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

Percentage Accurate: 86.4% → 99.5%

Time: 9.8s

Alternatives: 12

Speedup: 1.3×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.4% 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 88.1%

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

   1. sub-neg 88.1%

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

   2. distribute-rgt-in 88.1%

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

   3. *-lft-identity 88.1%

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

   4. associate-+r+ 88.1%

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

   5. cancel-sign-sub-inv 88.1%

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

   6. div-sub 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 99.1%

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

   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: 49.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -4.2 \cdot 10^{-177}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 3.6 \cdot 10^{-289}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.5 \cdot 10^{-170}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 6.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 4.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0)
   (/ x y)
   (if (<= (/ x y) -4.2e-177)
     -2.0
     (if (<= (/ x y) 3.6e-289)
       (/ 2.0 t)
       (if (<= (/ x y) 2.5e-170)
         -2.0
         (if (<= (/ x y) 6.5e-94)
           (/ 2.0 t)
           (if (<= (/ x y) 2.1e-26)
             -2.0
             (if (<= (/ x y) 4.5e+36) (/ 2.0 t) (/ 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) <= -4.2e-177) {
		tmp = -2.0;
	} else if ((x / y) <= 3.6e-289) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.5e-170) {
		tmp = -2.0;
	} else if ((x / y) <= 6.5e-94) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.1e-26) {
		tmp = -2.0;
	} else if ((x / y) <= 4.5e+36) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2.0d0)) then
        tmp = x / y
    else if ((x / y) <= (-4.2d-177)) then
        tmp = -2.0d0
    else if ((x / y) <= 3.6d-289) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2.5d-170) then
        tmp = -2.0d0
    else if ((x / y) <= 6.5d-94) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2.1d-26) then
        tmp = -2.0d0
    else if ((x / y) <= 4.5d+36) then
        tmp = 2.0d0 / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= -4.2e-177) {
		tmp = -2.0;
	} else if ((x / y) <= 3.6e-289) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.5e-170) {
		tmp = -2.0;
	} else if ((x / y) <= 6.5e-94) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.1e-26) {
		tmp = -2.0;
	} else if ((x / y) <= 4.5e+36) {
		tmp = 2.0 / t;
	} 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) <= -4.2e-177:
		tmp = -2.0
	elif (x / y) <= 3.6e-289:
		tmp = 2.0 / t
	elif (x / y) <= 2.5e-170:
		tmp = -2.0
	elif (x / y) <= 6.5e-94:
		tmp = 2.0 / t
	elif (x / y) <= 2.1e-26:
		tmp = -2.0
	elif (x / y) <= 4.5e+36:
		tmp = 2.0 / t
	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) <= -4.2e-177)
		tmp = -2.0;
	elseif (Float64(x / y) <= 3.6e-289)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2.5e-170)
		tmp = -2.0;
	elseif (Float64(x / y) <= 6.5e-94)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2.1e-26)
		tmp = -2.0;
	elseif (Float64(x / y) <= 4.5e+36)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2.0)
		tmp = x / y;
	elseif ((x / y) <= -4.2e-177)
		tmp = -2.0;
	elseif ((x / y) <= 3.6e-289)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2.5e-170)
		tmp = -2.0;
	elseif ((x / y) <= 6.5e-94)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2.1e-26)
		tmp = -2.0;
	elseif ((x / y) <= 4.5e+36)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -4.2e-177], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 3.6e-289], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.5e-170], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 6.5e-94], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.1e-26], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 4.5e+36], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2 or 4.49999999999999997e36 < (/.f64 x y)

   1. Initial program 88.0%

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

      1. sub-neg 88.0%

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

      2. distribute-rgt-in 88.0%

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

      3. *-lft-identity 88.0%

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

      4. associate-+r+ 88.0%

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

      5. cancel-sign-sub-inv 88.0%

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

      6. div-sub 77.8%

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

      7. associate-*r* 77.8%

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

      8. associate-*l/ 77.8%

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

      9. *-inverses 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/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 69.6%

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

   if -2 < (/.f64 x y) < -4.20000000000000002e-177 or 3.6e-289 < (/.f64 x y) < 2.50000000000000005e-170 or 6.4999999999999996e-94 < (/.f64 x y) < 2.10000000000000008e-26

