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

Percentage Accurate: 86.8% → 99.1%

Time: 15.2s

Alternatives: 14

Speedup: 1.3×

• 24.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

3. Taylor expanded in t around 0 99.9%

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

4. Taylor expanded in z around 0 99.9%

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

   1. associate-*r/ 99.9%

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

   2. metadata-eval 99.9%

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

   3. associate-/r* 99.9%

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

   4. associate-*r/ 99.9%

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

   5. metadata-eval 99.9%

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

   6. +-commutative 99.9%

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

6. Simplified 99.9%

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

7. Final simplification 99.9%

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

Alternative 2: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-88}:\\ \;\;\;\;2 \cdot \frac{1}{t \cdot z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+68} \lor \neg \left(z \leq 3.3 \cdot 10^{+162}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -1.55e-75)
     t_1
     (if (<= z 4.5e-88)
       (* 2.0 (/ 1.0 (* t z)))
       (if (or (<= z 4.3e+68) (not (<= z 3.3e+162)))
         t_1
         (+ (/ 2.0 t) -2.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -1.55e-75) {
		tmp = t_1;
	} else if (z <= 4.5e-88) {
		tmp = 2.0 * (1.0 / (t * z));
	} else if ((z <= 4.3e+68) || !(z <= 3.3e+162)) {
		tmp = t_1;
	} else {
		tmp = (2.0 / t) + -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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-1.55d-75)) then
        tmp = t_1
    else if (z <= 4.5d-88) then
        tmp = 2.0d0 * (1.0d0 / (t * z))
    else if ((z <= 4.3d+68) .or. (.not. (z <= 3.3d+162))) then
        tmp = t_1
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    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 <= -1.55e-75) {
		tmp = t_1;
	} else if (z <= 4.5e-88) {
		tmp = 2.0 * (1.0 / (t * z));
	} else if ((z <= 4.3e+68) || !(z <= 3.3e+162)) {
		tmp = t_1;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -1.55e-75:
		tmp = t_1
	elif z <= 4.5e-88:
		tmp = 2.0 * (1.0 / (t * z))
	elif (z <= 4.3e+68) or not (z <= 3.3e+162):
		tmp = t_1
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -1.55e-75)
		tmp = t_1;
	elseif (z <= 4.5e-88)
		tmp = Float64(2.0 * Float64(1.0 / Float64(t * z)));
	elseif ((z <= 4.3e+68) || !(z <= 3.3e+162))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -1.55e-75)
		tmp = t_1;
	elseif (z <= 4.5e-88)
		tmp = 2.0 * (1.0 / (t * z));
	elseif ((z <= 4.3e+68) || ~((z <= 3.3e+162)))
		tmp = t_1;
	else
		tmp = (2.0 / t) + -2.0;
	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, -1.55e-75], t$95$1, If[LessEqual[z, 4.5e-88], N[(2.0 * N[(1.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.3e+68], N[Not[LessEqual[z, 3.3e+162]], $MachinePrecision]], t$95$1, N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000003e-75 or 4.49999999999999991e-88 < z < 4.3000000000000001e68 or 3.29999999999999987e162 < z

   1. Initial program 75.9%

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

   3. Taylor expanded in t around inf 71.1%

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

   if -1.55000000000000003e-75 < z < 4.49999999999999991e-88

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. remove-double-neg 99.8%

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

      3. distribute-frac-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r* 99.8%

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

      7. distribute-rgt1-in 99.8%

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

      8. associate-/l* 99.7%

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

      9. fma-neg 99.7%

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

      10. *-commutative 99.7%

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

      11. fma-define 99.7%

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

      12. *-commutative 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. remove-double-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 73.7%

