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

Percentage Accurate: 87.2% → 99.1%

Time: 9.4s

Alternatives: 10

Speedup: 1.3×

• 23.1% 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: 87.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. sub-neg 85.8%

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

   2. distribute-rgt-in 85.8%

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

   3. *-lft-identity 85.8%

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

   4. associate-+r+ 85.8%

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

   5. cancel-sign-sub-inv 85.8%

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

   6. div-sub 75.3%

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

   7. associate-*r* 75.3%

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

   8. associate-*l/ 75.3%

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

   9. *-inverses 98.7%

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

   10. metadata-eval 98.7%

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

   11. sub-neg 98.7%

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

   12. metadata-eval 98.7%

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

   13. metadata-eval 98.7%

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

   14. +-commutative 98.7%

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

   15. metadata-eval 98.7%

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

   16. associate-/l/ 98.7%

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

3. Simplified 98.7%

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

4. Final simplification 98.7%

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

Alternative 2: 63.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -510000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-80} \lor \neg \left(z \leq 8 \cdot 10^{-70}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -6.2e+173)
     t_1
     (if (<= z -510000000.0)
       (+ -2.0 (/ 2.0 t))
       (if (or (<= z -2e-80) (not (<= z 8e-70))) t_1 (/ 2.0 (* z t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -6.2e+173) {
		tmp = t_1;
	} else if (z <= -510000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else if ((z <= -2e-80) || !(z <= 8e-70)) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-6.2d+173)) then
        tmp = t_1
    else if (z <= (-510000000.0d0)) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if ((z <= (-2d-80)) .or. (.not. (z <= 8d-70))) then
        tmp = t_1
    else
        tmp = 2.0d0 / (z * t)
    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 (z <= -6.2e+173) {
		tmp = t_1;
	} else if (z <= -510000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else if ((z <= -2e-80) || !(z <= 8e-70)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -6.2e+173:
		tmp = t_1
	elif z <= -510000000.0:
		tmp = -2.0 + (2.0 / t)
	elif (z <= -2e-80) or not (z <= 8e-70):
		tmp = t_1
	else:
		tmp = 2.0 / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -6.2e+173)
		tmp = t_1;
	elseif (z <= -510000000.0)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif ((z <= -2e-80) || !(z <= 8e-70))
		tmp = t_1;
	else
		tmp = Float64(2.0 / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -6.2e+173)
		tmp = t_1;
	elseif (z <= -510000000.0)
		tmp = -2.0 + (2.0 / t);
	elseif ((z <= -2e-80) || ~((z <= 8e-70)))
		tmp = t_1;
	else
		tmp = 2.0 / (z * t);
	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[z, -6.2e+173], t$95$1, If[LessEqual[z, -510000000.0], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2e-80], N[Not[LessEqual[z, 8e-70]], $MachinePrecision]], t$95$1, N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e173 or -5.1e8 < z < -1.99999999999999992e-80 or 7.99999999999999997e-70 < z

   1. Initial program 76.3%

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

      1. sub-neg 76.3%

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

      2. distribute-rgt-in 76.3%

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

      3. *-lft-identity 76.3%

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

      4. associate-+r+ 76.3%

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

      5. cancel-sign-sub-inv 76.3%

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

      6. div-sub 74.6%

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

      7. associate-*r* 74.6%

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

      8. associate-*l/ 74.6%

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

      9. *-inverses 99.0%

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

      10. metadata-eval 99.0%

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

      11. sub-neg 99.0%

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

      12. metadata-eval 99.0%

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

      13. metadata-eval 99.0%

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

      14. +-commutative 99.0%

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

      15. metadata-eval 99.0%

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

      16. associate-/l/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around inf 70.5%

