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

Percentage Accurate: 86.7% → 99.2%

Time: 10.0s

Alternatives: 12

Speedup: 1.3×

• 23.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

   1. +-commutative 89.3%

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

   2. remove-double-neg 89.3%

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

   3. distribute-frac-neg 89.3%

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

   4. unsub-neg 89.3%

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

   5. *-commutative 89.3%

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

   6. associate-*r* 89.3%

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

   7. distribute-rgt1-in 89.3%

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

   8. associate-/l* 89.2%

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

   9. fma-neg 89.2%

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

   10. *-commutative 89.2%

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

   11. fma-define 89.2%

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

   12. *-commutative 89.2%

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

   13. distribute-frac-neg 89.2%

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

   14. remove-double-neg 89.2%

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

3. Simplified 89.2%

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

5. Taylor expanded in t around inf 98.3%

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

   1. sub-neg 98.3%

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

   2. +-commutative 98.3%

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

   3. metadata-eval 98.3%

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

   4. associate-+l+ 98.3%

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

   5. associate-*r/ 98.3%

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

   6. distribute-lft-in 98.3%

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

   7. metadata-eval 98.3%

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

   8. associate-*r/ 98.3%

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

   9. metadata-eval 98.3%

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

7. Simplified 98.3%

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

Alternative 2: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -580000000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-71}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -4.2e+48)
     t_1
     (if (<= z -580000000000.0)
       (/ 2.0 t)
       (if (<= z -1.02e-43)
         (/ x y)
         (if (<= z 4.2e-71) (+ -2.0 (/ (/ 2.0 z) t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -4.2e+48) {
		tmp = t_1;
	} else if (z <= -580000000000.0) {
		tmp = 2.0 / t;
	} else if (z <= -1.02e-43) {
		tmp = x / y;
	} else if (z <= 4.2e-71) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-4.2d+48)) then
        tmp = t_1
    else if (z <= (-580000000000.0d0)) then
        tmp = 2.0d0 / t
    else if (z <= (-1.02d-43)) then
        tmp = x / y
    else if (z <= 4.2d-71) then
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -4.2e+48) {
		tmp = t_1;
	} else if (z <= -580000000000.0) {
		tmp = 2.0 / t;
	} else if (z <= -1.02e-43) {
		tmp = x / y;
	} else if (z <= 4.2e-71) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -4.2e+48:
		tmp = t_1
	elif z <= -580000000000.0:
		tmp = 2.0 / t
	elif z <= -1.02e-43:
		tmp = x / y
	elif z <= 4.2e-71:
		tmp = -2.0 + ((2.0 / z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -4.2e+48)
		tmp = t_1;
	elseif (z <= -580000000000.0)
		tmp = Float64(2.0 / t);
	elseif (z <= -1.02e-43)
		tmp = Float64(x / y);
	elseif (z <= 4.2e-71)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -4.2e+48)
		tmp = t_1;
	elseif (z <= -580000000000.0)
		tmp = 2.0 / t;
	elseif (z <= -1.02e-43)
		tmp = x / y;
	elseif (z <= 4.2e-71)
		tmp = -2.0 + ((2.0 / z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -4.2e+48], t$95$1, If[LessEqual[z, -580000000000.0], N[(2.0 / t), $MachinePrecision], If[LessEqual[z, -1.02e-43], N[(x / y), $MachinePrecision], If[LessEqual[z, 4.2e-71], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1999999999999997e48 or 4.2000000000000002e-71 < 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 t around inf 66.2%

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

   if -4.1999999999999997e48 < z < -5.8e11

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 97.2%

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

   if -5.8e11 < z < -1.0200000000000001e-43

   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 x around inf 75.6%

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

   if -1.0200000000000001e-43 < z < 4.2000000000000002e-71

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. remove-double-neg 97.3%

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

      3. distribute-frac-neg 97.3%

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

      4. unsub-neg 97.3%

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

      5. *-commutative 97.3%

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

      6. associate-*r* 97.3%

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

      7. distribute-rgt1-in 97.3%

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

      8. associate-/l* 97.3%

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

      9. fma-neg 97.3%

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

      10. *-commutative 97.3%

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

      11. fma-define 97.3%

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

      12. *-commutative 97.3%

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

      13. distribute-frac-neg 97.3%

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

      14. remove-double-neg 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 97.3%