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

   6. Taylor expanded in z around 0 73.7%

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

      1. *-commutative 73.7%

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

   8. Simplified 73.7%

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

   if 4.3000000000000001e68 < z < 3.29999999999999987e162

   1. Initial program 84.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 83.0%

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

      1. sub-neg 83.0%

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

      2. associate-*r/ 83.0%

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

      3. metadata-eval 83.0%

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

      4. metadata-eval 83.0%

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

   9. Simplified 83.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-88}:\\ \;\;\;\;2 \cdot \frac{1}{t \cdot z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+68} \lor \neg \left(z \leq 3.3 \cdot 10^{+162}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58} \lor \neg \left(\frac{x}{y} \leq 100000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+58) (not (<= (/ x y) 100000000000.0)))
   (+ (/ x y) (/ 2.0 (* t z)))
   (- (+ (/ 2.0 t) (/ (/ 2.0 t) z)) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+58) || !((x / y) <= 100000000000.0)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = ((2.0 / t) + ((2.0 / t) / z)) - 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 (((x / y) <= (-4d+58)) .or. (.not. ((x / y) <= 100000000000.0d0))) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = ((2.0d0 / t) + ((2.0d0 / t) / z)) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+58) || !((x / y) <= 100000000000.0)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = ((2.0 / t) + ((2.0 / t) / z)) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e+58) or not ((x / y) <= 100000000000.0):
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = ((2.0 / t) + ((2.0 / t) / z)) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e+58) || !(Float64(x / y) <= 100000000000.0))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(2.0 / t) + Float64(Float64(2.0 / t) / z)) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4e+58) || ~(((x / y) <= 100000000000.0)))
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = ((2.0 / t) + ((2.0 / t) / z)) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4e+58], N[Not[LessEqual[N[(x / y), $MachinePrecision], 100000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 / t), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.99999999999999978e58 or 1e11 < (/.f64 x y)

   1. Initial program 86.4%

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

   3. Taylor expanded in z around 0 95.0%

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

   if -3.99999999999999978e58 < (/.f64 x y) < 1e11

   1. Initial program 84.6%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in x around 0 96.7%

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

      1. associate-*r/ 96.7%

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

      2. metadata-eval 96.7%

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

      3. associate-*r/ 96.7%

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

      4. metadata-eval 96.7%

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

      5. associate-/r* 96.7%

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

   6. Simplified 96.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58} \lor \neg \left(\frac{x}{y} \leq 100000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.06 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -3.1 \cdot 10^{-174}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.054:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.06e+58)
   (/ x y)
   (if (<= (/ x y) -3.1e-174) (/ 2.0 t) (if (<= (/ x y) 0.054) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.06e+58) {
		tmp = x / y;
	} else if ((x / y) <= -3.1e-174) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 0.054) {
		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) <= (-1.06d+58)) then
        tmp = x / y
    else if ((x / y) <= (-3.1d-174)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 0.054d0) 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) <= -1.06e+58) {
		tmp = x / y;
	} else if ((x / y) <= -3.1e-174) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 0.054) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.06e+58:
		tmp = x / y
	elif (x / y) <= -3.1e-174:
		tmp = 2.0 / t
	elif (x / y) <= 0.054:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.06e+58)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -3.1e-174)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 0.054)
		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) <= -1.06e+58)
		tmp = x / y;
	elseif ((x / y) <= -3.1e-174)
		tmp = 2.0 / t;
	elseif ((x / y) <= 0.054)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.06e+58], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -3.1e-174], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.054], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.05999999999999997e58 or 0.0539999999999999994 < (/.f64 x y)

   1. Initial program 86.3%

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

   3. Taylor expanded in x around inf 74.3%

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

   if -1.05999999999999997e58 < (/.f64 x y) < -3.0999999999999999e-174

   1. Initial program 94.2%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in z around inf 59.5%

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

      1. associate-*r/ 59.5%

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

      2. metadata-eval 59.5%

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

      3. +-commutative 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in t around 0 36.8%

