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

Percentage Accurate: 86.4% → 99.3%

Time: 10.3s

Alternatives: 13

Speedup: 1.3×

• 23.5% 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: 99.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.5%

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

   1. +-commutative 86.5%

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

   2. remove-double-neg 86.5%

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

   3. distribute-frac-neg 86.5%

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

   4. unsub-neg 86.5%

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

   5. *-commutative 86.5%

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

   6. associate-*r* 86.5%

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

   7. distribute-rgt1-in 86.5%

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

   8. associate-/l* 86.5%

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

   9. fma-neg 86.5%

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

   10. *-commutative 86.5%

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

   11. fma-define 86.5%

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

   12. *-commutative 86.5%

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

   13. distribute-frac-neg 86.5%

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

   14. remove-double-neg 86.5%

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

3. Simplified 86.5%

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

5. Taylor expanded in t around inf 98.8%

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

   1. sub-neg 98.8%

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

   2. metadata-eval 98.8%

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

   3. +-commutative 98.8%

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

   4. +-commutative 98.8%

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

   5. associate-*r/ 98.8%

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

   6. distribute-lft-in 98.8%

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

   7. metadata-eval 98.8%

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

   8. associate-*r/ 98.8%

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

   9. metadata-eval 98.8%

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

7. Simplified 98.8%

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

Alternative 2: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -7.4 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4.7 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-323}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 6 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 6.2 \cdot 10^{-85}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq 61:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= (/ x y) -7.4e-9)
     t_1
     (if (<= (/ x y) -4.7e-209)
       t_2
       (if (<= (/ x y) -4e-323)
         (+ -2.0 (/ 2.0 (* z t)))
         (if (<= (/ x y) 6e-272)
           t_2
           (if (<= (/ x y) 6.2e-85)
             (+ -2.0 (/ (/ 2.0 t) z))
             (if (<= (/ x y) 61.0) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if ((x / y) <= -7.4e-9) {
		tmp = t_1;
	} else if ((x / y) <= -4.7e-209) {
		tmp = t_2;
	} else if ((x / y) <= -4e-323) {
		tmp = -2.0 + (2.0 / (z * t));
	} else if ((x / y) <= 6e-272) {
		tmp = t_2;
	} else if ((x / y) <= 6.2e-85) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else if ((x / y) <= 61.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    t_2 = (-2.0d0) + (2.0d0 / t)
    if ((x / y) <= (-7.4d-9)) then
        tmp = t_1
    else if ((x / y) <= (-4.7d-209)) then
        tmp = t_2
    else if ((x / y) <= (-4d-323)) then
        tmp = (-2.0d0) + (2.0d0 / (z * t))
    else if ((x / y) <= 6d-272) then
        tmp = t_2
    else if ((x / y) <= 6.2d-85) then
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    else if ((x / y) <= 61.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if ((x / y) <= -7.4e-9) {
		tmp = t_1;
	} else if ((x / y) <= -4.7e-209) {
		tmp = t_2;
	} else if ((x / y) <= -4e-323) {
		tmp = -2.0 + (2.0 / (z * t));
	} else if ((x / y) <= 6e-272) {
		tmp = t_2;
	} else if ((x / y) <= 6.2e-85) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else if ((x / y) <= 61.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	t_2 = -2.0 + (2.0 / t)
	tmp = 0
	if (x / y) <= -7.4e-9:
		tmp = t_1
	elif (x / y) <= -4.7e-209:
		tmp = t_2
	elif (x / y) <= -4e-323:
		tmp = -2.0 + (2.0 / (z * t))
	elif (x / y) <= 6e-272:
		tmp = t_2
	elif (x / y) <= 6.2e-85:
		tmp = -2.0 + ((2.0 / t) / z)
	elif (x / y) <= 61.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	t_2 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (Float64(x / y) <= -7.4e-9)
		tmp = t_1;
	elseif (Float64(x / y) <= -4.7e-209)
		tmp = t_2;
	elseif (Float64(x / y) <= -4e-323)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * t)));
	elseif (Float64(x / y) <= 6e-272)
		tmp = t_2;
	elseif (Float64(x / y) <= 6.2e-85)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	elseif (Float64(x / y) <= 61.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	t_2 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if ((x / y) <= -7.4e-9)
		tmp = t_1;
	elseif ((x / y) <= -4.7e-209)
		tmp = t_2;
	elseif ((x / y) <= -4e-323)
		tmp = -2.0 + (2.0 / (z * t));
	elseif ((x / y) <= 6e-272)
		tmp = t_2;
	elseif ((x / y) <= 6.2e-85)
		tmp = -2.0 + ((2.0 / t) / z);
	elseif ((x / y) <= 61.0)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -7.4e-9], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -4.7e-209], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -4e-323], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 6e-272], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 6.2e-85], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 61.0], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -7.4e-9 or 61 < (/.f64 x y)

