9e17 < (/.f64 x y)

   1. Initial program 84.0%

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

   3. Taylor expanded in x around inf 72.3%

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

   if -13500 < (/.f64 x y) < 2.1e-276

   1. Initial program 86.4%

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

      1. +-commutative 86.4%

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

      2. remove-double-neg 86.4%

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

      3. distribute-frac-neg 86.4%

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

      4. unsub-neg 86.4%

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

      5. *-commutative 86.4%

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

      6. associate-*r* 86.4%

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

      7. distribute-rgt1-in 86.4%

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

      8. associate-*r/ 86.3%

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

      9. /-rgt-identity 86.3%

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

      10. fma-neg 86.3%

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

      11. /-rgt-identity 86.3%

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

      12. *-commutative 86.3%

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

      13. fma-def 86.3%

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

      14. *-commutative 86.3%

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

      15. distribute-frac-neg 86.3%

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

      16. remove-double-neg 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in x around 0 84.4%

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

   6. Taylor expanded in t around inf 45.0%

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

   if 2.1e-276 < (/.f64 x y) < 2.9e17

   1. Initial program 89.6%

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

   3. Taylor expanded in t around 0 77.4%

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

      1. associate-*r/ 77.4%

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

      2. metadata-eval 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in z around inf 33.7%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -13500:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.1 \cdot 10^{-276}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{+17}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0054 \lor \neg \left(\frac{x}{y} \leq 3.3 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -0.0054) (not (<= (/ x y) 3.3e+16)))
   (+ (/ x y) (+ -2.0 (/ 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) <= -0.0054) || !((x / y) <= 3.3e+16)) {
		tmp = (x / y) + (-2.0 + (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) <= (-0.0054d0)) .or. (.not. ((x / y) <= 3.3d+16))) then
        tmp = (x / y) + ((-2.0d0) + (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) <= -0.0054) || !((x / y) <= 3.3e+16)) {
		tmp = (x / y) + (-2.0 + (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) <= -0.0054) or not ((x / y) <= 3.3e+16):
		tmp = (x / y) + (-2.0 + (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) <= -0.0054) || !(Float64(x / y) <= 3.3e+16))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + 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) <= -0.0054) || ~(((x / y) <= 3.3e+16)))
		tmp = (x / y) + (-2.0 + (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], -0.0054], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.3e+16]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $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) < -0.0054000000000000003 or 3.3e16 < (/.f64 x y)

   1. Initial program 84.4%

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

   3. Taylor expanded in t around 0 97.0%

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

      1. sub-neg 97.0%

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

      2. metadata-eval 97.0%

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

      3. associate-*r/ 97.0%

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

      4. +-commutative 97.0%

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

      5. associate-*r/ 97.0%

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

      6. metadata-eval 97.0%

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

      7. metadata-eval 97.0%

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

      8. +-commutative 97.0%

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

      9. associate-/l/ 97.0%

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

      10. metadata-eval 97.0%

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

      11. associate-*r/ 97.0%

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

      12. *-rgt-identity 97.0%

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

      13. associate-*r/ 97.0%

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

      14. distribute-rgt-out 97.0%

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

      15. associate-*r/ 97.0%

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

      16. metadata-eval 97.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in z around inf 84.7%

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

      1. sub-neg 84.7%

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

      2. associate-*r/ 84.7%

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

      3. metadata-eval 84.7%

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

      4. +-commutative 84.7%

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

      5. metadata-eval 84.7%

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

      6. associate-+l+ 84.7%

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

   8. Simplified 84.7%

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

   if -0.0054000000000000003 < (/.f64 x y) < 3.3e16

   1. Initial program 87.4%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

      9. associate-/l/ 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*r/ 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.8%

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

      15. associate-*r/ 99.8%

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

      16. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. *-rgt-identity 99.8%

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

      7. associate-*r/ 99.8%

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

      8. distribute-rgt-in 99.8%

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

      9. associate-*l/ 99.8%

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

      10. *-lft-identity 99.8%

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

      11. metadata-eval 99.8%

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

      12. +-commutative 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0054 \lor \neg \left(\frac{x}{y} \leq 3.3 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+123}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.6e+103)
   (/ x y)
   (if (<= (/ x y) 4e+123) (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t)) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.6e+103) {
		tmp = x / y;
	} else if ((x / y) <= 4e+123) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.6d+103)) then
        tmp = x / y
    else if ((x / y) <= 4d+123) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (x / y) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.6e+103) {
		tmp = x / y;
	} else if ((x / y) <= 4e+123) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.6e+103:
		tmp = x / y
	elif (x / y) <= 4e+123:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.6e+103)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4e+123)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.6e+103)
		tmp = x / y;
	elseif ((x / y) <= 4e+123)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.6e+103], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4e+123], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.59999999999999996e103