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

   if -3.0999999999999999e-174 < (/.f64 x y) < 0.0539999999999999994

   1. Initial program 81.3%

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

   3. Taylor expanded in t around inf 44.4%

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

   4. Taylor expanded in x around 0 43.0%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.06 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -3.1 \cdot 10^{-174}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.054:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.5 \cdot 10^{+57} \lor \neg \left(\frac{x}{y} \leq 67000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6.5e+57) (not (<= (/ x y) 67000000000.0)))
   (+ (/ x y) (/ 2.0 (* t z)))
   (- (/ (+ 2.0 (/ 2.0 z)) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.5e+57) || !((x / y) <= 67000000000.0)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) - 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 (((x / y) <= (-6.5d+57)) .or. (.not. ((x / y) <= 67000000000.0d0))) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.5e+57) || !((x / y) <= 67000000000.0)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -6.5e+57) or not ((x / y) <= 67000000000.0):
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = ((2.0 + (2.0 / z)) / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -6.5e+57) || !(Float64(x / y) <= 67000000000.0))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -6.5e+57) || ~(((x / y) <= 67000000000.0)))
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = ((2.0 + (2.0 / z)) / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -6.5e+57], N[Not[LessEqual[N[(x / y), $MachinePrecision], 67000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.4999999999999997e57 or 6.7e10 < (/.f64 x y)

   1. Initial program 86.4%

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

   3. Taylor expanded in z around 0 95.0%

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

   if -6.4999999999999997e57 < (/.f64 x y) < 6.7e10

   1. Initial program 84.6%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in t around 0 96.7%

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

      1. associate-*r/ 96.7%

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

      2. metadata-eval 96.7%

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

   6. Simplified 96.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.5 \cdot 10^{+57} \lor \neg \left(\frac{x}{y} \leq 67000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.2 \cdot 10^{+141}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 15:\\ \;\;\;\;\frac{\frac{2}{t}}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4.2e+141)
   (/ x y)
   (if (<= (/ x y) 15.0) (- (/ (/ 2.0 t) z) 2.0) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.2e+141) {
		tmp = x / y;
	} else if ((x / y) <= 15.0) {
		tmp = ((2.0 / t) / z) - 2.0;
	} else {
		tmp = (x / y) - 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 ((x / y) <= (-4.2d+141)) then
        tmp = x / y
    else if ((x / y) <= 15.0d0) then
        tmp = ((2.0d0 / t) / z) - 2.0d0
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.2e+141) {
		tmp = x / y;
	} else if ((x / y) <= 15.0) {
		tmp = ((2.0 / t) / z) - 2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4.2e+141:
		tmp = x / y
	elif (x / y) <= 15.0:
		tmp = ((2.0 / t) / z) - 2.0
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4.2e+141)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 15.0)
		tmp = Float64(Float64(Float64(2.0 / t) / z) - 2.0);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4.2e+141)
		tmp = x / y;
	elseif ((x / y) <= 15.0)
		tmp = ((2.0 / t) / z) - 2.0;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4.2e+141], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 15.0], N[(N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.1999999999999997e141

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf 90.4%

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

   if -4.1999999999999997e141 < (/.f64 x y) < 15

   1. Initial program 84.6%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in z around 0 72.8%

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

      1. associate-/r* 72.8%

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

   6. Simplified 72.8%

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

   if 15 < (/.f64 x y)

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 80.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.2 \cdot 10^{+141}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 15:\\ \;\;\;\;\frac{\frac{2}{t}}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.5 \cdot 10^{+57} \lor \neg \left(\frac{x}{y} \leq 1950000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6.5e+57) (not (<= (/ x y) 1950000000000.0)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.5e+57) || !((x / y) <= 1950000000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -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 (((x / y) <= (-6.5d+57)) .or. (.not. ((x / y) <= 1950000000000.0d0))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.5e+57) || !((x / y) <= 1950000000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -6.5e+57) or not ((x / y) <= 1950000000000.0):
		tmp = x / y
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -6.5e+57) || !(Float64(x / y) <= 1950000000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -6.5e+57) || ~(((x / y) <= 1950000000000.0)))
		tmp = x / y;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -6.5e+57], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1950000000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.4999999999999997e57 or 1.95e12 < (/.f64 x y)