   1. Initial program 82.6%

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

      1. clear-num 82.6%

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

      2. frac-add 58.5%

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

      3. *-un-lft-identity 58.5%

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

      4. *-commutative 58.5%

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

      5. +-commutative 58.5%

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

      6. associate-*l* 58.5%

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

      7. fma-def 58.5%

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

      8. *-commutative 58.5%

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

   3. Applied egg-rr 58.5%

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

   4. Taylor expanded in y around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. associate-/l* 65.4%

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

      3. fma-def 65.4%

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

      4. associate-/l* 64.1%

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

      5. associate-*r/ 64.1%

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

      6. metadata-eval 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in t around inf 52.7%

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

   if -4.20000000000000002e-177 < (/.f64 x y) < 3.6e-289 or 2.50000000000000005e-170 < (/.f64 x y) < 6.4999999999999996e-94 or 2.10000000000000008e-26 < (/.f64 x y) < 4.49999999999999997e36

   1. Initial program 92.3%

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

      1. sub-neg 92.3%

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

      2. distribute-rgt-in 92.3%

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

      3. *-lft-identity 92.3%

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

      4. associate-+r+ 92.3%

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

      5. cancel-sign-sub-inv 92.3%

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

      6. div-sub 82.3%

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

      7. associate-*r* 82.3%

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

      8. associate-*l/ 82.3%

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

      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/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. metadata-eval 81.3%

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

   6. Simplified 81.3%

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

   7. Taylor expanded in z around inf 42.7%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -4.2 \cdot 10^{-177}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 3.6 \cdot 10^{-289}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.5 \cdot 10^{-170}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 6.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 4.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3: 69.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;\frac{x}{y} \leq -3.3 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq 6.2 \cdot 10^{-234}:\\ \;\;\;\;-2 + t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0155:\\ \;\;\;\;2 \cdot \frac{1 - t}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t))) (t_2 (- (/ x y) 2.0)))
   (if (<= (/ x y) -3.3e-9)
     t_2
     (if (<= (/ x y) 6.2e-234)
       (+ -2.0 t_1)
       (if (<= (/ x y) 0.0155)
         (* 2.0 (/ (- 1.0 t) t))
         (if (<= (/ x y) 2.4e+66) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if ((x / y) <= -3.3e-9) {
		tmp = t_2;
	} else if ((x / y) <= 6.2e-234) {
		tmp = -2.0 + t_1;
	} else if ((x / y) <= 0.0155) {
		tmp = 2.0 * ((1.0 - t) / t);
	} else if ((x / y) <= 2.4e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 / (z * t)
    t_2 = (x / y) - 2.0d0
    if ((x / y) <= (-3.3d-9)) then
        tmp = t_2
    else if ((x / y) <= 6.2d-234) then
        tmp = (-2.0d0) + t_1
    else if ((x / y) <= 0.0155d0) then
        tmp = 2.0d0 * ((1.0d0 - t) / t)
    else if ((x / y) <= 2.4d+66) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if ((x / y) <= -3.3e-9) {
		tmp = t_2;
	} else if ((x / y) <= 6.2e-234) {
		tmp = -2.0 + t_1;
	} else if ((x / y) <= 0.0155) {
		tmp = 2.0 * ((1.0 - t) / t);
	} else if ((x / y) <= 2.4e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (z * t)
	t_2 = (x / y) - 2.0
	tmp = 0
	if (x / y) <= -3.3e-9:
		tmp = t_2
	elif (x / y) <= 6.2e-234:
		tmp = -2.0 + t_1
	elif (x / y) <= 0.0155:
		tmp = 2.0 * ((1.0 - t) / t)
	elif (x / y) <= 2.4e+66:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(z * t))
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (Float64(x / y) <= -3.3e-9)
		tmp = t_2;
	elseif (Float64(x / y) <= 6.2e-234)
		tmp = Float64(-2.0 + t_1);
	elseif (Float64(x / y) <= 0.0155)
		tmp = Float64(2.0 * Float64(Float64(1.0 - t) / t));
	elseif (Float64(x / y) <= 2.4e+66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (z * t);
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if ((x / y) <= -3.3e-9)
		tmp = t_2;
	elseif ((x / y) <= 6.2e-234)
		tmp = -2.0 + t_1;
	elseif ((x / y) <= 0.0155)
		tmp = 2.0 * ((1.0 - t) / t);
	elseif ((x / y) <= 2.4e+66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -3.3e-9], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 6.2e-234], N[(-2.0 + t$95$1), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0155], N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.4e+66], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -3.30000000000000018e-9 or 2.4000000000000002e66 < (/.f64 x y)