   1. Initial program 86.3%

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

   3. Taylor expanded in t around inf 73.2%

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

   if -7.4e-9 < (/.f64 x y) < -4.7000000000000001e-209 or -3.95253e-323 < (/.f64 x y) < 6.0000000000000006e-272 or 6.2000000000000005e-85 < (/.f64 x y) < 61

   1. Initial program 91.1%

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

   3. Taylor expanded in z around inf 80.1%

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

      1. div-sub 80.1%

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

      2. sub-neg 80.1%

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

      3. *-inverses 80.1%

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

      4. metadata-eval 80.1%

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

      5. distribute-lft-in 80.1%

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

      6. metadata-eval 80.1%

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

      7. associate-*r/ 80.1%

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

      8. metadata-eval 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in x around 0 80.1%

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

      1. sub-neg 80.1%

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

      2. associate-*r/ 80.1%

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

      3. metadata-eval 80.1%

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

      4. metadata-eval 80.1%

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

   8. Simplified 80.1%

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

   if -4.7000000000000001e-209 < (/.f64 x y) < -3.95253e-323

   1. Initial program 78.5%

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

      1. +-commutative 78.5%

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

      2. remove-double-neg 78.5%

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

      3. distribute-frac-neg 78.5%

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

      4. unsub-neg 78.5%

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

      5. *-commutative 78.5%

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

      6. associate-*r* 78.5%

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

      7. distribute-rgt1-in 78.5%

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

      8. associate-/l* 78.2%

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

      9. fma-neg 78.2%

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

      10. *-commutative 78.2%

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

      11. fma-define 78.2%

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

      12. *-commutative 78.2%

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

      13. distribute-frac-neg 78.2%

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

      14. remove-double-neg 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 93.2%

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

   if 6.0000000000000006e-272 < (/.f64 x y) < 6.2000000000000005e-85

   1. Initial program 79.8%

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

      1. +-commutative 79.8%

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

      2. remove-double-neg 79.8%

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

      3. distribute-frac-neg 79.8%

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

      4. unsub-neg 79.8%

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

      5. *-commutative 79.8%

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

      6. associate-*r* 79.8%

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

      7. distribute-rgt1-in 79.8%

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

      8. associate-/l* 79.6%

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

      9. fma-neg 79.6%

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

      10. *-commutative 79.6%

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

      11. fma-define 79.6%

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

      12. *-commutative 79.6%

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

      13. distribute-frac-neg 79.6%

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

      14. remove-double-neg 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-*r/ 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

