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

Percentage Accurate: 86.7% → 99.5%

Time: 9.4s

Alternatives: 10

Speedup: 1.3×

• 24.0% 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: 86.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.0%

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

   1. sub-neg 85.0%

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

   2. distribute-rgt-in 85.0%

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

   3. *-lft-identity 85.0%

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

   4. associate-+r+ 85.0%

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

   5. cancel-sign-sub-inv 85.0%

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

   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 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/ 99.1%

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

3. Simplified 99.1%

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

   1. div-inv 99.0%

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

   2. fma-def 99.4%

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

5. Applied egg-rr 99.4%

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

6. Final simplification 99.4%

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

Alternative 2: 89.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+33} \lor \neg \left(\frac{x}{y} \leq 10000000\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} \cdot \left(1 + \left(\frac{1}{z} - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+33) (not (<= (/ x y) 10000000.0)))
   (+ (/ x y) (- (/ 2.0 t) 2.0))
   (* (/ 2.0 t) (+ 1.0 (- (/ 1.0 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+33) || !((x / y) <= 10000000.0)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (2.0 / t) * (1.0 + ((1.0 / 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) <= (-4d+33)) .or. (.not. ((x / y) <= 10000000.0d0))) then
        tmp = (x / y) + ((2.0d0 / t) - 2.0d0)
    else
        tmp = (2.0d0 / t) * (1.0d0 + ((1.0d0 / 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) <= -4e+33) || !((x / y) <= 10000000.0)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (2.0 / t) * (1.0 + ((1.0 / z) - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e+33) or not ((x / y) <= 10000000.0):
		tmp = (x / y) + ((2.0 / t) - 2.0)
	else:
		tmp = (2.0 / t) * (1.0 + ((1.0 / z) - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e+33) || !(Float64(x / y) <= 10000000.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) - 2.0));
	else
		tmp = Float64(Float64(2.0 / t) * Float64(1.0 + Float64(Float64(1.0 / z) - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4e+33) || ~(((x / y) <= 10000000.0)))
		tmp = (x / y) + ((2.0 / t) - 2.0);
	else
		tmp = (2.0 / t) * (1.0 + ((1.0 / z) - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4e+33], N[Not[LessEqual[N[(x / y), $MachinePrecision], 10000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] * N[(1.0 + N[(N[(1.0 / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.9999999999999998e33 or 1e7 < (/.f64 x y)

   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. sub-neg 85.5%

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

      2. distribute-rgt-in 85.5%

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

      3. *-lft-identity 85.5%

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

      4. associate-+r+ 85.5%

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

      5. cancel-sign-sub-inv 85.5%

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

      6. div-sub 77.5%

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

      7. associate-*r* 77.5%

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

      8. associate-*l/ 77.5%

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

      9. *-inverses 98.3%

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

      10. metadata-eval 98.3%

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

      11. sub-neg 98.3%

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

      12. metadata-eval 98.3%

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

      13. metadata-eval 98.3%

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

      14. +-commutative 98.3%

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

      15. metadata-eval 98.3%

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

      16. associate-/l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around inf 83.2%

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

      1. associate--l+ 83.2%

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

      2. associate-*r/ 83.2%

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

      3. metadata-eval 83.2%

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

   6. Simplified 83.2%

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

   if -3.9999999999999998e33 < (/.f64 x y) < 1e7

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-*r* 84.4%

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

      4. distribute-rgt1-in 84.4%

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

      5. *-commutative 84.4%

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

      6. times-frac 84.8%

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

      7. fma-def 84.8%

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

      8. *-commutative 84.8%

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

      9. fma-def 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in z around 0 99.6%

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

   5. Taylor expanded in x around 0 98.8%

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

      1. associate-+r- 98.8%

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

      2. associate-*r/ 98.8%

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

      3. associate-*l/ 98.6%

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

   7. Simplified 98.6%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+33} \lor \neg \left(\frac{x}{y} \leq 10000000\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} \cdot \left(1 + \left(\frac{1}{z} - t\right)\right)\\ \end{array} \]