   1. Initial program 87.3%

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

      1. sub-neg 87.3%

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

      2. distribute-rgt-in 87.3%

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

      3. *-lft-identity 87.3%

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

      4. associate-+r+ 87.3%

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

      5. cancel-sign-sub-inv 87.3%

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

      6. div-sub 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 98.1%

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

      10. metadata-eval 98.1%

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

      11. sub-neg 98.1%

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

      12. metadata-eval 98.1%

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

      13. metadata-eval 98.1%

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

      14. +-commutative 98.1%

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

      15. metadata-eval 98.1%

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

      16. associate-/l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around inf 72.7%

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

   if -3.30000000000000018e-9 < (/.f64 x y) < 6.2000000000000003e-234

   1. Initial program 88.7%

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

      1. sub-neg 88.7%

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

      2. distribute-rgt-in 88.7%

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

      3. *-lft-identity 88.7%

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

      4. associate-+r+ 88.7%

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

      5. cancel-sign-sub-inv 88.7%

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

      6. div-sub 76.5%

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

      7. associate-*r* 76.5%

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

      8. associate-*l/ 76.5%

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

      9. *-inverses 99.8%

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

      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 0 72.0%

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

   5. Taylor expanded in x around 0 72.0%

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

      1. sub-neg 72.0%

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

      2. associate-*r/ 72.0%

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

      3. metadata-eval 72.0%

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

      4. metadata-eval 72.0%

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

   7. Simplified 72.0%

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

   if 6.2000000000000003e-234 < (/.f64 x y) < 0.0155

   1. Initial program 84.0%

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

      1. clear-num 84.0%

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

      2. frac-add 53.0%

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

      3. *-un-lft-identity 53.0%

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

      4. *-commutative 53.0%

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

      5. +-commutative 53.0%

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

      6. associate-*l* 53.0%

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

      7. fma-def 53.0%

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

      8. *-commutative 53.0%

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

   3. Applied egg-rr 53.0%

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

   4. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. associate-/l* 58.3%

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

      3. fma-def 58.3%

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

      4. associate-/l* 58.1%

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

      5. associate-*r/ 58.1%

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

      6. metadata-eval 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in z around inf 86.1%