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

      1. sub-neg 97.3%

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

      2. +-commutative 97.3%

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

      3. metadata-eval 97.3%

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

      4. associate-+l+ 97.3%

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

      5. associate-*r/ 97.3%

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

      6. distribute-lft-in 97.3%

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

      7. metadata-eval 97.3%

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

      8. associate-*r/ 97.3%

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

      9. metadata-eval 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in z around 0 97.3%

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

   9. Taylor expanded in x around 0 84.5%

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

       1. sub-neg 84.5%

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

       2. associate-*r/ 84.5%

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

       3. metadata-eval 84.5%

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

       4. *-commutative 84.5%

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

       5. metadata-eval 84.5%

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

       6. +-commutative 84.5%

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

       7. associate-/r* 84.5%

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

   11. Simplified 84.5%

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

Alternative 3: 62.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -1.18 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -135000000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -1.18e+51)
     t_1
     (if (<= z -135000000000.0)
       (/ 2.0 t)
       (if (<= z -2.9e-44) (/ x y) (if (<= z 6.8e-72) (/ (/ 2.0 t) z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -1.18e+51) {
		tmp = t_1;
	} else if (z <= -135000000000.0) {
		tmp = 2.0 / t;
	} else if (z <= -2.9e-44) {
		tmp = x / y;
	} else if (z <= 6.8e-72) {
		tmp = (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
    if (z <= (-1.18d+51)) then
        tmp = t_1
    else if (z <= (-135000000000.0d0)) then
        tmp = 2.0d0 / t
    else if (z <= (-2.9d-44)) then
        tmp = x / y
    else if (z <= 6.8d-72) then
        tmp = (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;
	double tmp;
	if (z <= -1.18e+51) {
		tmp = t_1;
	} else if (z <= -135000000000.0) {
		tmp = 2.0 / t;
	} else if (z <= -2.9e-44) {
		tmp = x / y;
	} else if (z <= 6.8e-72) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -1.18e+51:
		tmp = t_1
	elif z <= -135000000000.0:
		tmp = 2.0 / t
	elif z <= -2.9e-44:
		tmp = x / y
	elif z <= 6.8e-72:
		tmp = (2.0 / t) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -1.18e+51)
		tmp = t_1;
	elseif (z <= -135000000000.0)
		tmp = Float64(2.0 / t);
	elseif (z <= -2.9e-44)
		tmp = Float64(x / y);
	elseif (z <= 6.8e-72)
		tmp = 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;
	tmp = 0.0;
	if (z <= -1.18e+51)
		tmp = t_1;
	elseif (z <= -135000000000.0)
		tmp = 2.0 / t;
	elseif (z <= -2.9e-44)
		tmp = x / y;
	elseif (z <= 6.8e-72)
		tmp = (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] - 2.0), $MachinePrecision]}, If[LessEqual[z, -1.18e+51], t$95$1, If[LessEqual[z, -135000000000.0], N[(2.0 / t), $MachinePrecision], If[LessEqual[z, -2.9e-44], N[(x / y), $MachinePrecision], If[LessEqual[z, 6.8e-72], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.18e51 or 6.7999999999999997e-72 < 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 t around inf 66.2%

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

   if -1.18e51 < z < -1.35e11

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 97.2%

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

   if -1.35e11 < z < -2.9000000000000001e-44

   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 x around inf 75.6%

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

   if -2.9000000000000001e-44 < z < 6.7999999999999997e-72

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. remove-double-neg 97.3%

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

      3. distribute-frac-neg 97.3%

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

      4. unsub-neg 97.3%

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

      5. *-commutative 97.3%

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

      6. associate-*r* 97.3%

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

      7. distribute-rgt1-in 97.3%

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

      8. associate-/l* 97.3%

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

      9. fma-neg 97.3%

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

      10. *-commutative 97.3%

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

      11. fma-define 97.3%

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

      12. *-commutative 97.3%

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

      13. distribute-frac-neg 97.3%

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

      14. remove-double-neg 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 97.3%