Alternative 3: 89.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t} - 2\\ \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+33} \lor \neg \left(\frac{x}{y} \leq 10000000\right):\\ \;\;\;\;\frac{x}{y} + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ 2.0 t) 2.0)))
   (if (or (<= (/ x y) -4e+33) (not (<= (/ x y) 10000000.0)))
     (+ (/ x y) t_1)
     (+ t_1 (/ 2.0 (* z t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) - 2.0;
	double tmp;
	if (((x / y) <= -4e+33) || !((x / y) <= 10000000.0)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = t_1 + (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 = (2.0d0 / t) - 2.0d0
    if (((x / y) <= (-4d+33)) .or. (.not. ((x / y) <= 10000000.0d0))) then
        tmp = (x / y) + t_1
    else
        tmp = t_1 + (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 = (2.0 / t) - 2.0;
	double tmp;
	if (((x / y) <= -4e+33) || !((x / y) <= 10000000.0)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = t_1 + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) - 2.0
	tmp = 0
	if ((x / y) <= -4e+33) or not ((x / y) <= 10000000.0):
		tmp = (x / y) + t_1
	else:
		tmp = t_1 + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) - 2.0)
	tmp = 0.0
	if ((Float64(x / y) <= -4e+33) || !(Float64(x / y) <= 10000000.0))
		tmp = Float64(Float64(x / y) + t_1);
	else
		tmp = Float64(t_1 + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) - 2.0;
	tmp = 0.0;
	if (((x / y) <= -4e+33) || ~(((x / y) <= 10000000.0)))
		tmp = (x / y) + t_1;
	else
		tmp = t_1 + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]}, If[Or[LessEqual[N[(x / y), $MachinePrecision], -4e+33], N[Not[LessEqual[N[(x / y), $MachinePrecision], 10000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.9999999999999998e33 or 1e7 < (/.f64 x y)

   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. sub-neg 85.5%

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

      2. distribute-rgt-in 85.5%

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

      3. *-lft-identity 85.5%

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

      4. associate-+r+ 85.5%

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

      5. cancel-sign-sub-inv 85.5%

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

      6. div-sub 77.5%

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

      7. associate-*r* 77.5%

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

      8. associate-*l/ 77.5%

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

      9. *-inverses 98.3%

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

      10. metadata-eval 98.3%

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

      11. sub-neg 98.3%

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

      12. metadata-eval 98.3%

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

      13. metadata-eval 98.3%

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

      14. +-commutative 98.3%

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

      15. metadata-eval 98.3%

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

      16. associate-/l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around inf 83.2%

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

      1. associate--l+ 83.2%

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

      2. associate-*r/ 83.2%

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

      3. metadata-eval 83.2%

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

   6. Simplified 83.2%

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

   if -3.9999999999999998e33 < (/.f64 x y) < 1e7

   1. Initial program 84.4%

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

      1. sub-neg 84.4%

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

      2. distribute-rgt-in 84.5%

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

      3. *-lft-identity 84.5%

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

      4. associate-+r+ 84.5%

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

      5. cancel-sign-sub-inv 84.5%

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

      6. div-sub 73.8%

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

      7. associate-*r* 73.8%

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

      8. associate-*l/ 73.8%

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

      9. *-inverses 99.7%

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

      10. metadata-eval 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

      14. +-commutative 99.7%

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

      15. metadata-eval 99.7%

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

      16. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 98.9%

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

      1. associate-*r/ 98.9%

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

      2. metadata-eval 98.9%

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

      3. +-commutative 98.9%

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

      4. associate--l+ 98.9%

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

      5. associate-*r/ 98.9%

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

      6. metadata-eval 98.9%

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

   6. Simplified 98.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+33} \lor \neg \left(\frac{x}{y} \leq 10000000\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{t} - 2\right) + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 4: 81.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-36} \lor \neg \left(t \leq 1.5 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.3e-36) (not (<= t 1.5e-67)))
   (+ (/ 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 <= -1.3e-36) || !(t <= 1.5e-67)) {
		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 <= (-1.3d-36)) .or. (.not. (t <= 1.5d-67))) 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 <= -1.3e-36) || !(t <= 1.5e-67)) {
		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 <= -1.3e-36) or not (t <= 1.5e-67):
		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 <= -1.3e-36) || !(t <= 1.5e-67))
		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 <= -1.3e-36) || ~((t <= 1.5e-67)))
		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, -1.3e-36], N[Not[LessEqual[t, 1.5e-67]], $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 < -1.3e-36 or 1.50000000000000016e-67 < t