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

   if 0.0155 < (/.f64 x y) < 2.4000000000000002e66

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-rgt-in 99.8%

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

      3. *-lft-identity 99.8%

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

      4. associate-+r+ 99.8%

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

      5. cancel-sign-sub-inv 99.8%

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

      6. div-sub 88.1%

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

      7. associate-*r* 88.1%

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

      8. associate-*l/ 88.1%

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

      9. *-inverses 99.8%

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

      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/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 60.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.3 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 6.2 \cdot 10^{-234}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0155:\\ \;\;\;\;2 \cdot \frac{1 - t}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 4: 63.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+43}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-96}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+15} \lor \neg \left(z \leq 1.4 \cdot 10^{+57}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -2.5e+60)
     t_1
     (if (<= z -1.6e+43)
       (/ 2.0 t)
       (if (<= z -5.2e-104)
         t_1
         (if (<= z 2.9e-96)
           (/ 2.0 (* z t))
           (if (or (<= z 4.1e+15) (not (<= z 1.4e+57))) t_1 (/ 2.0 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -2.5e+60) {
		tmp = t_1;
	} else if (z <= -1.6e+43) {
		tmp = 2.0 / t;
	} else if (z <= -5.2e-104) {
		tmp = t_1;
	} else if (z <= 2.9e-96) {
		tmp = 2.0 / (z * t);
	} else if ((z <= 4.1e+15) || !(z <= 1.4e+57)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-2.5d+60)) then
        tmp = t_1
    else if (z <= (-1.6d+43)) then
        tmp = 2.0d0 / t
    else if (z <= (-5.2d-104)) then
        tmp = t_1
    else if (z <= 2.9d-96) then
        tmp = 2.0d0 / (z * t)
    else if ((z <= 4.1d+15) .or. (.not. (z <= 1.4d+57))) then
        tmp = t_1
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -2.5e+60) {
		tmp = t_1;
	} else if (z <= -1.6e+43) {
		tmp = 2.0 / t;
	} else if (z <= -5.2e-104) {
		tmp = t_1;
	} else if (z <= 2.9e-96) {
		tmp = 2.0 / (z * t);
	} else if ((z <= 4.1e+15) || !(z <= 1.4e+57)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -2.5e+60:
		tmp = t_1
	elif z <= -1.6e+43:
		tmp = 2.0 / t
	elif z <= -5.2e-104:
		tmp = t_1
	elif z <= 2.9e-96:
		tmp = 2.0 / (z * t)
	elif (z <= 4.1e+15) or not (z <= 1.4e+57):
		tmp = t_1
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -2.5e+60)
		tmp = t_1;
	elseif (z <= -1.6e+43)
		tmp = Float64(2.0 / t);
	elseif (z <= -5.2e-104)
		tmp = t_1;
	elseif (z <= 2.9e-96)
		tmp = Float64(2.0 / Float64(z * t));
	elseif ((z <= 4.1e+15) || !(z <= 1.4e+57))
		tmp = t_1;
	else
		tmp = Float64(2.0 / 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 <= -2.5e+60)
		tmp = t_1;
	elseif (z <= -1.6e+43)
		tmp = 2.0 / t;
	elseif (z <= -5.2e-104)
		tmp = t_1;
	elseif (z <= 2.9e-96)
		tmp = 2.0 / (z * t);
	elseif ((z <= 4.1e+15) || ~((z <= 1.4e+57)))
		tmp = t_1;
	else
		tmp = 2.0 / 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, -2.5e+60], t$95$1, If[LessEqual[z, -1.6e+43], N[(2.0 / t), $MachinePrecision], If[LessEqual[z, -5.2e-104], t$95$1, If[LessEqual[z, 2.9e-96], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.1e+15], N[Not[LessEqual[z, 1.4e+57]], $MachinePrecision]], t$95$1, N[(2.0 / t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999987e60 or -1.60000000000000007e43 < z < -5.20000000000000005e-104 or 2.89999999999999994e-96 < z < 4.1e15 or 1.4e57 < z

   1. Initial program 81.6%

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

      1. sub-neg 81.6%

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

      2. distribute-rgt-in 81.6%

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

      3. *-lft-identity 81.6%

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

      4. associate-+r+ 81.6%

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

      5. cancel-sign-sub-inv 81.6%

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

      6. div-sub 80.9%

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

      7. associate-*r* 80.9%

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

      8. associate-*l/ 80.9%

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

      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/ 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 65.3%

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

   if -2.49999999999999987e60 < z < -1.60000000000000007e43 or 4.1e15 < z < 1.4e57

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-rgt-in 99.5%

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

      3. *-lft-identity 99.5%

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

      4. associate-+r+ 99.5%

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

      5. cancel-sign-sub-inv 99.5%

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

      6. div-sub 99.5%

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

      7. associate-*r* 99.5%

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

      8. associate-*l/ 99.5%

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

      9. *-inverses 99.5%

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

      10. metadata-eval 99.5%

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

      11. sub-neg 99.5%

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

      12. metadata-eval 99.5%

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

      13. metadata-eval 99.5%

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

      14. +-commutative 99.5%

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

      15. metadata-eval 99.5%

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

      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 0 94.9%

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

      1. associate-*r/ 94.9%

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

      2. metadata-eval 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in z around inf 94.8%