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

      1. sub-neg 97.3%

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

      2. +-commutative 97.3%

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

      3. metadata-eval 97.3%

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

      4. associate-+l+ 97.3%

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

      5. associate-*r/ 97.3%

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

      6. distribute-lft-in 97.3%

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

      7. metadata-eval 97.3%

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

      8. associate-*r/ 97.3%

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

      9. metadata-eval 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in z around 0 71.1%

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

      1. associate-/r* 71.1%

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

   10. Simplified 71.1%

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

Alternative 4: 62.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -115000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-71}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -4.2e+48)
     t_1
     (if (<= z -115000000.0)
       (/ 2.0 t)
       (if (<= z -3.6e-44)
         (/ x y)
         (if (<= z 1.65e-71) (/ 2.0 (* z t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -4.2e+48) {
		tmp = t_1;
	} else if (z <= -115000000.0) {
		tmp = 2.0 / t;
	} else if (z <= -3.6e-44) {
		tmp = x / y;
	} else if (z <= 1.65e-71) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-4.2d+48)) then
        tmp = t_1
    else if (z <= (-115000000.0d0)) then
        tmp = 2.0d0 / t
    else if (z <= (-3.6d-44)) then
        tmp = x / y
    else if (z <= 1.65d-71) then
        tmp = 2.0d0 / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -4.2e+48) {
		tmp = t_1;
	} else if (z <= -115000000.0) {
		tmp = 2.0 / t;
	} else if (z <= -3.6e-44) {
		tmp = x / y;
	} else if (z <= 1.65e-71) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -4.2e+48:
		tmp = t_1
	elif z <= -115000000.0:
		tmp = 2.0 / t
	elif z <= -3.6e-44:
		tmp = x / y
	elif z <= 1.65e-71:
		tmp = 2.0 / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -4.2e+48)
		tmp = t_1;
	elseif (z <= -115000000.0)
		tmp = Float64(2.0 / t);
	elseif (z <= -3.6e-44)
		tmp = Float64(x / y);
	elseif (z <= 1.65e-71)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -4.2e+48)
		tmp = t_1;
	elseif (z <= -115000000.0)
		tmp = 2.0 / t;
	elseif (z <= -3.6e-44)
		tmp = x / y;
	elseif (z <= 1.65e-71)
		tmp = 2.0 / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -4.2e+48], t$95$1, If[LessEqual[z, -115000000.0], N[(2.0 / t), $MachinePrecision], If[LessEqual[z, -3.6e-44], N[(x / y), $MachinePrecision], If[LessEqual[z, 1.65e-71], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1999999999999997e48 or 1.6500000000000001e-71 < 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 t around inf 66.2%

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

   if -4.1999999999999997e48 < z < -1.15e8

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 97.2%

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

   if -1.15e8 < z < -3.5999999999999999e-44

   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 x around inf 75.6%

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

   if -3.5999999999999999e-44 < z < 1.6500000000000001e-71

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. remove-double-neg 97.3%

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

      3. distribute-frac-neg 97.3%

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

      4. unsub-neg 97.3%

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

      5. *-commutative 97.3%

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

      6. associate-*r* 97.3%

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

      7. distribute-rgt1-in 97.3%

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

      8. associate-/l* 97.3%

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

      9. fma-neg 97.3%

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

      10. *-commutative 97.3%

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

      11. fma-define 97.3%

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

      12. *-commutative 97.3%

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

      13. distribute-frac-neg 97.3%

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

      14. remove-double-neg 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 97.3%