      1. +-commutative 99.9%

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

      2. frac-add 72.9%

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

   9. Applied egg-rr 72.9%

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

   10. Taylor expanded in z around 0 60.7%

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

   11. Taylor expanded in y around 0 83.9%

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

       1. sub-neg 83.9%

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

       2. metadata-eval 83.9%

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

       3. associate-*r/ 83.9%

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

       4. metadata-eval 83.9%

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

       5. associate-/r* 84.0%

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

   13. Simplified 84.0%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq -4.7 \cdot 10^{-209}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-323}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 6 \cdot 10^{-272}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.2 \cdot 10^{-85}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq 61:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{2}{z \cdot t}\\ t_2 := \frac{x}{y} - 2\\ t_3 := -2 + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5.5 \cdot 10^{-219}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-323}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5.4 \cdot 10^{-282}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 48:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ 2.0 (* z t))))
        (t_2 (- (/ x y) 2.0))
        (t_3 (+ -2.0 (/ 2.0 t))))
   (if (<= (/ x y) -5.8e-10)
     t_2
     (if (<= (/ x y) -5.5e-219)
       t_3
       (if (<= (/ x y) -4e-323)
         t_1
         (if (<= (/ x y) 5.4e-282)
           t_3
           (if (<= (/ x y) 4e-85) t_1 (if (<= (/ x y) 48.0) t_3 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 t_3 = -2.0 + (2.0 / t);
	double tmp;
	if ((x / y) <= -5.8e-10) {
		tmp = t_2;
	} else if ((x / y) <= -5.5e-219) {
		tmp = t_3;
	} else if ((x / y) <= -4e-323) {
		tmp = t_1;
	} else if ((x / y) <= 5.4e-282) {
		tmp = t_3;
	} else if ((x / y) <= 4e-85) {
		tmp = t_1;
	} else if ((x / y) <= 48.0) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (-2.0d0) + (2.0d0 / (z * t))
    t_2 = (x / y) - 2.0d0
    t_3 = (-2.0d0) + (2.0d0 / t)
    if ((x / y) <= (-5.8d-10)) then
        tmp = t_2
    else if ((x / y) <= (-5.5d-219)) then
        tmp = t_3
    else if ((x / y) <= (-4d-323)) then
        tmp = t_1
    else if ((x / y) <= 5.4d-282) then
        tmp = t_3
    else if ((x / y) <= 4d-85) then
        tmp = t_1
    else if ((x / y) <= 48.0d0) then
        tmp = t_3
    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 t_3 = -2.0 + (2.0 / t);
	double tmp;
	if ((x / y) <= -5.8e-10) {
		tmp = t_2;
	} else if ((x / y) <= -5.5e-219) {
		tmp = t_3;
	} else if ((x / y) <= -4e-323) {
		tmp = t_1;
	} else if ((x / y) <= 5.4e-282) {
		tmp = t_3;
	} else if ((x / y) <= 4e-85) {
		tmp = t_1;
	} else if ((x / y) <= 48.0) {
		tmp = t_3;
	} 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
	t_3 = -2.0 + (2.0 / t)
	tmp = 0
	if (x / y) <= -5.8e-10:
		tmp = t_2
	elif (x / y) <= -5.5e-219:
		tmp = t_3
	elif (x / y) <= -4e-323:
		tmp = t_1
	elif (x / y) <= 5.4e-282:
		tmp = t_3
	elif (x / y) <= 4e-85:
		tmp = t_1
	elif (x / y) <= 48.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(2.0 / Float64(z * t)))
	t_2 = Float64(Float64(x / y) - 2.0)
	t_3 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (Float64(x / y) <= -5.8e-10)
		tmp = t_2;
	elseif (Float64(x / y) <= -5.5e-219)
		tmp = t_3;
	elseif (Float64(x / y) <= -4e-323)
		tmp = t_1;
	elseif (Float64(x / y) <= 5.4e-282)
		tmp = t_3;
	elseif (Float64(x / y) <= 4e-85)
		tmp = t_1;
	elseif (Float64(x / y) <= 48.0)
		tmp = t_3;
	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;
	t_3 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if ((x / y) <= -5.8e-10)
		tmp = t_2;
	elseif ((x / y) <= -5.5e-219)
		tmp = t_3;
	elseif ((x / y) <= -4e-323)
		tmp = t_1;
	elseif ((x / y) <= 5.4e-282)
		tmp = t_3;
	elseif ((x / y) <= 4e-85)
		tmp = t_1;
	elseif ((x / y) <= 48.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5.8e-10], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -5.5e-219], t$95$3, If[LessEqual[N[(x / y), $MachinePrecision], -4e-323], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5.4e-282], t$95$3, If[LessEqual[N[(x / y), $MachinePrecision], 4e-85], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 48.0], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.79999999999999962e-10 or 48 < (/.f64 x y)

   1. Initial program 86.3%

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

   3. Taylor expanded in t around inf 73.2%

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

   if -5.79999999999999962e-10 < (/.f64 x y) < -5.50000000000000017e-219 or -3.95253e-323 < (/.f64 x y) < 5.39999999999999964e-282 or 3.9999999999999999e-85 < (/.f64 x y) < 48