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

   if -5.20000000000000005e-104 < z < 2.89999999999999994e-96

   1. Initial program 97.5%

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

      1. sub-neg 97.5%

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

      2. distribute-rgt-in 97.5%

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

      3. *-lft-identity 97.5%

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

      4. associate-+r+ 97.5%

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

      5. cancel-sign-sub-inv 97.5%

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

      6. div-sub 71.3%

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

      7. associate-*r* 71.3%

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

      8. associate-*l/ 71.3%

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

      9. *-inverses 97.5%

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

      10. metadata-eval 97.5%

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

      11. sub-neg 97.5%

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

      12. metadata-eval 97.5%

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

      13. metadata-eval 97.5%

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

      14. +-commutative 97.5%

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

      15. metadata-eval 97.5%

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

      16. associate-/l/ 97.5%

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

   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 0 69.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+43}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-96}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+15} \lor \neg \left(z \leq 1.4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 5: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;\frac{x}{y} \leq -0.21:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 7 \cdot 10^{-6}:\\ \;\;\;\;2 \cdot \frac{1 - t}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 7.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= (/ x y) -0.21)
     t_1
     (if (<= (/ x y) 7e-6)
       (* 2.0 (/ (- 1.0 t) t))
       (if (<= (/ x y) 7.2e+67) (/ 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if ((x / y) <= -0.21) {
		tmp = t_1;
	} else if ((x / y) <= 7e-6) {
		tmp = 2.0 * ((1.0 - t) / t);
	} else if ((x / y) <= 7.2e+67) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if ((x / y) <= (-0.21d0)) then
        tmp = t_1
    else if ((x / y) <= 7d-6) then
        tmp = 2.0d0 * ((1.0d0 - t) / t)
    else if ((x / y) <= 7.2d+67) then
        tmp = 2.0d0 / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if ((x / y) <= -0.21) {
		tmp = t_1;
	} else if ((x / y) <= 7e-6) {
		tmp = 2.0 * ((1.0 - t) / t);
	} else if ((x / y) <= 7.2e+67) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if (x / y) <= -0.21:
		tmp = t_1
	elif (x / y) <= 7e-6:
		tmp = 2.0 * ((1.0 - t) / t)
	elif (x / y) <= 7.2e+67:
		tmp = 2.0 / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (Float64(x / y) <= -0.21)
		tmp = t_1;
	elseif (Float64(x / y) <= 7e-6)
		tmp = Float64(2.0 * Float64(Float64(1.0 - t) / t));
	elseif (Float64(x / y) <= 7.2e+67)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if ((x / y) <= -0.21)
		tmp = t_1;
	elseif ((x / y) <= 7e-6)
		tmp = 2.0 * ((1.0 - t) / t);
	elseif ((x / y) <= 7.2e+67)
		tmp = 2.0 / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -0.21], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 7e-6], N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 7.2e+67], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -0.209999999999999992 or 7.1999999999999998e67 < (/.f64 x y)

   1. Initial program 87.2%

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

      1. sub-neg 87.2%

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

      2. distribute-rgt-in 87.2%

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

      3. *-lft-identity 87.2%

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

      4. associate-+r+ 87.2%

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

      5. cancel-sign-sub-inv 87.2%

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

      6. div-sub 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 98.1%

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

      10. metadata-eval 98.1%

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

      11. sub-neg 98.1%

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

      12. metadata-eval 98.1%

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

      13. metadata-eval 98.1%

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

      14. +-commutative 98.1%

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

      15. metadata-eval 98.1%

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

      16. associate-/l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around inf 73.3%

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

   if -0.209999999999999992 < (/.f64 x y) < 6.99999999999999989e-6

   1. Initial program 87.4%

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

      1. clear-num 87.4%

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

      2. frac-add 41.3%

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

      3. *-un-lft-identity 41.3%

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

      4. *-commutative 41.3%

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

      5. +-commutative 41.3%

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

      6. associate-*l* 41.3%

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

      7. fma-def 41.3%

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

      8. *-commutative 41.3%

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

   3. Applied egg-rr 41.3%

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

   4. Taylor expanded in y around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-/l* 63.9%

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

      3. fma-def 63.9%

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

      4. associate-/l* 63.2%

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

      5. associate-*r/ 63.2%

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

      6. metadata-eval 63.2%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in z around inf 65.3%