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

      1. sub-neg 97.3%

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

      2. +-commutative 97.3%

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

      3. metadata-eval 97.3%

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

      4. associate-+l+ 97.3%

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

      5. associate-*r/ 97.3%

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

      6. distribute-lft-in 97.3%

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

      7. metadata-eval 97.3%

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

      8. associate-*r/ 97.3%

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

      9. metadata-eval 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in z around 0 71.1%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq -115000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-71}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -0.00094:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-71}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -0.00094)
     t_1
     (if (<= z 8.5e-105)
       (+ (/ x y) (/ 2.0 (* z t)))
       (if (<= z 1.8e-71) (+ -2.0 (/ (/ 2.0 z) t)) 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 <= -0.00094) {
		tmp = t_1;
	} else if (z <= 8.5e-105) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if (z <= 1.8e-71) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + ((-2.0d0) + (2.0d0 / t))
    if (z <= (-0.00094d0)) then
        tmp = t_1
    else if (z <= 8.5d-105) then
        tmp = (x / y) + (2.0d0 / (z * t))
    else if (z <= 1.8d-71) then
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -0.00094) {
		tmp = t_1;
	} else if (z <= 8.5e-105) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if (z <= 1.8e-71) {
		tmp = -2.0 + ((2.0 / z) / t);
	} 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 <= -0.00094:
		tmp = t_1
	elif z <= 8.5e-105:
		tmp = (x / y) + (2.0 / (z * t))
	elif z <= 1.8e-71:
		tmp = -2.0 + ((2.0 / z) / t)
	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 <= -0.00094)
		tmp = t_1;
	elseif (z <= 8.5e-105)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	elseif (z <= 1.8e-71)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if (z <= -0.00094)
		tmp = t_1;
	elseif (z <= 8.5e-105)
		tmp = (x / y) + (2.0 / (z * t));
	elseif (z <= 1.8e-71)
		tmp = -2.0 + ((2.0 / z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.00094], t$95$1, If[LessEqual[z, 8.5e-105], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-71], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.39999999999999972e-4 or 1.8e-71 < z

   1. Initial program 81.2%

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

   3. Taylor expanded in z around inf 94.9%

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

      1. div-sub 94.9%

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

      2. sub-neg 94.9%

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

      3. *-inverses 94.9%

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

      4. metadata-eval 94.9%

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

      5. distribute-lft-in 94.9%

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

      6. associate-*r/ 94.9%

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

      7. metadata-eval 94.9%

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

      8. metadata-eval 94.9%

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

   5. Simplified 94.9%

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

   if -9.39999999999999972e-4 < z < 8.50000000000000038e-105

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 87.0%

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

   if 8.50000000000000038e-105 < z < 1.8e-71

   1. Initial program 88.7%

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

      1. +-commutative 88.7%

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

      2. remove-double-neg 88.7%

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

      3. distribute-frac-neg 88.7%

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

      4. unsub-neg 88.7%

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

      5. *-commutative 88.7%

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

      6. associate-*r* 88.7%

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

      7. distribute-rgt1-in 88.7%

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

      8. associate-/l* 88.7%

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

      9. fma-neg 88.7%

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

      10. *-commutative 88.7%

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

      11. fma-define 88.7%

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

      12. *-commutative 88.7%

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

      13. distribute-frac-neg 88.7%

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

      14. remove-double-neg 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in t around inf 88.9%

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

      1. sub-neg 88.9%

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

      2. +-commutative 88.9%

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

      3. metadata-eval 88.9%

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

      4. associate-+l+ 88.9%

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

      5. associate-*r/ 88.9%

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

      6. distribute-lft-in 88.9%

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

      7. metadata-eval 88.9%

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

      8. associate-*r/ 88.9%

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

      9. metadata-eval 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in z around 0 88.9%

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

   9. Taylor expanded in x around 0 99.8%

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

       1. sub-neg 99.8%

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

       2. associate-*r/ 99.8%

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

       3. metadata-eval 99.8%

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

       4. *-commutative 99.8%

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

       5. metadata-eval 99.8%

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

       6. +-commutative 99.8%

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

       7. associate-/r* 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00094:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-71}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.75 \cdot 10^{-297}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 42000000000000:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -7e+25)
   (/ x y)
   (if (<= (/ x y) -2.75e-297)
     (/ 2.0 t)
     (if (<= (/ x y) 42000000000000.0) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -7e+25) {
		tmp = x / y;
	} else if ((x / y) <= -2.75e-297) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 42000000000000.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-7d+25)) then
        tmp = x / y
    else if ((x / y) <= (-2.75d-297)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 42000000000000.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -7e+25) {
		tmp = x / y;
	} else if ((x / y) <= -2.75e-297) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 42000000000000.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -7e+25:
		tmp = x / y
	elif (x / y) <= -2.75e-297:
		tmp = 2.0 / t
	elif (x / y) <= 42000000000000.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -7e+25)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -2.75e-297)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 42000000000000.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -7e+25)
		tmp = x / y;
	elseif ((x / y) <= -2.75e-297)
		tmp = 2.0 / t;
	elseif ((x / y) <= 42000000000000.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -7e+25], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2.75e-297], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 42000000000000.0], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -6.99999999999999999e25 or 4.2e13 < (/.f64 x y)

