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

Percentage Accurate: 86.1% → 99.3%

Time: 8.7s

Alternatives: 10

Speedup: 0.9×

• 23.2% 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: 86.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (* 2.0 z) (- 1.0 t))) (* z t)))))
   (if (<= t_1 INFINITY) t_1 (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(2.0 * z) * Float64(1.0 - t))) / Float64(z * t)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))) < +inf.0

   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

   if +inf.0 < (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)))

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 79.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+73} \lor \neg \left(t \leq 2.55 \cdot 10^{+88}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -5.6e+28)
     t_1
     (if (<= t 2e+27)
       (/ (+ 2.0 (/ 2.0 z)) t)
       (if (or (<= t 1.6e+73) (not (<= t 2.55e+88))) t_1 (/ (/ 2.0 t) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -5.6e+28) {
		tmp = t_1;
	} else if (t <= 2e+27) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if ((t <= 1.6e+73) || !(t <= 2.55e+88)) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-5.6d+28)) then
        tmp = t_1
    else if (t <= 2d+27) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else if ((t <= 1.6d+73) .or. (.not. (t <= 2.55d+88))) then
        tmp = t_1
    else
        tmp = (2.0d0 / t) / z
    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 (t <= -5.6e+28) {
		tmp = t_1;
	} else if (t <= 2e+27) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if ((t <= 1.6e+73) || !(t <= 2.55e+88)) {
		tmp = t_1;
	} else {
		tmp = (2.0 / t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -5.6e+28:
		tmp = t_1
	elif t <= 2e+27:
		tmp = (2.0 + (2.0 / z)) / t
	elif (t <= 1.6e+73) or not (t <= 2.55e+88):
		tmp = t_1
	else:
		tmp = (2.0 / t) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -5.6e+28)
		tmp = t_1;
	elseif (t <= 2e+27)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	elseif ((t <= 1.6e+73) || !(t <= 2.55e+88))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 / t) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -5.6e+28)
		tmp = t_1;
	elseif (t <= 2e+27)
		tmp = (2.0 + (2.0 / z)) / t;
	elseif ((t <= 1.6e+73) || ~((t <= 2.55e+88)))
		tmp = t_1;
	else
		tmp = (2.0 / t) / z;
	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[t, -5.6e+28], t$95$1, If[LessEqual[t, 2e+27], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[t, 1.6e+73], N[Not[LessEqual[t, 2.55e+88]], $MachinePrecision]], t$95$1, N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.6000000000000003e28 or 2e27 < t < 1.59999999999999991e73 or 2.5499999999999999e88 < 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 85.8%

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

   if -5.6000000000000003e28 < t < 2e27

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 0 74.4%

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

      1. associate-*r/ 74.4%

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

      2. metadata-eval 74.4%

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

   5. Simplified 74.4%

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

   if 1.59999999999999991e73 < t < 2.5499999999999999e88

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/r* 100.0%

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

      3. frac-add 83.5%

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

      4. +-commutative 83.5%

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

      5. fma-define 83.5%

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

      6. *-commutative 83.5%

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

   4. Applied egg-rr 83.5%

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

   5. Taylor expanded in z around 0 83.7%

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

      1. associate-*r/ 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in y around inf 99.7%

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

      1. associate-/r* 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+73} \lor \neg \left(t \leq 2.55 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -22000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 9.2 \cdot 10^{-72}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 4.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -22000000000.0)
   (/ x y)
   (if (<= (/ x y) 9.2e-72) -2.0 (if (<= (/ x y) 4.8e+28) (/ 2.0 t) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -22000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 9.2e-72) {
		tmp = -2.0;
	} else if ((x / y) <= 4.8e+28) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-22000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 9.2d-72) then
        tmp = -2.0d0
    else if ((x / y) <= 4.8d+28) then
        tmp = 2.0d0 / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -22000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 9.2e-72) {
		tmp = -2.0;
	} else if ((x / y) <= 4.8e+28) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -22000000000.0:
		tmp = x / y
	elif (x / y) <= 9.2e-72:
		tmp = -2.0
	elif (x / y) <= 4.8e+28:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -22000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 9.2e-72)
		tmp = -2.0;
	elseif (Float64(x / y) <= 4.8e+28)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -22000000000.0)
		tmp = x / y;
	elseif ((x / y) <= 9.2e-72)
		tmp = -2.0;
	elseif ((x / y) <= 4.8e+28)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -22000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 9.2e-72], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 4.8e+28], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.2e10 or 4.79999999999999962e28 < (/.f64 x y)