   1. Initial program 77.2%

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

      1. sub-neg 77.2%

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

      2. distribute-rgt-in 77.2%

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

      3. *-lft-identity 77.2%

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

      4. associate-+r+ 77.2%

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

      5. cancel-sign-sub-inv 77.2%

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

      6. div-sub 76.6%

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

      7. associate-*r* 76.6%

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

      8. associate-*l/ 76.6%

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

      9. *-inverses 99.3%

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

      10. metadata-eval 99.3%

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

      11. sub-neg 99.3%

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

      12. metadata-eval 99.3%

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

      13. metadata-eval 99.3%

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

      14. +-commutative 99.3%

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

      15. metadata-eval 99.3%

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

      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 84.3%

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

      1. associate--l+ 84.3%

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

      2. associate-*r/ 84.3%

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

      3. metadata-eval 84.3%

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

   6. Simplified 84.3%

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

   if -1.3e-36 < t < 1.50000000000000016e-67

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. distribute-rgt-in 98.7%

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

      3. *-lft-identity 98.7%

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

      4. associate-+r+ 98.7%

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

      5. cancel-sign-sub-inv 98.7%

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

      6. div-sub 73.9%

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

      7. associate-*r* 73.9%

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

      8. associate-*l/ 73.9%

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

      9. *-inverses 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/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in t around 0 86.3%

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

      1. associate-*r/ 86.3%

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

      2. metadata-eval 86.3%

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

   6. Simplified 86.3%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-36} \lor \neg \left(t \leq 1.5 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 5: 65.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 8200000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6.8e+29)
   (/ x y)
   (if (<= (/ x y) 8200000000.0) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6.8e+29) {
		tmp = x / y;
	} else if ((x / y) <= 8200000000.0) {
		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) <= (-6.8d+29)) then
        tmp = x / y
    else if ((x / y) <= 8200000000.0d0) 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) <= -6.8e+29) {
		tmp = x / y;
	} else if ((x / y) <= 8200000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -6.8e+29:
		tmp = x / y
	elif (x / y) <= 8200000000.0:
		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) <= -6.8e+29)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 8200000000.0)
		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) <= -6.8e+29)
		tmp = x / y;
	elseif ((x / y) <= 8200000000.0)
		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], -6.8e+29], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 8200000000.0], 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) < -6.79999999999999963e29 or 8.2e9 < (/.f64 x y)

   1. Initial program 85.4%

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

      1. sub-neg 85.4%

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

      2. distribute-rgt-in 85.4%

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

      3. *-lft-identity 85.4%

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

      4. associate-+r+ 85.4%

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

      5. cancel-sign-sub-inv 85.4%

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

      6. div-sub 77.4%

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

      7. associate-*r* 77.4%

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

      8. associate-*l/ 77.4%

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

      9. *-inverses 98.3%

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

      10. metadata-eval 98.3%

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

      11. sub-neg 98.3%

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

      12. metadata-eval 98.3%

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

      13. metadata-eval 98.3%

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

      14. +-commutative 98.3%

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

      15. metadata-eval 98.3%

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

      16. associate-/l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in x around inf 73.3%