   1. Initial program 86.4%

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

   3. Taylor expanded in x around inf 78.6%

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

   if -6.4999999999999997e57 < (/.f64 x y) < 1.95e12

   1. Initial program 84.6%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in z around inf 62.4%

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

      1. associate-*r/ 62.4%

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

      2. metadata-eval 62.4%

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

      3. +-commutative 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in x around 0 59.3%

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

      1. sub-neg 59.3%

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

      2. associate-*r/ 59.3%

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

      3. metadata-eval 59.3%

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

      4. metadata-eval 59.3%

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

   9. Simplified 59.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.5 \cdot 10^{+57} \lor \neg \left(\frac{x}{y} \leq 1950000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-61} \lor \neg \left(z \leq 3.15 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e-61) (not (<= z 3.15e-86)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (- (/ (/ 2.0 t) z) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e-61) || !(z <= 3.15e-86)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((2.0 / t) / z) - 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 ((z <= (-6d-61)) .or. (.not. (z <= 3.15d-86))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = ((2.0d0 / t) / z) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e-61) || !(z <= 3.15e-86)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((2.0 / t) / z) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e-61) or not (z <= 3.15e-86):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = ((2.0 / t) / z) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e-61) || !(z <= 3.15e-86))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(Float64(2.0 / t) / z) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6e-61) || ~((z <= 3.15e-86)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = ((2.0 / t) / z) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e-61], N[Not[LessEqual[z, 3.15e-86]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000024e-61 or 3.15e-86 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 94.1%

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

      1. div-sub 94.1%

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

      2. sub-neg 94.1%

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

      3. *-inverses 94.1%

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

      4. metadata-eval 94.1%

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

      5. distribute-lft-in 94.1%

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

      6. associate-*r/ 94.1%

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

      7. metadata-eval 94.1%

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

      8. metadata-eval 94.1%

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

   5. Simplified 94.1%

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

   if -6.00000000000000024e-61 < z < 3.15e-86

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.8%

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

   4. Taylor expanded in z around 0 77.9%

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

      1. associate-/r* 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-61} \lor \neg \left(z \leq 3.15 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-5} \lor \neg \left(z \leq 4.1 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.9e-5) (not (<= z 4.1e-57)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.9e-5) || !(z <= 4.1e-57)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.9d-5)) .or. (.not. (z <= 4.1d-57))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (x / y) + (2.0d0 / (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.9e-5) || !(z <= 4.1e-57)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.9e-5) or not (z <= 4.1e-57):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.9e-5) || !(z <= 4.1e-57))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.9e-5) || ~((z <= 4.1e-57)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.9e-5], N[Not[LessEqual[z, 4.1e-57]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9e-5 or 4.1000000000000001e-57 < z

   1. Initial program 73.1%

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

   3. Taylor expanded in z around inf 98.1%

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

      1. div-sub 98.1%

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

      2. sub-neg 98.1%

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

      3. *-inverses 98.1%

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

      4. metadata-eval 98.1%

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

      5. distribute-lft-in 98.1%

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

      6. associate-*r/ 98.1%

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

      7. metadata-eval 98.1%

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

      8. metadata-eval 98.1%

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

   5. Simplified 98.1%

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

   if -4.9e-5 < z < 4.1000000000000001e-57

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 92.8%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-5} \lor \neg \left(z \leq 4.1 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 59000000000:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6.5e+57)
   (/ x y)
   (if (<= (/ x y) 59000000000.0) (+ (/ 2.0 t) -2.0) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6.5e+57) {
		tmp = x / y;
	} else if ((x / y) <= 59000000000.0) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) - 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 ((x / y) <= (-6.5d+57)) then
        tmp = x / y
    else if ((x / y) <= 59000000000.0d0) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6.5e+57) {
		tmp = x / y;
	} else if ((x / y) <= 59000000000.0) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -6.5e+57:
		tmp = x / y
	elif (x / y) <= 59000000000.0:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -6.5e+57)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 59000000000.0)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -6.5e+57)
		tmp = x / y;
	elseif ((x / y) <= 59000000000.0)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -6.5e+57], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 59000000000.0], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -6.4999999999999997e57