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

   if -6.2e173 < z < -5.1e8

   1. Initial program 83.7%

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

      1. sub-neg 83.7%

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

      2. distribute-rgt-in 83.7%

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

      3. *-lft-identity 83.7%

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

      4. associate-+r+ 83.7%

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

      5. cancel-sign-sub-inv 83.7%

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

      6. div-sub 83.7%

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

      7. associate-*r* 83.7%

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

      8. associate-*l/ 83.7%

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

      9. *-inverses 99.8%

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

      10. metadata-eval 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

      14. +-commutative 99.8%

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

      15. metadata-eval 99.8%

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

      16. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. metadata-eval 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in x around 0 79.3%

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

      1. sub-neg 79.3%

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

      2. associate-*r/ 79.3%

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

      3. metadata-eval 79.3%

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

      4. metadata-eval 79.3%

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

   9. Simplified 79.3%

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

   if -1.99999999999999992e-80 < z < 7.99999999999999997e-70

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. distribute-rgt-in 97.9%

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

      3. *-lft-identity 97.9%

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

      4. associate-+r+ 97.9%

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

      5. cancel-sign-sub-inv 97.9%

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

      6. div-sub 73.4%

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

      7. associate-*r* 73.4%

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

      8. associate-*l/ 73.4%

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

      9. *-inverses 97.9%

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

      10. metadata-eval 97.9%

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

      11. sub-neg 97.9%

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

      12. metadata-eval 97.9%

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

      13. metadata-eval 97.9%

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

      14. +-commutative 97.9%

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

      15. metadata-eval 97.9%

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

      16. associate-/l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around 0 66.7%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+173}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq -510000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-80} \lor \neg \left(z \leq 8 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]

Alternative 3: 65.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.7 \cdot 10^{-8} \lor \neg \left(\frac{x}{y} \leq 5.9 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5.7e-8) (not (<= (/ x y) 5.9e-5)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.7e-8) || !((x / y) <= 5.9e-5)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5.7d-8)) .or. (.not. ((x / y) <= 5.9d-5))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.7e-8) || !((x / y) <= 5.9e-5)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5.7e-8) or not ((x / y) <= 5.9e-5):
		tmp = (x / y) - 2.0
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5.7e-8) || !(Float64(x / y) <= 5.9e-5))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5.7e-8) || ~(((x / y) <= 5.9e-5)))
		tmp = (x / y) - 2.0;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5.7e-8], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5.9e-5]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.70000000000000009e-8 or 5.8999999999999998e-5 < (/.f64 x y)

   1. Initial program 83.2%

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

      1. sub-neg 83.2%

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

      2. distribute-rgt-in 83.2%

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

      3. *-lft-identity 83.2%

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

      4. associate-+r+ 83.2%

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

      5. cancel-sign-sub-inv 83.2%

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

      6. div-sub 72.5%

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

      7. associate-*r* 72.5%

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

      8. associate-*l/ 72.5%

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

      9. *-inverses 97.9%

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

      10. metadata-eval 97.9%

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

      11. sub-neg 97.9%

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

      12. metadata-eval 97.9%

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

      13. metadata-eval 97.9%

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

      14. +-commutative 97.9%

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

      15. metadata-eval 97.9%

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

      16. associate-/l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in t around inf 65.2%

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

   if -5.70000000000000009e-8 < (/.f64 x y) < 5.8999999999999998e-5

   1. Initial program 89.5%

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

      1. sub-neg 89.5%

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

      2. distribute-rgt-in 89.5%

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

      3. *-lft-identity 89.5%

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

      4. associate-+r+ 89.5%

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

      5. cancel-sign-sub-inv 89.5%

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

      6. div-sub 79.1%

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

      7. associate-*r* 79.1%

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

      8. associate-*l/ 79.1%

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

      9. *-inverses 99.9%

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

      10. metadata-eval 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. metadata-eval 99.9%