   1. Initial program 91.1%

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

   3. Taylor expanded in z around inf 80.1%

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

      1. div-sub 80.1%

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

      2. sub-neg 80.1%

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

      3. *-inverses 80.1%

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

      4. metadata-eval 80.1%

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

      5. distribute-lft-in 80.1%

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

      6. metadata-eval 80.1%

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

      7. associate-*r/ 80.1%

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

      8. metadata-eval 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in x around 0 80.1%

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

      1. sub-neg 80.1%

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

      2. associate-*r/ 80.1%

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

      3. metadata-eval 80.1%

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

      4. metadata-eval 80.1%

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

   8. Simplified 80.1%

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

   if -5.50000000000000017e-219 < (/.f64 x y) < -3.95253e-323 or 5.39999999999999964e-282 < (/.f64 x y) < 3.9999999999999999e-85

   1. Initial program 79.3%

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

      1. +-commutative 79.3%

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

      2. remove-double-neg 79.3%

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

      3. distribute-frac-neg 79.3%

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

      4. unsub-neg 79.3%

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

      5. *-commutative 79.3%

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

      6. associate-*r* 79.3%

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

      7. distribute-rgt1-in 79.3%

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

      8. associate-/l* 79.1%

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

      9. fma-neg 79.1%

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

      10. *-commutative 79.1%

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

      11. fma-define 79.1%

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

      12. *-commutative 79.1%

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

      13. distribute-frac-neg 79.1%

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

      14. remove-double-neg 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 87.2%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq -5.5 \cdot 10^{-219}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-323}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 5.4 \cdot 10^{-282}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-85}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 48:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-321}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-270}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 8.2 \cdot 10^{-79}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+50}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0)
   (/ x y)
   (if (<= (/ x y) -2e-321)
     -2.0
     (if (<= (/ x y) 5e-270)
       (/ 2.0 t)
       (if (<= (/ x y) 8.2e-79)
         -2.0
         (if (<= (/ x y) 4e+50) (/ 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) <= -2e-321) {
		tmp = -2.0;
	} else if ((x / y) <= 5e-270) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 8.2e-79) {
		tmp = -2.0;
	} else if ((x / y) <= 4e+50) {
		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) <= (-2d-321)) then
        tmp = -2.0d0
    else if ((x / y) <= 5d-270) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 8.2d-79) then
        tmp = -2.0d0
    else if ((x / y) <= 4d+50) 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) <= -2e-321) {
		tmp = -2.0;
	} else if ((x / y) <= 5e-270) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 8.2e-79) {
		tmp = -2.0;
	} else if ((x / y) <= 4e+50) {
		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) <= -2e-321:
		tmp = -2.0
	elif (x / y) <= 5e-270:
		tmp = 2.0 / t
	elif (x / y) <= 8.2e-79:
		tmp = -2.0
	elif (x / y) <= 4e+50:
		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) <= -2e-321)
		tmp = -2.0;
	elseif (Float64(x / y) <= 5e-270)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 8.2e-79)
		tmp = -2.0;
	elseif (Float64(x / y) <= 4e+50)
		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) <= -2e-321)
		tmp = -2.0;
	elseif ((x / y) <= 5e-270)
		tmp = 2.0 / t;
	elseif ((x / y) <= 8.2e-79)
		tmp = -2.0;
	elseif ((x / y) <= 4e+50)
		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], -2e-321], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 5e-270], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 8.2e-79], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 4e+50], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2 or 4.0000000000000003e50 < (/.f64 x y)

   1. Initial program 85.4%

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

   3. Taylor expanded in x around inf 74.4%

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

   if -2 < (/.f64 x y) < -2.00097e-321 or 4.9999999999999998e-270 < (/.f64 x y) < 8.19999999999999987e-79

   1. Initial program 82.0%

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

      1. +-commutative 82.0%

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

      2. remove-double-neg 82.0%

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

      3. distribute-frac-neg 82.0%

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

      4. unsub-neg 82.0%

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

      5. *-commutative 82.0%

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

      6. associate-*r* 82.0%

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

      7. distribute-rgt1-in 82.0%

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

      8. associate-/l* 81.8%

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

      9. fma-neg 81.8%

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

      10. *-commutative 81.8%

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

      11. fma-define 81.8%

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

      12. *-commutative 81.8%

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

      13. distribute-frac-neg 81.8%

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

      14. remove-double-neg 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 73.8%