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

   if -6.79999999999999963e29 < (/.f64 x y) < 8.2e9

   1. Initial program 84.6%

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

      1. sub-neg 84.6%

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

      2. distribute-rgt-in 84.6%

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

      3. *-lft-identity 84.6%

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

      4. associate-+r+ 84.6%

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

      5. cancel-sign-sub-inv 84.6%

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

      6. div-sub 74.0%

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

      7. associate-*r* 74.0%

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

      8. associate-*l/ 74.0%

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

      9. *-inverses 99.7%

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

      10. metadata-eval 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

      14. +-commutative 99.7%

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

      15. metadata-eval 99.7%

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

      16. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 98.9%

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

      1. associate-*r/ 98.9%

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

      2. metadata-eval 98.9%

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

      3. +-commutative 98.9%

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

      4. associate--l+ 98.9%

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

      5. associate-*r/ 98.9%

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

      6. metadata-eval 98.9%

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

   6. Simplified 98.9%

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

   7. Taylor expanded in z around inf 65.0%

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

      1. sub-neg 65.0%

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

      2. metadata-eval 65.0%

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

      3. associate-*r/ 65.0%

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

      4. metadata-eval 65.0%

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

      5. +-commutative 65.0%

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

   9. Simplified 65.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 8200000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 6: 99.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.0%

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

   1. sub-neg 85.0%

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

   2. distribute-rgt-in 85.0%

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

   3. *-lft-identity 85.0%

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

   4. associate-+r+ 85.0%

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

   5. cancel-sign-sub-inv 85.0%

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

   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 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/ 99.1%

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

3. Simplified 99.1%

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

4. Final simplification 99.1%

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

Alternative 7: 80.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-9} \lor \neg \left(t \leq 1.65 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.8e-9) (not (<= t 1.65e-55)))
   (- (/ 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 <= -3.8e-9) || !(t <= 1.65e-55)) {
		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 <= (-3.8d-9)) .or. (.not. (t <= 1.65d-55))) 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 <= -3.8e-9) || !(t <= 1.65e-55)) {
		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 <= -3.8e-9) or not (t <= 1.65e-55):
		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 <= -3.8e-9) || !(t <= 1.65e-55))
		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 <= -3.8e-9) || ~((t <= 1.65e-55)))
		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, -3.8e-9], N[Not[LessEqual[t, 1.65e-55]], $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 < -3.80000000000000011e-9 or 1.65e-55 < t

   1. Initial program 75.6%

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

      1. sub-neg 75.6%

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

      2. distribute-rgt-in 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 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 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 t around inf 81.6%

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

   if -3.80000000000000011e-9 < t < 1.65e-55

   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 75.7%

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

      7. associate-*r* 75.7%

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

      8. associate-*l/ 75.7%

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

      9. *-inverses 97.9%

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

      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/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around 0 83.4%

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

      1. associate-*r/ 83.4%

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

      2. metadata-eval 83.4%

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

   6. Simplified 83.4%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-9} \lor \neg \left(t \leq 1.65 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 8: 52.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6.2e+29) (/ x y) (if (<= (/ x y) 2.0) -2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6.2e+29) {
		tmp = x / y;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-6.2d+29)) then
        tmp = x / y
    else if ((x / y) <= 2.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6.2e+29) {
		tmp = x / y;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -6.2e+29:
		tmp = x / y
	elif (x / y) <= 2.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -6.2e+29)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -6.2e+29)
		tmp = x / y;
	elseif ((x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -6.2e+29], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.0], -2.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.1999999999999998e29 or 2 < (/.f64 x y)

   1. Initial program 85.9%

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

      1. sub-neg 85.9%

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

      2. distribute-rgt-in 85.9%

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

      3. *-lft-identity 85.9%

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

      4. associate-+r+ 85.9%

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

      5. cancel-sign-sub-inv 85.9%

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

      6. div-sub 78.1%

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

      7. associate-*r* 78.1%

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

      8. associate-*l/ 78.1%

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

      9. *-inverses 98.4%

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

      10. metadata-eval 98.4%

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

      11. sub-neg 98.4%

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

      12. metadata-eval 98.4%

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

      13. metadata-eval 98.4%

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

      14. +-commutative 98.4%

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

      15. metadata-eval 98.4%

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

      16. associate-/l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around inf 71.1%