   1. Initial program 84.5%

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

   3. Taylor expanded in x around inf 63.9%

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

   if -6.99999999999999999e25 < (/.f64 x y) < -2.75000000000000015e-297

   1. Initial program 95.7%

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

   3. Taylor expanded in t around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. metadata-eval 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in z around inf 34.3%

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

   if -2.75000000000000015e-297 < (/.f64 x y) < 4.2e13

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. remove-double-neg 91.7%

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

      3. distribute-frac-neg 91.7%

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

      4. unsub-neg 91.7%

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

      5. *-commutative 91.7%

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

      6. associate-*r* 91.7%

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

      7. distribute-rgt1-in 91.7%

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

      8. associate-/l* 91.6%

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

      9. fma-neg 91.6%

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

      10. *-commutative 91.6%

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

      11. fma-define 91.6%

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

      12. *-commutative 91.6%

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

      13. distribute-frac-neg 91.6%

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

      14. remove-double-neg 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, 1 - t, 1\right), \frac{2}{z \cdot t}, \frac{x}{y}\right)} \]
   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. +-commutative 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-+l+ 99.9%

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

      5. associate-*r/ 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 77.9%

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

   9. Taylor expanded in x around 0 77.2%

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

       1. sub-neg 77.2%

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

       2. associate-*r/ 77.2%

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

       3. metadata-eval 77.2%

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

       4. *-commutative 77.2%

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

       5. metadata-eval 77.2%

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

       6. +-commutative 77.2%

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

       7. associate-/r* 77.3%

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

   11. Simplified 77.3%

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

   12. Taylor expanded in z around inf 39.6%

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

Alternative 7: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5.3 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{z}}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 5.3e-5)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (+ -2.0 (/ (/ 2.0 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 5.3e-5)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 5.3d-5))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + ((-2.0d0) + ((2.0d0 / z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 5.3e-5)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 5.3e-5):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 5.3e-5))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(Float64(2.0 / z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 5.3e-5)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (-2.0 + ((2.0 / z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 5.3e-5]], $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[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 5.3000000000000001e-5 < z

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf 98.9%

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

      1. div-sub 98.9%

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

      2. sub-neg 98.9%

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

      3. *-inverses 98.9%

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

      4. metadata-eval 98.9%

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

      5. distribute-lft-in 98.9%

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

      6. associate-*r/ 98.9%

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

      7. metadata-eval 98.9%

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

      8. metadata-eval 98.9%

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

   5. Simplified 98.9%

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

   if -1 < z < 5.3000000000000001e-5

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. remove-double-neg 97.1%

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

      3. distribute-frac-neg 97.1%

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

      4. unsub-neg 97.1%

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

      5. *-commutative 97.1%

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

      6. associate-*r* 97.1%

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

      7. distribute-rgt1-in 97.1%

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

      8. associate-/l* 97.1%

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

      9. fma-neg 97.1%

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

      10. *-commutative 97.1%

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

      11. fma-define 97.1%

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

      12. *-commutative 97.1%

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

      13. distribute-frac-neg 97.1%

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

      14. remove-double-neg 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t around inf 97.2%

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

      1. sub-neg 97.2%

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

      2. +-commutative 97.2%

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

      3. metadata-eval 97.2%

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

      4. associate-+l+ 97.2%

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

      5. associate-*r/ 97.2%

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

      6. distribute-lft-in 97.2%

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

      7. metadata-eval 97.2%

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

      8. associate-*r/ 97.2%

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

      9. metadata-eval 97.2%

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

   7. Simplified 97.2%

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

   8. Taylor expanded in z around 0 96.3%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5.3 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{z}}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-36} \lor \neg \left(z \leq 1.2 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.4e-36) (not (<= z 1.2e-70)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ -2.0 (/ (/ 2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e-36) || !(z <= 1.2e-70)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 / z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.4d-36)) .or. (.not. (z <= 1.2d-70))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e-36) || !(z <= 1.2e-70)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.4e-36) or not (z <= 1.2e-70):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = -2.0 + ((2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.4e-36) || !(z <= 1.2e-70))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.4e-36) || ~((z <= 1.2e-70)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = -2.0 + ((2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.4e-36], N[Not[LessEqual[z, 1.2e-70]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000003e-36 or 1.2000000000000001e-70 < z