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

   9. Taylor expanded in t around inf 47.9%

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

   if -2.00097e-321 < (/.f64 x y) < 4.9999999999999998e-270 or 8.19999999999999987e-79 < (/.f64 x y) < 4.0000000000000003e50

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 68.3%

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

      1. div-sub 68.3%

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

      2. sub-neg 68.3%

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

      3. *-inverses 68.3%

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

      4. metadata-eval 68.3%

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

      5. distribute-lft-in 68.3%

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

      6. metadata-eval 68.3%

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

      7. associate-*r/ 68.3%

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

      8. metadata-eval 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in y around 0 43.0%

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

      1. sub-neg 43.0%

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

      2. associate-*r/ 43.0%

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

      3. metadata-eval 43.0%

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

      4. metadata-eval 43.0%

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

   8. Simplified 43.0%

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

   9. Taylor expanded in t around 0 52.3%

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

Alternative 5: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -1.18 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-145}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-74}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -1.18e-105)
     t_1
     (if (<= z -1.8e-145)
       (+ -2.0 (/ 2.0 (* z t)))
       (if (<= z -2.8e-198)
         (- (/ x y) 2.0)
         (if (<= z 5.2e-74) (+ -2.0 (/ (/ 2.0 t) z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -1.18e-105) {
		tmp = t_1;
	} else if (z <= -1.8e-145) {
		tmp = -2.0 + (2.0 / (z * t));
	} else if (z <= -2.8e-198) {
		tmp = (x / y) - 2.0;
	} else if (z <= 5.2e-74) {
		tmp = -2.0 + ((2.0 / t) / z);
	} 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) + (2.0d0 / t))
    if (z <= (-1.18d-105)) then
        tmp = t_1
    else if (z <= (-1.8d-145)) then
        tmp = (-2.0d0) + (2.0d0 / (z * t))
    else if (z <= (-2.8d-198)) then
        tmp = (x / y) - 2.0d0
    else if (z <= 5.2d-74) then
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    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 + (2.0 / t));
	double tmp;
	if (z <= -1.18e-105) {
		tmp = t_1;
	} else if (z <= -1.8e-145) {
		tmp = -2.0 + (2.0 / (z * t));
	} else if (z <= -2.8e-198) {
		tmp = (x / y) - 2.0;
	} else if (z <= 5.2e-74) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (-2.0 + (2.0 / t))
	tmp = 0
	if z <= -1.18e-105:
		tmp = t_1
	elif z <= -1.8e-145:
		tmp = -2.0 + (2.0 / (z * t))
	elif z <= -2.8e-198:
		tmp = (x / y) - 2.0
	elif z <= 5.2e-74:
		tmp = -2.0 + ((2.0 / t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)))
	tmp = 0.0
	if (z <= -1.18e-105)
		tmp = t_1;
	elseif (z <= -1.8e-145)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * t)));
	elseif (z <= -2.8e-198)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (z <= 5.2e-74)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if (z <= -1.18e-105)
		tmp = t_1;
	elseif (z <= -1.8e-145)
		tmp = -2.0 + (2.0 / (z * t));
	elseif (z <= -2.8e-198)
		tmp = (x / y) - 2.0;
	elseif (z <= 5.2e-74)
		tmp = -2.0 + ((2.0 / t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.18e-105], t$95$1, If[LessEqual[z, -1.8e-145], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-198], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[z, 5.2e-74], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1799999999999999e-105 or 5.2000000000000002e-74 < z

   1. Initial program 82.9%

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

   3. Taylor expanded in z around inf 93.7%

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

      1. div-sub 93.7%

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

      2. sub-neg 93.7%

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

      3. *-inverses 93.7%

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

      4. metadata-eval 93.7%

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

      5. distribute-lft-in 93.7%

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

      6. metadata-eval 93.7%

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

      7. associate-*r/ 93.7%

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

      8. metadata-eval 93.7%

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

   5. Simplified 93.7%

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

   if -1.1799999999999999e-105 < z < -1.8e-145

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-*r* 100.0%

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

      7. distribute-rgt1-in 100.0%

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

      8. associate-/l* 100.0%

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

      9. fma-neg 100.0%

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

      10. *-commutative 100.0%

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

      11. fma-define 100.0%

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

      12. *-commutative 100.0%

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

      13. distribute-frac-neg 100.0%

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

      14. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. +-commutative 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-*r/ 99.7%