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

      16. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 66.2%

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

      1. associate--l+ 66.2%

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

      2. associate-*r/ 66.2%

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

      3. metadata-eval 66.2%

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

   6. Simplified 66.2%

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

   7. Taylor expanded in x around 0 65.7%

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

      1. sub-neg 65.7%

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

      2. associate-*r/ 65.7%

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

      3. metadata-eval 65.7%

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

      4. metadata-eval 65.7%

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

   9. Simplified 65.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.7 \cdot 10^{-8} \lor \neg \left(\frac{x}{y} \leq 5.9 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 4: 80.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-5} \lor \neg \left(t \leq 3.1 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.2e-5) (not (<= t 3.1e-12)))
   (+ (/ x y) (- (/ 2.0 t) 2.0))
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-5) || !(t <= 3.1e-12)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-6.2d-5)) .or. (.not. (t <= 3.1d-12))) then
        tmp = (x / y) + ((2.0d0 / t) - 2.0d0)
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-5) || !(t <= 3.1e-12)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.2e-5) or not (t <= 3.1e-12):
		tmp = (x / y) + ((2.0 / t) - 2.0)
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.2e-5) || !(t <= 3.1e-12))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) - 2.0));
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.2e-5) || ~((t <= 3.1e-12)))
		tmp = (x / y) + ((2.0 / t) - 2.0);
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.2e-5], N[Not[LessEqual[t, 3.1e-12]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.20000000000000027e-5 or 3.1000000000000001e-12 < t

   1. Initial program 75.5%

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

      1. sub-neg 75.5%

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

      2. distribute-rgt-in 75.5%

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

      3. *-lft-identity 75.5%

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

      4. associate-+r+ 75.5%

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

      5. cancel-sign-sub-inv 75.5%

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

      6. div-sub 75.5%

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

      7. associate-*r* 75.5%

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

      8. associate-*l/ 75.5%

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

      9. *-inverses 99.9%

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

      10. metadata-eval 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. metadata-eval 99.9%

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

      16. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 87.7%

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

      1. associate--l+ 87.7%

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

      2. associate-*r/ 87.7%

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

      3. metadata-eval 87.7%

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

   6. Simplified 87.7%

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

   if -6.20000000000000027e-5 < t < 3.1000000000000001e-12

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. distribute-rgt-in 97.3%

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

      3. *-lft-identity 97.3%

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

      4. associate-+r+ 97.3%

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

      5. cancel-sign-sub-inv 97.3%

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

      6. div-sub 75.0%

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

      7. associate-*r* 75.0%

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

      8. associate-*l/ 75.0%

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

      9. *-inverses 97.3%

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

      10. metadata-eval 97.3%

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

      11. sub-neg 97.3%

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

      12. metadata-eval 97.3%

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

      13. metadata-eval 97.3%

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

      14. +-commutative 97.3%

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

      15. metadata-eval 97.3%

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

      16. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 81.1%

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

      1. associate-*r/ 81.1%

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

      2. metadata-eval 81.1%

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

   6. Simplified 81.1%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-5} \lor \neg \left(t \leq 3.1 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 5: 91.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-17} \lor \neg \left(z \leq 6 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.4e-17) (not (<= z 6e-67)))
   (+ (/ x y) (- (/ 2.0 t) 2.0))
   (+ (/ x y) (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e-17) || !(z <= 6e-67)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (x / y) + (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 ((z <= (-3.4d-17)) .or. (.not. (z <= 6d-67))) then
        tmp = (x / y) + ((2.0d0 / t) - 2.0d0)
    else
        tmp = (x / y) + (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 ((z <= -3.4e-17) || !(z <= 6e-67)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.4e-17) or not (z <= 6e-67):
		tmp = (x / y) + ((2.0 / t) - 2.0)
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.4e-17) || !(z <= 6e-67))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) - 2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.4e-17) || ~((z <= 6e-67)))
		tmp = (x / y) + ((2.0 / t) - 2.0);
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.4e-17], N[Not[LessEqual[z, 6e-67]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3999999999999998e-17 or 6.00000000000000065e-67 < z