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

   if 6.99999999999999989e-6 < (/.f64 x y) < 7.1999999999999998e67

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-rgt-in 99.8%

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

      3. *-lft-identity 99.8%

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

      4. associate-+r+ 99.8%

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

      5. cancel-sign-sub-inv 99.8%

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

      6. div-sub 88.1%

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

      7. associate-*r* 88.1%

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

      8. associate-*l/ 88.1%

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

      9. *-inverses 99.8%

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

      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/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 60.3%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.21:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 7 \cdot 10^{-6}:\\ \;\;\;\;2 \cdot \frac{1 - t}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 7.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 6: 79.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (- (/ x y) 2.0)))
   (if (<= t -1.5e-20)
     t_2
     (if (<= t -1.9e-127)
       t_1
       (if (<= t -9e-148) (/ x y) (if (<= t 4.2e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.5e-20) {
		tmp = t_2;
	} else if (t <= -1.9e-127) {
		tmp = t_1;
	} else if (t <= -9e-148) {
		tmp = x / y;
	} else if (t <= 4.2e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = (x / y) - 2.0d0
    if (t <= (-1.5d-20)) then
        tmp = t_2
    else if (t <= (-1.9d-127)) then
        tmp = t_1
    else if (t <= (-9d-148)) then
        tmp = x / y
    else if (t <= 4.2d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.5e-20) {
		tmp = t_2;
	} else if (t <= -1.9e-127) {
		tmp = t_1;
	} else if (t <= -9e-148) {
		tmp = x / y;
	} else if (t <= 4.2e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -1.5e-20:
		tmp = t_2
	elif t <= -1.9e-127:
		tmp = t_1
	elif t <= -9e-148:
		tmp = x / y
	elif t <= 4.2e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.5e-20)
		tmp = t_2;
	elseif (t <= -1.9e-127)
		tmp = t_1;
	elseif (t <= -9e-148)
		tmp = Float64(x / y);
	elseif (t <= 4.2e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.5e-20)
		tmp = t_2;
	elseif (t <= -1.9e-127)
		tmp = t_1;
	elseif (t <= -9e-148)
		tmp = x / y;
	elseif (t <= 4.2e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.5e-20], t$95$2, If[LessEqual[t, -1.9e-127], t$95$1, If[LessEqual[t, -9e-148], N[(x / y), $MachinePrecision], If[LessEqual[t, 4.2e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.50000000000000014e-20 or 4.2000000000000002e37 < 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 75.6%

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

      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 82.3%

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

   if -1.50000000000000014e-20 < t < -1.90000000000000001e-127 or -9.00000000000000029e-148 < t < 4.2000000000000002e37

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-rgt-in 98.3%

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

      3. *-lft-identity 98.3%

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

      4. associate-+r+ 98.3%

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

      5. cancel-sign-sub-inv 98.3%

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

      6. div-sub 81.1%

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

      7. associate-*r* 81.1%

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

      8. associate-*l/ 81.1%

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

      9. *-inverses 98.3%

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

      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/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around 0 80.0%

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

      1. associate-*r/ 80.0%

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

      2. metadata-eval 80.0%

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

   6. Simplified 80.0%

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

   if -1.90000000000000001e-127 < t < -9.00000000000000029e-148

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-rgt-in 99.8%

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

      3. *-lft-identity 99.8%

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

      4. associate-+r+ 99.8%

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

      5. cancel-sign-sub-inv 99.8%

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

      6. div-sub 99.8%

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

      7. associate-*r* 99.8%

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

      8. associate-*l/ 99.8%

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

      9. *-inverses 99.8%

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

      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/ 99.8%

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

   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 inf 85.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-127}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 7: 98.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 78.3%

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

      1. sub-neg 78.3%

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

      2. distribute-rgt-in 78.3%

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

      3. *-lft-identity 78.3%

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

      4. associate-+r+ 78.3%

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

      5. cancel-sign-sub-inv 78.3%

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

      6. div-sub 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/ 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%

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

   if -1 < z < 1

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-rgt-in 98.3%

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

      3. *-lft-identity 98.3%

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

      4. associate-+r+ 98.3%

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

      5. cancel-sign-sub-inv 98.3%

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

      6. div-sub 80.0%

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

      7. associate-*r* 80.0%

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

      8. associate-*l/ 80.0%

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

      9. *-inverses 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/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 96.9%