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

   if -6.1999999999999998e29 < (/.f64 x y) < 2

   1. Initial program 84.1%

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

      1. sub-neg 84.1%

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

      2. distribute-rgt-in 84.1%

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

      3. *-lft-identity 84.1%

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

      4. associate-+r+ 84.1%

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

      5. cancel-sign-sub-inv 84.1%

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

      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 99.7%

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

      10. metadata-eval 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

      14. +-commutative 99.7%

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

      15. metadata-eval 99.7%

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

      16. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 98.8%

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

      1. associate-*r/ 98.8%

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

      2. metadata-eval 98.8%

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

      3. +-commutative 98.8%

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

      4. associate--l+ 98.8%

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

      5. associate-*r/ 98.8%

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

      6. metadata-eval 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in t around inf 39.5%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 9: 36.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -290000:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 5400:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -290000.0) -2.0 (if (<= t 5400.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -290000.0) {
		tmp = -2.0;
	} else if (t <= 5400.0) {
		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 <= (-290000.0d0)) then
        tmp = -2.0d0
    else if (t <= 5400.0d0) 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 <= -290000.0) {
		tmp = -2.0;
	} else if (t <= 5400.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -290000.0:
		tmp = -2.0
	elif t <= 5400.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -290000.0)
		tmp = -2.0;
	elseif (t <= 5400.0)
		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 <= -290000.0)
		tmp = -2.0;
	elseif (t <= 5400.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -290000.0], -2.0, If[LessEqual[t, 5400.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9e5 or 5400 < t

   1. Initial program 71.6%

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

      1. sub-neg 71.6%

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

      2. distribute-rgt-in 71.6%

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

      3. *-lft-identity 71.6%

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

      4. associate-+r+ 71.6%

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

      5. cancel-sign-sub-inv 71.6%

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

      6. div-sub 71.6%

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

      7. associate-*r* 71.6%

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

      8. associate-*l/ 71.6%

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

      9. *-inverses 99.9%

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

      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 54.8%

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

      1. associate-*r/ 54.8%

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

      2. metadata-eval 54.8%

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

      3. +-commutative 54.8%

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

      4. associate--l+ 54.8%

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

      5. associate-*r/ 54.8%

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

      6. metadata-eval 54.8%

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

   6. Simplified 54.8%

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

   7. Taylor expanded in t around inf 39.8%

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

   if -2.9e5 < t < 5400

   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. sub-neg 98.2%

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

      2. distribute-rgt-in 98.2%

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

      3. *-lft-identity 98.2%

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

      4. associate-+r+ 98.2%

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

      5. cancel-sign-sub-inv 98.2%

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

      6. div-sub 79.6%

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

      7. associate-*r* 79.6%

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

      8. associate-*l/ 79.6%

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

      9. *-inverses 98.2%

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

      10. metadata-eval 98.2%

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

      11. sub-neg 98.2%

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

      12. metadata-eval 98.2%

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

      13. metadata-eval 98.2%

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

      14. +-commutative 98.2%

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

      15. metadata-eval 98.2%

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

      16. associate-/l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. metadata-eval 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in z around inf 38.3%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -290000:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 5400:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 10: 19.8% 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 85.0%

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

   1. sub-neg 85.0%

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

   2. distribute-rgt-in 85.0%

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

   3. *-lft-identity 85.0%

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

   4. associate-+r+ 85.0%

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

   5. cancel-sign-sub-inv 85.0%

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

   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 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/ 99.1%

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

3. Simplified 99.1%

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

4. Taylor expanded in x around 0 65.8%

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

   1. associate-*r/ 65.8%

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

   2. metadata-eval 65.8%

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

   3. +-commutative 65.8%

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

   4. associate--l+ 65.8%

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

   5. associate-*r/ 65.8%

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

   6. metadata-eval 65.8%

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

6. Simplified 65.8%

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

7. Taylor expanded in t around inf 21.0%

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

8. Final simplification 21.0%

   \[\leadsto -2 \]

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 2023238 
(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))))