   1. Initial program 75.5%

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

      1. sub-neg 75.5%

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

      2. distribute-rgt-in 75.6%

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

      3. *-lft-identity 75.6%

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

      4. associate-+r+ 75.6%

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

      5. cancel-sign-sub-inv 75.6%

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

      6. div-sub 74.8%

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

      7. associate-*r* 74.8%

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

      8. associate-*l/ 74.8%

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

      9. *-inverses 99.1%

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

      10. metadata-eval 99.1%

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

      11. sub-neg 99.1%

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

      12. metadata-eval 99.1%

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

      13. metadata-eval 99.1%

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

      14. +-commutative 99.1%

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

      15. metadata-eval 99.1%

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

      16. associate-/l/ 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around inf 97.2%

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

      1. associate--l+ 97.2%

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

      2. associate-*r/ 97.2%

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

      3. metadata-eval 97.2%

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

   6. Simplified 97.2%

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

   if -3.3999999999999998e-17 < z < 6.00000000000000065e-67

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-*r* 98.2%

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

      4. distribute-rgt1-in 98.2%

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

      5. *-commutative 98.2%

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

      6. times-frac 98.1%

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

      7. fma-def 98.9%

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

      8. *-commutative 98.9%

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

      9. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 94.8%

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

   5. Taylor expanded in z around 0 94.0%

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

      1. associate-*r/ 94.0%

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

      2. metadata-eval 94.0%

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

      3. +-commutative 94.0%

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

   7. Simplified 94.0%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-17} \lor \neg \left(z \leq 6 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 6: 64.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.3:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -9.4e+36)
   (/ x y)
   (if (<= (/ x y) 2.3) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -9.4e+36) {
		tmp = x / y;
	} else if ((x / y) <= 2.3) {
		tmp = -2.0 + (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) <= (-9.4d+36)) then
        tmp = x / y
    else if ((x / y) <= 2.3d0) then
        tmp = (-2.0d0) + (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) <= -9.4e+36) {
		tmp = x / y;
	} else if ((x / y) <= 2.3) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -9.4e+36:
		tmp = x / y
	elif (x / y) <= 2.3:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -9.4e+36)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.3)
		tmp = Float64(-2.0 + 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) <= -9.4e+36)
		tmp = x / y;
	elseif ((x / y) <= 2.3)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -9.4e+36], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.3], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.39999999999999978e36 or 2.2999999999999998 < (/.f64 x y)

   1. Initial program 83.5%

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

      1. sub-neg 83.5%

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

      2. distribute-rgt-in 83.5%

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

      3. *-lft-identity 83.5%

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

      4. associate-+r+ 83.5%

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

      5. cancel-sign-sub-inv 83.5%

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

      6. div-sub 72.7%

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

      7. associate-*r* 72.7%

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

      8. associate-*l/ 72.7%

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

      9. *-inverses 97.7%

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

      10. metadata-eval 97.7%

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

      11. sub-neg 97.7%

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

      12. metadata-eval 97.7%

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

      13. metadata-eval 97.7%

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

      14. +-commutative 97.7%

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

      15. metadata-eval 97.7%

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

      16. associate-/l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around inf 67.1%