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

4. Final simplification 98.3%

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

Alternative 8: 60.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-46} \lor \neg \left(t \leq -8.2 \cdot 10^{-97}\right) \land \left(t \leq -6.5 \cdot 10^{-168} \lor \neg \left(t \leq 2.1 \cdot 10^{-87}\right)\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.55e-46)
         (and (not (<= t -8.2e-97))
              (or (<= t -6.5e-168) (not (<= t 2.1e-87)))))
   (- (/ x y) 2.0)
   (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.55e-46) || (!(t <= -8.2e-97) && ((t <= -6.5e-168) || !(t <= 2.1e-87)))) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.55d-46)) .or. (.not. (t <= (-8.2d-97))) .and. (t <= (-6.5d-168)) .or. (.not. (t <= 2.1d-87))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.55e-46) || (!(t <= -8.2e-97) && ((t <= -6.5e-168) || !(t <= 2.1e-87)))) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.55e-46) or (not (t <= -8.2e-97) and ((t <= -6.5e-168) or not (t <= 2.1e-87))):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.55e-46) || (!(t <= -8.2e-97) && ((t <= -6.5e-168) || !(t <= 2.1e-87))))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.55e-46) || (~((t <= -8.2e-97)) && ((t <= -6.5e-168) || ~((t <= 2.1e-87)))))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.55e-46], And[N[Not[LessEqual[t, -8.2e-97]], $MachinePrecision], Or[LessEqual[t, -6.5e-168], N[Not[LessEqual[t, 2.1e-87]], $MachinePrecision]]]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55e-46 or -8.19999999999999986e-97 < t < -6.4999999999999997e-168 or 2.10000000000000007e-87 < t

   1. Initial program 83.1%

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

      1. sub-neg 83.1%

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

      2. distribute-rgt-in 83.1%

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

      3. *-lft-identity 83.1%

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

      4. associate-+r+ 83.1%

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

      5. cancel-sign-sub-inv 83.1%

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

      6. div-sub 80.7%

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

      7. associate-*r* 80.7%

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

      8. associate-*l/ 80.7%

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

      9. *-inverses 99.9%

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

      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 69.1%

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

   if -1.55e-46 < t < -8.19999999999999986e-97 or -6.4999999999999997e-168 < t < 2.10000000000000007e-87

   1. Initial program 97.5%

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

      1. sub-neg 97.5%

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

      2. distribute-rgt-in 97.5%

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

      3. *-lft-identity 97.5%

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

      4. associate-+r+ 97.5%

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

      5. cancel-sign-sub-inv 97.5%

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

      6. div-sub 76.2%

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

      7. associate-*r* 76.2%

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

      8. associate-*l/ 76.2%

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

      9. *-inverses 97.5%

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

      10. metadata-eval 97.5%

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

      11. sub-neg 97.5%

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

      12. metadata-eval 97.5%

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

      13. metadata-eval 97.5%

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

      14. +-commutative 97.5%

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

      15. metadata-eval 97.5%

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

      16. associate-/l/ 97.7%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in t around 0 89.1%

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

      1. associate-*r/ 89.1%

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

      2. metadata-eval 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in z around inf 54.2%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-46} \lor \neg \left(t \leq -8.2 \cdot 10^{-97}\right) \land \left(t \leq -6.5 \cdot 10^{-168} \lor \neg \left(t \leq 2.1 \cdot 10^{-87}\right)\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 9: 85.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-16} \lor \neg \left(z \leq 2.05 \cdot 10^{-96}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e-16) (not (<= z 2.05e-96)))
   (+ (/ 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 ((z <= -1.8e-16) || !(z <= 2.05e-96)) {
		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 ((z <= (-1.8d-16)) .or. (.not. (z <= 2.05d-96))) 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 ((z <= -1.8e-16) || !(z <= 2.05e-96)) {
		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 (z <= -1.8e-16) or not (z <= 2.05e-96):
		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 ((z <= -1.8e-16) || !(z <= 2.05e-96))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) - 2.0));
	else
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e-16) || ~((z <= 2.05e-96)))
		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[z, -1.8e-16], N[Not[LessEqual[z, 2.05e-96]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999991e-16 or 2.05000000000000012e-96 < z