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

      6. distribute-lft-in 99.7%

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

      7. metadata-eval 99.7%

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

      8. associate-*r/ 99.7%

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

      9. metadata-eval 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around 0 100.0%

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

   if -1.8e-145 < z < -2.7999999999999999e-198

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

   if -2.7999999999999999e-198 < z < 5.2000000000000002e-74

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. remove-double-neg 94.9%

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

      3. distribute-frac-neg 94.9%

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

      4. unsub-neg 94.9%

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

      5. *-commutative 94.9%

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

      6. associate-*r* 94.9%

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

      7. distribute-rgt1-in 94.9%

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

      8. associate-/l* 94.8%

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

      9. fma-neg 94.8%

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

      10. *-commutative 94.8%

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

      11. fma-define 94.8%

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

      12. *-commutative 94.8%

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

      13. distribute-frac-neg 94.8%

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

      14. remove-double-neg 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around inf 94.9%

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

      1. sub-neg 94.9%

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

      2. metadata-eval 94.9%

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

      3. +-commutative 94.9%

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

      4. +-commutative 94.9%

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

      5. associate-*r/ 94.9%

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

      6. distribute-lft-in 94.9%

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

      7. metadata-eval 94.9%

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

      8. associate-*r/ 94.9%

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

      9. metadata-eval 94.9%

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

   7. Simplified 94.9%

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

      1. +-commutative 94.9%

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

      2. frac-add 77.9%

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

   9. Applied egg-rr 77.9%

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

   10. Taylor expanded in z around 0 57.0%

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

   11. Taylor expanded in y around 0 75.2%

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

       1. sub-neg 75.2%

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

       2. metadata-eval 75.2%

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

       3. associate-*r/ 75.2%

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

       4. metadata-eval 75.2%

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

       5. associate-/r* 75.2%

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

   13. Simplified 75.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-145}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-74}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-26} \lor \neg \left(z \leq 4.3 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{z}{y} - \frac{-2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.22e-26) (not (<= z 4.3e-11)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (/ (- (* x (/ z y)) (/ -2.0 t)) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.22e-26) || !(z <= 4.3e-11)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = ((x * (z / y)) - (-2.0 / t)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.22d-26)) .or. (.not. (z <= 4.3d-11))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = ((x * (z / y)) - ((-2.0d0) / t)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.22e-26) || !(z <= 4.3e-11)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = ((x * (z / y)) - (-2.0 / t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.22e-26) or not (z <= 4.3e-11):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = ((x * (z / y)) - (-2.0 / t)) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.22e-26) || !(z <= 4.3e-11))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(Float64(x * Float64(z / y)) - Float64(-2.0 / t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.22e-26) || ~((z <= 4.3e-11)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = ((x * (z / y)) - (-2.0 / t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.22e-26], N[Not[LessEqual[z, 4.3e-11]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e-26 or 4.30000000000000001e-11 < z

   1. Initial program 79.8%

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

   3. Taylor expanded in z around inf 99.3%

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

      1. div-sub 99.3%

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

      2. sub-neg 99.3%

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

      3. *-inverses 99.3%

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

      4. metadata-eval 99.3%

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

      5. distribute-lft-in 99.3%

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

      6. metadata-eval 99.3%

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

      7. associate-*r/ 99.3%

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

      8. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   if -1.22e-26 < z < 4.30000000000000001e-11

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 97.8%

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

   4. Taylor expanded in x around inf 88.8%

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

      1. associate-/l* 90.9%

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

   6. Simplified 90.9%

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

      1. div-inv 90.9%

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

      2. frac-2neg 90.9%

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

      3. metadata-eval 90.9%

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

   8. Applied egg-rr 90.9%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-26} \lor \neg \left(z \leq 4.3 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{z}{y} - \frac{-2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-26} \lor \neg \left(z \leq 7.8 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e-26) (not (<= z 7.8e-13)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-26) || !(z <= 7.8e-13)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2d-26)) .or. (.not. (z <= 7.8d-13))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-26) || !(z <= 7.8e-13)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e-26) or not (z <= 7.8e-13):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e-26) || !(z <= 7.8e-13))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e-26) || ~((z <= 7.8e-13)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e-26], N[Not[LessEqual[z, 7.8e-13]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-26 or 7.80000000000000009e-13 < z