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 70.3%

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

   if -6.4999999999999997e57 < (/.f64 x y) < 5.9e10

   1. Initial program 84.6%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in z around inf 62.4%

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

      1. associate-*r/ 62.4%

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

      2. metadata-eval 62.4%

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

      3. +-commutative 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in x around 0 59.3%

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

      1. sub-neg 59.3%

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

      2. associate-*r/ 59.3%

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

      3. metadata-eval 59.3%

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

      4. metadata-eval 59.3%

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

   9. Simplified 59.3%

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

   if 5.9e10 < (/.f64 x y)

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf 85.6%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 59000000000:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-20} \lor \neg \left(t \leq 8.2\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.2e-20) (not (<= t 8.2)))
   (- (/ 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 <= -9.2e-20) || !(t <= 8.2)) {
		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 <= (-9.2d-20)) .or. (.not. (t <= 8.2d0))) 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 <= -9.2e-20) || !(t <= 8.2)) {
		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 <= -9.2e-20) or not (t <= 8.2):
		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 <= -9.2e-20) || !(t <= 8.2))
		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 <= -9.2e-20) || ~((t <= 8.2)))
		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, -9.2e-20], N[Not[LessEqual[t, 8.2]], $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 < -9.1999999999999997e-20 or 8.1999999999999993 < t

   1. Initial program 72.7%

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

   3. Taylor expanded in t around inf 83.9%

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

   if -9.1999999999999997e-20 < t < 8.1999999999999993

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 81.4%

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

      1. associate-*r/ 81.4%

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

      2. metadata-eval 81.4%

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

   5. Simplified 81.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-20} \lor \neg \left(t \leq 8.2\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-19}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.95:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.95e-19) -2.0 (if (<= t 0.95) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.95e-19) {
		tmp = -2.0;
	} else if (t <= 0.95) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.95d-19)) then
        tmp = -2.0d0
    else if (t <= 0.95d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.95e-19) {
		tmp = -2.0;
	} else if (t <= 0.95) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.95e-19:
		tmp = -2.0
	elif t <= 0.95:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.95e-19)
		tmp = -2.0;
	elseif (t <= 0.95)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.95e-19)
		tmp = -2.0;
	elseif (t <= 0.95)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.95e-19], -2.0, If[LessEqual[t, 0.95], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1.94999999999999998e-19 or 0.94999999999999996 < t

   1. Initial program 72.9%

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

   3. Taylor expanded in t around inf 82.6%

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

   4. Taylor expanded in x around 0 37.1%

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

   if -1.94999999999999998e-19 < t < 0.94999999999999996

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.9%

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

   4. Taylor expanded in z around inf 58.8%

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

      1. associate-*r/ 58.8%

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

      2. metadata-eval 58.8%

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

      3. +-commutative 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in t around 0 35.3%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-19}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.95:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.1% 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 85.4%

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

   1. +-commutative 85.4%

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

   2. remove-double-neg 85.4%

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

   3. distribute-frac-neg 85.4%

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

   4. unsub-neg 85.4%

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

   5. *-commutative 85.4%

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

   6. associate-*r* 85.4%

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

   7. distribute-rgt1-in 85.4%

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

   8. associate-/l* 85.3%

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

   9. fma-neg 85.3%

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

   10. *-commutative 85.3%

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

   11. fma-define 85.3%

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

   12. *-commutative 85.3%

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

   13. distribute-frac-neg 85.3%

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

   14. remove-double-neg 85.3%

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

3. Simplified 85.3%

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

5. Taylor expanded in t around inf 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. Final simplification 99.9%

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

Alternative 14: 19.6% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := -2.0

Derivation

1. Initial program 85.4%

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

3. Taylor expanded in t around inf 55.9%

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

4. Taylor expanded in x around 0 21.1%

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

5. Final simplification 21.1%

   \[\leadsto -2 \]
6. Add Preprocessing

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

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