   1. Initial program 81.5%

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

      1. sub-neg 81.5%

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

      2. distribute-rgt-in 81.5%

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

      3. *-lft-identity 81.5%

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

      4. associate-+r+ 81.5%

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

      5. cancel-sign-sub-inv 81.5%

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

      6. div-sub 81.5%

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

      7. associate-*r* 81.5%

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

      8. associate-*l/ 81.5%

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

      9. *-inverses 99.8%

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

      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 99.9%

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

   4. Taylor expanded in z around inf 94.6%

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

      1. associate--l+ 94.6%

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

      2. associate-*r/ 94.6%

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

      3. metadata-eval 94.6%

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

   6. Simplified 94.6%

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

   if -1.79999999999999991e-16 < z < 2.05000000000000012e-96

   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 75.6%

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

      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 97.9%

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

      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 97.9%

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

   5. Taylor expanded in x around 0 75.5%

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

      1. sub-neg 75.5%

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

      2. associate-*r/ 75.5%

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

      3. metadata-eval 75.5%

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

      4. metadata-eval 75.5%

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

   7. Simplified 75.5%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-16} \lor \neg \left(z \leq 2.05 \cdot 10^{-96}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 10: 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 88.1%

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

   1. sub-neg 88.1%

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

   2. distribute-rgt-in 88.1%

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

   3. *-lft-identity 88.1%

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

   4. associate-+r+ 88.1%

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

   5. cancel-sign-sub-inv 88.1%

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

   6. div-sub 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 99.1%

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

   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 11: 36.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 750:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 750.0) (/ 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 <= 750.0) {
		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 <= 750.0d0) 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 <= 750.0) {
		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 <= 750.0:
		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 <= 750.0)
		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 <= 750.0)
		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, 750.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 750 < t

   1. Initial program 76.2%

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

      1. clear-num 76.1%

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

      2. frac-add 51.8%

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

      3. *-un-lft-identity 51.8%

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

      4. *-commutative 51.8%

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

      5. +-commutative 51.8%

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

      6. associate-*l* 51.8%

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

      7. fma-def 51.8%

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

      8. *-commutative 51.8%

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

   3. Applied egg-rr 51.8%

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

   4. Taylor expanded in y around inf 34.3%

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

      1. *-commutative 34.3%

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

      2. associate-/l* 34.8%

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

      3. fma-def 34.8%

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

      4. associate-/l* 34.3%

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

      5. associate-*r/ 34.3%

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

      6. metadata-eval 34.3%

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

   6. Simplified 34.3%

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

   7. Taylor expanded in t around inf 38.6%

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

   if -1 < t < 750

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-rgt-in 98.3%

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

      3. *-lft-identity 98.3%

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

      4. associate-+r+ 98.3%

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

      5. cancel-sign-sub-inv 98.3%

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

      6. div-sub 81.7%

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

      7. associate-*r* 81.7%

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

      8. associate-*l/ 81.7%

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

      9. *-inverses 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/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. metadata-eval 77.1%

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

   6. Simplified 77.1%

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

   7. Taylor expanded in z around inf 40.5%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 750:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 12: 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 88.1%

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

   1. clear-num 88.0%

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

   2. frac-add 59.4%

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

   3. *-un-lft-identity 59.4%

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

   4. *-commutative 59.4%

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

   5. +-commutative 59.4%

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

   6. associate-*l* 59.4%

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

   7. fma-def 59.4%

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

   8. *-commutative 59.4%

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

3. Applied egg-rr 59.4%

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

4. Taylor expanded in y around inf 50.4%

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

   1. *-commutative 50.4%

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

   2. associate-/l* 49.4%

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

   3. fma-def 49.4%

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

   4. associate-/l* 49.2%

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

   5. associate-*r/ 49.2%

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

   6. metadata-eval 49.2%

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

6. Simplified 49.2%

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

7. Taylor expanded in t around inf 19.1%

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

8. Final simplification 19.1%

   \[\leadsto -2 \]

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 2023240 
(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))))