   1. Initial program 79.8%

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

   3. Taylor expanded in z around inf 99.3%

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

      1. div-sub 99.3%

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

      2. sub-neg 99.3%

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

      3. *-inverses 99.3%

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

      4. metadata-eval 99.3%

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

      5. distribute-lft-in 99.3%

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

      6. metadata-eval 99.3%

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

      7. associate-*r/ 99.3%

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

      8. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   if -2.0000000000000001e-26 < z < 7.80000000000000009e-13

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 88.1%

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

      1. associate-/r* 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-26} \lor \neg \left(z \leq 7.8 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-26} \lor \neg \left(z \leq 1.38 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e-26) (not (<= z 1.38e-11)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-26) || !(z <= 1.38e-11)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.65d-26)) .or. (.not. (z <= 1.38d-11))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + (2.0d0 / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-26) || !(z <= 1.38e-11)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e-26) or not (z <= 1.38e-11):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e-26) || !(z <= 1.38e-11))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.65e-26) || ~((z <= 1.38e-11)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e-26], N[Not[LessEqual[z, 1.38e-11]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999e-26 or 1.38e-11 < z

   1. Initial program 79.8%

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

   3. Taylor expanded in z around inf 99.3%

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

      1. div-sub 99.3%

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

      2. sub-neg 99.3%

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

      3. *-inverses 99.3%

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

      4. metadata-eval 99.3%

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

      5. distribute-lft-in 99.3%

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

      6. metadata-eval 99.3%

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

      7. associate-*r/ 99.3%

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

      8. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   if -1.6499999999999999e-26 < z < 1.38e-11

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 88.1%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-26} \lor \neg \left(z \leq 1.38 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{-9} \lor \neg \left(\frac{x}{y} \leq 53\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6e-9) (not (<= (/ x y) 53.0)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6e-9) || !((x / y) <= 53.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-6d-9)) .or. (.not. ((x / y) <= 53.0d0))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6e-9) || !((x / y) <= 53.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -6e-9) or not ((x / y) <= 53.0):
		tmp = (x / y) - 2.0
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -6e-9) || !(Float64(x / y) <= 53.0))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -6e-9) || ~(((x / y) <= 53.0)))
		tmp = (x / y) - 2.0;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -6e-9], N[Not[LessEqual[N[(x / y), $MachinePrecision], 53.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.99999999999999996e-9 or 53 < (/.f64 x y)

   1. Initial program 86.3%

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

   3. Taylor expanded in t around inf 73.2%

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

   if -5.99999999999999996e-9 < (/.f64 x y) < 53

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 72.3%

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

      1. div-sub 72.4%

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

      2. sub-neg 72.4%

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

      3. *-inverses 72.4%

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

      4. metadata-eval 72.4%

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

      5. distribute-lft-in 72.4%

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

      6. metadata-eval 72.4%

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

      7. associate-*r/ 72.4%

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

      8. metadata-eval 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in x around 0 72.4%

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

      1. sub-neg 72.4%

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

      2. associate-*r/ 72.4%

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

      3. metadata-eval 72.4%

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

      4. metadata-eval 72.4%

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

   8. Simplified 72.4%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{-9} \lor \neg \left(\frac{x}{y} \leq 53\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+36} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+36) (not (<= (/ x y) 4e+50)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+36) || !((x / y) <= 4e+50)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d+36)) .or. (.not. ((x / y) <= 4d+50))) then
        tmp = x / y
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+36) || !((x / y) <= 4e+50)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+36) or not ((x / y) <= 4e+50):
		tmp = x / y
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+36) || !(Float64(x / y) <= 4e+50))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+36) || ~(((x / y) <= 4e+50)))
		tmp = x / y;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+36], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+50]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.00000000000000008e36 or 4.0000000000000003e50 < (/.f64 x y)

   1. Initial program 85.7%

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

   3. Taylor expanded in x around inf 78.2%

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

   if -2.00000000000000008e36 < (/.f64 x y) < 4.0000000000000003e50

   1. Initial program 87.3%

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

   3. Taylor expanded in z around inf 72.1%

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

      1. div-sub 72.2%

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

      2. sub-neg 72.2%

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

      3. *-inverses 72.2%

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

      4. metadata-eval 72.2%

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

      5. distribute-lft-in 72.2%

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

      6. metadata-eval 72.2%

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

      7. associate-*r/ 72.2%

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

      8. metadata-eval 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in x around 0 66.7%