   1. Initial program 82.0%

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

   3. Taylor expanded in z around inf 94.4%

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

      1. div-sub 94.4%

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

      2. sub-neg 94.4%

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

      3. *-inverses 94.4%

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

      4. metadata-eval 94.4%

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

      5. distribute-lft-in 94.4%

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

      6. associate-*r/ 94.4%

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

      7. metadata-eval 94.4%

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

      8. metadata-eval 94.4%

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

   5. Simplified 94.4%

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

   if -3.4000000000000003e-36 < z < 1.2000000000000001e-70

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. remove-double-neg 97.3%

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

      3. distribute-frac-neg 97.3%

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

      4. unsub-neg 97.3%

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

      5. *-commutative 97.3%

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

      6. associate-*r* 97.3%

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

      7. distribute-rgt1-in 97.3%

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

      8. associate-/l* 97.3%

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

      9. fma-neg 97.3%

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

      10. *-commutative 97.3%

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

      11. fma-define 97.3%

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

      12. *-commutative 97.3%

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

      13. distribute-frac-neg 97.3%

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

      14. remove-double-neg 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 97.3%

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

      1. sub-neg 97.3%

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

      2. +-commutative 97.3%

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

      3. metadata-eval 97.3%

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

      4. associate-+l+ 97.3%

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

      5. associate-*r/ 97.3%

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

      6. distribute-lft-in 97.3%

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

      7. metadata-eval 97.3%

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

      8. associate-*r/ 97.3%

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

      9. metadata-eval 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in z around 0 97.3%

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

   9. Taylor expanded in x around 0 84.0%

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

       1. sub-neg 84.0%

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

       2. associate-*r/ 84.0%

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

       3. metadata-eval 84.0%

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

       4. *-commutative 84.0%

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

       5. metadata-eval 84.0%

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

       6. +-commutative 84.0%

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

       7. associate-/r* 84.0%

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

   11. Simplified 84.0%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-36} \lor \neg \left(z \leq 1.2 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+45} \lor \neg \left(t \leq 2.35 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.3e+45) (not (<= t 2.35e-37)))
   (- (/ 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 <= -2.3e+45) || !(t <= 2.35e-37)) {
		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 <= (-2.3d+45)) .or. (.not. (t <= 2.35d-37))) 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 <= -2.3e+45) || !(t <= 2.35e-37)) {
		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 <= -2.3e+45) or not (t <= 2.35e-37):
		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 <= -2.3e+45) || !(t <= 2.35e-37))
		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 <= -2.3e+45) || ~((t <= 2.35e-37)))
		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, -2.3e+45], N[Not[LessEqual[t, 2.35e-37]], $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 < -2.30000000000000012e45 or 2.3500000000000001e-37 < t

   1. Initial program 80.2%

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

   3. Taylor expanded in t around inf 78.5%

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

   if -2.30000000000000012e45 < t < 2.3500000000000001e-37

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0 81.2%

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

      1. associate-*r/ 81.2%

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

      2. metadata-eval 81.2%

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

   5. Simplified 81.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+45} \lor \neg \left(t \leq 2.35 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-20} \lor \neg \left(t \leq 2.9 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.95e-20) (not (<= t 2.9e-38))) (- (/ x y) 2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.95e-20) || !(t <= 2.9e-38)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.95d-20)) .or. (.not. (t <= 2.9d-38))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.95e-20) || !(t <= 2.9e-38)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.95e-20) or not (t <= 2.9e-38):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.95e-20) || !(t <= 2.9e-38))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.95e-20) || ~((t <= 2.9e-38)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.95e-20], N[Not[LessEqual[t, 2.9e-38]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.94999999999999983e-20 or 2.89999999999999994e-38 < t