   1. Initial program 88.1%

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

   3. Taylor expanded in x around inf 88.4%

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

   if -1.59999999999999996e103 < (/.f64 x y) < 3.99999999999999991e123

   1. Initial program 88.5%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

      9. associate-/l/ 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*r/ 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.8%

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

      15. associate-*r/ 99.8%

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

      16. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 88.5%

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

      1. sub-neg 88.5%

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

      2. associate-*r/ 88.5%

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

      3. metadata-eval 88.5%

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

      4. *-commutative 88.5%

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

      5. associate-/r* 88.5%

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

      6. *-rgt-identity 88.5%

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

      7. associate-*r/ 88.5%

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

      8. distribute-rgt-in 88.5%

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

      9. associate-*l/ 88.5%

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

      10. *-lft-identity 88.5%

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

      11. metadata-eval 88.5%

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

      12. +-commutative 88.5%

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

   8. Simplified 88.5%

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

   if 3.99999999999999991e123 < (/.f64 x y)

   1. Initial program 73.9%

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

   3. Taylor expanded in t around inf 89.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+123}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   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 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. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 99.2%

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

      1. sub-neg 99.2%

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

      2. associate-*r/ 99.2%

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

      3. metadata-eval 99.2%

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

      4. +-commutative 99.2%

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

      5. metadata-eval 99.2%

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

      6. associate-+l+ 99.2%

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

   8. Simplified 99.2%

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

   if -1 < z < 1

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0 96.7%

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

      1. sub-neg 96.7%

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

      2. metadata-eval 96.7%

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

      3. associate-*r/ 96.7%

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

      4. +-commutative 96.7%

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

      5. associate-*r/ 96.7%

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

      6. metadata-eval 96.7%

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

      7. metadata-eval 96.7%

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

      8. +-commutative 96.7%

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

      9. associate-/l/ 96.7%

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

      10. metadata-eval 96.7%

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

      11. associate-*r/ 96.7%

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

      12. *-rgt-identity 96.7%

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

      13. associate-*r/ 96.8%

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

      14. distribute-rgt-out 96.8%

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

      15. associate-*r/ 96.8%

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

      16. metadata-eval 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in x around 0 96.7%

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

      1. associate-+r+ 96.7%

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

      2. associate-*r/ 96.7%

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

      3. metadata-eval 96.7%

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

      4. *-commutative 96.7%

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

      5. associate-/r* 96.7%

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

      6. *-rgt-identity 96.7%

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

      7. associate-*r/ 96.8%

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

      8. distribute-rgt-in 96.8%

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

      9. associate-*l/ 96.7%

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

      10. *-lft-identity 96.7%

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

      11. associate--l+ 96.7%

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

      12. sub-neg 96.7%

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

      13. metadata-eval 96.7%

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

   8. Simplified 96.7%

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

   9. Taylor expanded in z around 0 95.3%

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

4. Final simplification 97.2%

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

Alternative 12: 61.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-62} \lor \neg \left(t \leq 1.38 \cdot 10^{-160}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.8e-62) (not (<= t 1.38e-160))) (+ (/ x y) -2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-62) || !(t <= 1.38e-160)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.8d-62)) .or. (.not. (t <= 1.38d-160))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-62) || !(t <= 1.38e-160)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.8e-62) or not (t <= 1.38e-160):
		tmp = (x / y) + -2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.8e-62) || !(t <= 1.38e-160))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.8e-62) || ~((t <= 1.38e-160)))
		tmp = (x / y) + -2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.8e-62], N[Not[LessEqual[t, 1.38e-160]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000002e-62 or 1.38e-160 < t