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

   if -9.39999999999999978e36 < (/.f64 x y) < 2.2999999999999998

   1. Initial program 88.6%

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

      1. sub-neg 88.6%

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

      2. distribute-rgt-in 88.6%

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

      3. *-lft-identity 88.6%

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

      4. associate-+r+ 88.6%

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

      5. cancel-sign-sub-inv 88.6%

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

      6. div-sub 78.3%

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

      7. associate-*r* 78.3%

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

      8. associate-*l/ 78.3%

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

      9. *-inverses 99.8%

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

      10. metadata-eval 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

      14. +-commutative 99.8%

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

      15. metadata-eval 99.8%

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

      16. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 65.0%

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

      1. associate--l+ 65.0%

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

      2. associate-*r/ 65.0%

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

      3. metadata-eval 65.0%

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

   6. Simplified 65.0%

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

   7. Taylor expanded in x around 0 62.6%

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

      1. sub-neg 62.6%

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

      2. associate-*r/ 62.6%

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

      3. metadata-eval 62.6%

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

      4. metadata-eval 62.6%

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

   9. Simplified 62.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.3:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 7: 80.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.21 \lor \neg \left(t \leq 2.3 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.21) (not (<= t 2.3e-11)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.21) || !(t <= 2.3e-11)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-0.21d0)) .or. (.not. (t <= 2.3d-11))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.21) || !(t <= 2.3e-11)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.21) or not (t <= 2.3e-11):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.21) || !(t <= 2.3e-11))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -0.21) || ~((t <= 2.3e-11)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.21], N[Not[LessEqual[t, 2.3e-11]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.209999999999999992 or 2.30000000000000014e-11 < t

   1. Initial program 75.5%

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

      1. sub-neg 75.5%

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

      2. distribute-rgt-in 75.5%

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

      3. *-lft-identity 75.5%

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

      4. associate-+r+ 75.5%

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

      5. cancel-sign-sub-inv 75.5%

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

      6. div-sub 75.5%

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

      7. associate-*r* 75.5%

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

      8. associate-*l/ 75.5%

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

      9. *-inverses 99.9%

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

      10. metadata-eval 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. metadata-eval 99.9%

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

      16. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 85.1%

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

   if -0.209999999999999992 < t < 2.30000000000000014e-11

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. distribute-rgt-in 97.3%

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

      3. *-lft-identity 97.3%

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

      4. associate-+r+ 97.3%

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

      5. cancel-sign-sub-inv 97.3%

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

      6. div-sub 75.0%

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

      7. associate-*r* 75.0%

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

      8. associate-*l/ 75.0%

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

      9. *-inverses 97.3%

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

      10. metadata-eval 97.3%

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

      11. sub-neg 97.3%

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

      12. metadata-eval 97.3%

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

      13. metadata-eval 97.3%

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

      14. +-commutative 97.3%

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

      15. metadata-eval 97.3%

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

      16. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 81.1%

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

      1. associate-*r/ 81.1%

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

      2. metadata-eval 81.1%

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

   6. Simplified 81.1%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.21 \lor \neg \left(t \leq 2.3 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 8: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.8 \cdot 10^{-5}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0) (/ x y) (if (<= (/ x y) 2.8e-5) -2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 2.8e-5) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2.0d0)) then
        tmp = x / y
    else if ((x / y) <= 2.8d-5) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 2.8e-5) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.0:
		tmp = x / y
	elif (x / y) <= 2.8e-5:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.8e-5)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2.0)
		tmp = x / y;
	elseif ((x / y) <= 2.8e-5)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.8e-5], -2.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2 or 2.79999999999999996e-5 < (/.f64 x y)

   1. Initial program 83.9%

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

      1. sub-neg 83.9%

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

      2. distribute-rgt-in 83.9%

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

      3. *-lft-identity 83.9%

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

      4. associate-+r+ 83.9%

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

      5. cancel-sign-sub-inv 83.9%

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

      6. div-sub 73.2%

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

      7. associate-*r* 73.2%

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

      8. associate-*l/ 73.2%

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

      9. *-inverses 97.9%

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

      10. metadata-eval 97.9%

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

      11. sub-neg 97.9%

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

      12. metadata-eval 97.9%

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

      13. metadata-eval 97.9%

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

      14. +-commutative 97.9%

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

      15. metadata-eval 97.9%

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

      16. associate-/l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 63.3%

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

   if -2 < (/.f64 x y) < 2.79999999999999996e-5

   1. Initial program 88.5%

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

      1. sub-neg 88.5%

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

      2. distribute-rgt-in 88.5%

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

      3. *-lft-identity 88.5%

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

      4. associate-+r+ 88.5%

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

      5. cancel-sign-sub-inv 88.5%

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

      6. div-sub 78.2%

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

      7. associate-*r* 78.2%

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

      8. associate-*l/ 78.2%

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

      9. *-inverses 99.9%

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

      10. metadata-eval 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. metadata-eval 99.9%