   1. Initial program 82.8%

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

   3. Taylor expanded in t around inf 73.4%

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

   if -2.94999999999999983e-20 < t < 2.89999999999999994e-38

   1. Initial program 96.4%

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

   3. Taylor expanded in t around 0 84.0%

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

      1. associate-*r/ 84.0%

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

      2. metadata-eval 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around inf 36.8%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-20} \lor \neg \left(t \leq 2.9 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-18}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.7:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.5e-18) -2.0 (if (<= t 0.7) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e-18) {
		tmp = -2.0;
	} else if (t <= 0.7) {
		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 <= (-3.5d-18)) then
        tmp = -2.0d0
    else if (t <= 0.7d0) 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 <= -3.5e-18) {
		tmp = -2.0;
	} else if (t <= 0.7) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.5e-18:
		tmp = -2.0
	elif t <= 0.7:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.5e-18)
		tmp = -2.0;
	elseif (t <= 0.7)
		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 <= -3.5e-18)
		tmp = -2.0;
	elseif (t <= 0.7)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.5e-18], -2.0, If[LessEqual[t, 0.7], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999999e-18 or 0.69999999999999996 < t

   1. Initial program 82.2%

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

      1. +-commutative 82.2%

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

      2. remove-double-neg 82.2%

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

      3. distribute-frac-neg 82.2%

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

      4. unsub-neg 82.2%

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

      5. *-commutative 82.2%

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

      6. associate-*r* 82.2%

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

      7. distribute-rgt1-in 82.2%

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

      8. associate-/l* 82.1%

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

      9. fma-neg 82.1%

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

      10. *-commutative 82.1%

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

      11. fma-define 82.1%

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

      12. *-commutative 82.1%

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

      13. distribute-frac-neg 82.1%

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

      14. remove-double-neg 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in t around inf 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. +-commutative 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-+l+ 99.9%

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

      5. associate-*r/ 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 99.4%

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

   9. Taylor expanded in x around 0 61.9%

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

       1. sub-neg 61.9%

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

       2. associate-*r/ 61.9%

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

       3. metadata-eval 61.9%

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

       4. *-commutative 61.9%

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

       5. metadata-eval 61.9%

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

       6. +-commutative 61.9%

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

       7. associate-/r* 61.9%

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

   11. Simplified 61.9%

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

   12. Taylor expanded in z around inf 36.8%

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

   if -3.4999999999999999e-18 < t < 0.69999999999999996

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 82.4%

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

      1. associate-*r/ 82.4%

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

      2. metadata-eval 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in z around inf 36.2%

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

Alternative 12: 20.0% 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 89.3%

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

   1. +-commutative 89.3%

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

   2. remove-double-neg 89.3%

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

   3. distribute-frac-neg 89.3%

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

   4. unsub-neg 89.3%

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

   5. *-commutative 89.3%

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

   6. associate-*r* 89.3%

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

   7. distribute-rgt1-in 89.3%

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

   8. associate-/l* 89.2%

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

   9. fma-neg 89.2%

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

   10. *-commutative 89.2%

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

   11. fma-define 89.2%

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

   12. *-commutative 89.2%

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

   13. distribute-frac-neg 89.2%

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

   14. remove-double-neg 89.2%

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

3. Simplified 89.2%

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

5. Taylor expanded in t around inf 98.3%

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

   1. sub-neg 98.3%

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

   2. +-commutative 98.3%

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

   3. metadata-eval 98.3%

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

   4. associate-+l+ 98.3%

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

   5. associate-*r/ 98.3%

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

   6. distribute-lft-in 98.3%

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

   7. metadata-eval 98.3%

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

   8. associate-*r/ 98.3%

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

   9. metadata-eval 98.3%

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

7. Simplified 98.3%

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

8. Taylor expanded in z around 0 80.9%

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

9. Taylor expanded in x around 0 54.7%

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

    1. sub-neg 54.7%

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

    2. associate-*r/ 54.7%

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

    3. metadata-eval 54.7%

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

    4. *-commutative 54.7%

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

    5. metadata-eval 54.7%

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

    6. +-commutative 54.7%

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

    7. associate-/r* 54.7%

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

11. Simplified 54.7%

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

12. Taylor expanded in z around inf 19.9%

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

Developer Target 1: 99.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024116 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

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