   1. Initial program 81.0%

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

   3. Taylor expanded in t around inf 73.8%

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

   if -2.80000000000000002e-62 < t < 1.38e-160

   1. Initial program 96.1%

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

   3. Taylor expanded in t around 0 87.7%

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

      1. associate-*r/ 87.7%

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

      2. metadata-eval 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in z around inf 47.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-62} \lor \neg \left(t \leq 1.38 \cdot 10^{-160}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-6}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.05e-6) -2.0 (if (<= t 1.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.05e-6) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.05d-6)) then
        tmp = -2.0d0
    else if (t <= 1.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.05e-6) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.05e-6:
		tmp = -2.0
	elif t <= 1.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.05e-6)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.05e-6)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.05e-6], -2.0, If[LessEqual[t, 1.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0499999999999999e-6 or 1 < t

   1. Initial program 77.0%

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

      1. +-commutative 77.0%

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

      2. remove-double-neg 77.0%

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

      3. distribute-frac-neg 77.0%

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

      4. unsub-neg 77.0%

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

      5. *-commutative 77.0%

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

      6. associate-*r* 77.0%

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

      7. distribute-rgt1-in 77.0%

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

      8. associate-*r/ 77.0%

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

      9. /-rgt-identity 77.0%

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

      10. fma-neg 77.0%

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

      11. /-rgt-identity 77.0%

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

      12. *-commutative 77.0%

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

      13. fma-def 77.0%

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

      14. *-commutative 77.0%

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

      15. distribute-frac-neg 77.0%

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

      16. remove-double-neg 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in x around 0 37.7%

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

   6. Taylor expanded in t around inf 33.0%

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

   if -2.0499999999999999e-6 < t < 1

   1. Initial program 96.4%

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

   3. Taylor expanded in t around 0 79.6%

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

      1. associate-*r/ 79.6%

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

      2. metadata-eval 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in z around inf 40.8%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-6}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

3. Taylor expanded in t around 0 98.3%

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

   1. sub-neg 98.3%

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

   2. metadata-eval 98.3%

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

   3. associate-*r/ 98.3%

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

   4. +-commutative 98.3%

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

   5. associate-*r/ 98.3%

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

   6. metadata-eval 98.3%

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

   7. metadata-eval 98.3%

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

   8. +-commutative 98.3%

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

   9. associate-/l/ 98.3%

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

   10. metadata-eval 98.3%

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

   11. associate-*r/ 98.3%

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

   12. *-rgt-identity 98.3%

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

   13. associate-*r/ 98.3%

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

   14. distribute-rgt-out 98.3%

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

   15. associate-*r/ 98.3%

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

   16. metadata-eval 98.3%

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

5. Simplified 98.3%

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

6. Taylor expanded in x around 0 98.3%

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

   1. associate-+r+ 98.3%

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

   2. associate-*r/ 98.3%

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

   3. metadata-eval 98.3%

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

   4. *-commutative 98.3%

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

   5. associate-/r* 98.3%

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

   6. *-rgt-identity 98.3%

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

   7. associate-*r/ 98.3%

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

   8. distribute-rgt-in 98.3%

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

   9. associate-*l/ 98.3%

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

   10. *-lft-identity 98.3%

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

   11. associate--l+ 98.3%

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

   12. sub-neg 98.3%

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

   13. metadata-eval 98.3%

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

8. Simplified 98.3%

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

9. Final simplification 98.3%

   \[\leadsto \frac{2 + \frac{2}{z}}{t} + \left(\frac{x}{y} + -2\right) \]
10. 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 85.8%

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

   1. +-commutative 85.8%

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

   2. remove-double-neg 85.8%

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

   3. distribute-frac-neg 85.8%

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

   4. unsub-neg 85.8%

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

   5. *-commutative 85.8%

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

   6. associate-*r* 85.8%

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

   7. distribute-rgt1-in 85.8%

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

   8. associate-*r/ 85.7%

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

   9. /-rgt-identity 85.7%

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

   10. fma-neg 85.7%

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

   11. /-rgt-identity 85.7%

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

   12. *-commutative 85.7%

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

   13. fma-def 85.7%

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

   14. *-commutative 85.7%

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

   15. distribute-frac-neg 85.7%

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

   16. remove-double-neg 85.7%

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

3. Simplified 85.7%

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

5. Taylor expanded in x around 0 56.9%

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

6. Taylor expanded in t around inf 19.1%

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

7. Final simplification 19.1%

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

Developer target: 99.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024029 
(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))))