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

      1. sub-neg 66.7%

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

      2. associate-*r/ 66.7%

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

      3. metadata-eval 66.7%

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

      4. metadata-eval 66.7%

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

   8. Simplified 66.7%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+36} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-106} \lor \neg \left(t \leq 3.8 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.8e-106) (not (<= t 3.8e-114)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e-106) || !(t <= 3.8e-114)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.8d-106)) .or. (.not. (t <= 3.8d-114))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e-106) || !(t <= 3.8e-114)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.8e-106) or not (t <= 3.8e-114):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.8e-106) || !(t <= 3.8e-114))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.8e-106) || ~((t <= 3.8e-114)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.8e-106], N[Not[LessEqual[t, 3.8e-114]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7999999999999999e-106 or 3.7999999999999998e-114 < t

   1. Initial program 81.0%

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

   3. Taylor expanded in t around inf 77.1%

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

   if -3.7999999999999999e-106 < t < 3.7999999999999998e-114

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 86.3%

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

      1. associate-*r/ 86.3%

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

      2. metadata-eval 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-106} \lor \neg \left(t \leq 3.8 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if t < -1 or 1 < t

   1. Initial program 75.9%

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

      1. +-commutative 75.9%

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

      2. remove-double-neg 75.9%

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

      3. distribute-frac-neg 75.9%

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

      4. unsub-neg 75.9%

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

      5. *-commutative 75.9%

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

      6. associate-*r* 75.9%

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

      7. distribute-rgt1-in 75.9%

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

      8. associate-/l* 75.8%

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

      9. fma-neg 75.8%

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

      10. *-commutative 75.8%

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

      11. fma-define 75.8%

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

      12. *-commutative 75.8%

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

      13. distribute-frac-neg 75.8%

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

      14. remove-double-neg 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-*r/ 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 46.0%

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

   9. Taylor expanded in t around inf 31.6%

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

   if -1 < t < 1

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 71.1%

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

      1. div-sub 71.1%

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

      2. sub-neg 71.1%

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

      3. *-inverses 71.1%

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

      4. metadata-eval 71.1%

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

      5. distribute-lft-in 71.1%

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

      6. metadata-eval 71.1%

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

      7. associate-*r/ 71.1%

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

      8. metadata-eval 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in y around 0 57.0%

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

      1. sub-neg 57.0%

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

      2. associate-*r/ 57.0%

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

      3. metadata-eval 57.0%

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

      4. metadata-eval 57.0%

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

   8. Simplified 57.0%

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

   9. Taylor expanded in t around 0 42.0%

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

Alternative 13: 20.3% 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 86.5%

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

   1. +-commutative 86.5%

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

   2. remove-double-neg 86.5%

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

   3. distribute-frac-neg 86.5%

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

   4. unsub-neg 86.5%

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

   5. *-commutative 86.5%

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

   6. associate-*r* 86.5%

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

   7. distribute-rgt1-in 86.5%

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

   8. associate-/l* 86.5%

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

   9. fma-neg 86.5%

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

   10. *-commutative 86.5%

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

   11. fma-define 86.5%

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

   12. *-commutative 86.5%

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

   13. distribute-frac-neg 86.5%

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

   14. remove-double-neg 86.5%

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

3. Simplified 86.5%

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

5. Taylor expanded in t around inf 98.8%

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

   1. sub-neg 98.8%

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

   2. metadata-eval 98.8%

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

   3. +-commutative 98.8%

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

   4. +-commutative 98.8%

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

   5. associate-*r/ 98.8%

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

   6. distribute-lft-in 98.8%

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

   7. metadata-eval 98.8%

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

   8. associate-*r/ 98.8%

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

   9. metadata-eval 98.8%

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

7. Simplified 98.8%

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

8. Taylor expanded in z around 0 40.2%

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

9. Taylor expanded in t around inf 17.2%

   \[\leadsto \color{blue}{-2} \]
10. Add Preprocessing

Developer target: 99.3% 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 2024108 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))