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

      16. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.0%

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

      1. associate-*r/ 99.0%

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

      2. metadata-eval 99.0%

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

      3. +-commutative 99.0%

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

      4. associate--l+ 99.0%

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

      5. associate-*r/ 99.0%

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

      6. metadata-eval 99.0%

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

   6. Simplified 99.0%

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

   7. Taylor expanded in t around inf 40.0%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.8 \cdot 10^{-5}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 9: 36.8% accurate, 2.4× speedup

Math

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

FPCore

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

Derivation

1. Split input into 2 regimes

2. if t < -1 or 1 < t

   1. Initial program 74.9%

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

      1. sub-neg 74.9%

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

      2. distribute-rgt-in 74.9%

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

      3. *-lft-identity 74.9%

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

      4. associate-+r+ 74.9%

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

      5. cancel-sign-sub-inv 74.9%

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

      6. div-sub 74.9%

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

      7. associate-*r* 74.9%

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

      8. associate-*l/ 74.9%

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

      9. *-inverses 99.9%

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

      10. metadata-eval 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. metadata-eval 99.9%

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

      16. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 46.3%

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

      1. associate-*r/ 46.3%

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

      2. metadata-eval 46.3%

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

      3. +-commutative 46.3%

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

      4. associate--l+ 46.3%

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

      5. associate-*r/ 46.3%

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

      6. metadata-eval 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in t around inf 33.0%

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

   if -1 < t < 1

   1. Initial program 97.4%

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

      1. sub-neg 97.4%

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

      2. distribute-rgt-in 97.4%

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

      3. *-lft-identity 97.4%

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

      4. associate-+r+ 97.4%

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

      5. cancel-sign-sub-inv 97.4%

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

      6. div-sub 75.6%

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

      7. associate-*r* 75.6%

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

      8. associate-*l/ 75.6%

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

      9. *-inverses 97.4%

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

      10. metadata-eval 97.4%

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

      11. sub-neg 97.4%

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

      12. metadata-eval 97.4%

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

      13. metadata-eval 97.4%

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

      14. +-commutative 97.4%

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

      15. metadata-eval 97.4%

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

      16. associate-/l/ 97.4%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 52.7%

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

      1. associate--l+ 52.7%

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

      2. associate-*r/ 52.7%

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

      3. metadata-eval 52.7%

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

   6. Simplified 52.7%

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

   7. Taylor expanded in t around 0 32.9%

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

4. Final simplification 32.9%

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

Alternative 10: 19.7% 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. sub-neg 85.8%

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

   2. distribute-rgt-in 85.8%

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

   3. *-lft-identity 85.8%

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

   4. associate-+r+ 85.8%

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

   5. cancel-sign-sub-inv 85.8%

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

   6. div-sub 75.3%

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

   7. associate-*r* 75.3%

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

   8. associate-*l/ 75.3%

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

   9. *-inverses 98.7%

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

   10. metadata-eval 98.7%

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

   11. sub-neg 98.7%

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

   12. metadata-eval 98.7%

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

   13. metadata-eval 98.7%

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

   14. +-commutative 98.7%

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

   15. metadata-eval 98.7%

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

   16. associate-/l/ 98.7%

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

3. Simplified 98.7%

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

4. Taylor expanded in x around 0 63.0%

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

   1. associate-*r/ 63.0%

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

   2. metadata-eval 63.0%

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

   3. +-commutative 63.0%

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

   4. associate--l+ 63.0%

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

   5. associate-*r/ 63.0%

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

   6. metadata-eval 63.0%

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

6. Simplified 63.0%

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

7. Taylor expanded in t around inf 18.1%

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

8. Final simplification 18.1%

   \[\leadsto -2 \]

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023185 
(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))))