   1. Initial program 84.1%

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

   3. Taylor expanded in x around inf 67.0%

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

   if -2.2e10 < (/.f64 x y) < 9.19999999999999978e-72

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-/r* 80.1%

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

      3. frac-add 64.3%

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

      4. +-commutative 64.3%

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

      5. fma-define 64.3%

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

      6. *-commutative 64.3%

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

   4. Applied egg-rr 64.3%

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

   5. Taylor expanded in y around -inf 90.0%

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

   6. Taylor expanded in t around inf 31.9%

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

   if 9.19999999999999978e-72 < (/.f64 x y) < 4.79999999999999962e28

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 79.0%

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

      1. associate-*r/ 79.0%

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

      2. metadata-eval 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in z around inf 54.9%

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

Alternative 4: 91.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{-9} \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.7e-9) (not (<= z 0.00018)))
   (+ (/ 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 <= -6.7e-9) || !(z <= 0.00018)) {
		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 <= (-6.7d-9)) .or. (.not. (z <= 0.00018d0))) 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 <= -6.7e-9) || !(z <= 0.00018)) {
		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 <= -6.7e-9) or not (z <= 0.00018):
		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 <= -6.7e-9) || !(z <= 0.00018))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.7e-9) || ~((z <= 0.00018)))
		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, -6.7e-9], N[Not[LessEqual[z, 0.00018]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.69999999999999961e-9 or 1.80000000000000011e-4 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf 99.2%

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

      1. div-sub 99.2%

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

      2. sub-neg 99.2%

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

      3. *-inverses 99.2%

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

      4. metadata-eval 99.2%

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

      5. distribute-lft-in 99.2%

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

      6. associate-*r/ 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   5. Simplified 99.2%

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

   if -6.69999999999999961e-9 < z < 1.80000000000000011e-4

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0 86.4%

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

      1. associate-/r* 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{-9} \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-84} \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{z + 1}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.05e-84) (not (<= z 0.00018)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (* 2.0 (/ (+ z 1.0) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-84) || !(z <= 0.00018)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = 2.0 * ((z + 1.0) / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.05d-84)) .or. (.not. (z <= 0.00018d0))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = 2.0d0 * ((z + 1.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-84) || !(z <= 0.00018)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = 2.0 * ((z + 1.0) / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.05e-84) or not (z <= 0.00018):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = 2.0 * ((z + 1.0) / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.05e-84) || !(z <= 0.00018))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(2.0 * Float64(Float64(z + 1.0) / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05e-84) || ~((z <= 0.00018)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = 2.0 * ((z + 1.0) / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05e-84], N[Not[LessEqual[z, 0.00018]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z + 1.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999999e-84 or 1.80000000000000011e-4 < z

   1. Initial program 80.0%

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

   3. Taylor expanded in z around inf 95.6%

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

      1. div-sub 95.6%

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

      2. sub-neg 95.6%

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

      3. *-inverses 95.6%

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

      4. metadata-eval 95.6%

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

      5. distribute-lft-in 95.6%

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

      6. associate-*r/ 95.6%

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

      7. metadata-eval 95.6%

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

      8. metadata-eval 95.6%

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

   5. Simplified 95.6%

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

   if -1.04999999999999999e-84 < z < 1.80000000000000011e-4

   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 0 73.8%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-84} \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{z + 1}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.1 \cdot 10^{+25} \lor \neg \left(\frac{x}{y} \leq 1.5 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.1e+25) (not (<= (/ x y) 1.5e+28)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.1e+25) || !((x / y) <= 1.5e+28)) {
		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) <= (-1.1d+25)) .or. (.not. ((x / y) <= 1.5d+28))) 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) <= -1.1e+25) || !((x / y) <= 1.5e+28)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.1e+25) or not ((x / y) <= 1.5e+28):
		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) <= -1.1e+25) || !(Float64(x / y) <= 1.5e+28))
		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) <= -1.1e+25) || ~(((x / y) <= 1.5e+28)))
		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], -1.1e+25], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.5e+28]], $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) < -1.1e25 or 1.5e28 < (/.f64 x y)

   1. Initial program 83.8%

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

   3. Taylor expanded in x around inf 68.1%

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

   if -1.1e25 < (/.f64 x y) < 1.5e28

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. associate-/r* 79.3%

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

      3. frac-add 65.4%

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

      4. +-commutative 65.4%

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

      5. fma-define 65.4%

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

      6. *-commutative 65.4%

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

   4. Applied egg-rr 65.4%

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

   5. Taylor expanded in y around -inf 90.3%

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

   6. Taylor expanded in z around inf 53.8%

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

      1. div-sub 53.8%

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

      2. sub-neg 53.8%

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

      3. *-inverses 53.8%

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

      4. metadata-eval 53.8%

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

      5. distribute-lft-in 53.8%

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

      6. metadata-eval 53.8%

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

      7. associate-*r/ 53.8%

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

      8. metadata-eval 53.8%

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

   8. Simplified 53.8%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.1 \cdot 10^{+25} \lor \neg \left(\frac{x}{y} \leq 1.5 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 0.00022:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e-85)
   (- (/ x y) 2.0)
   (if (<= z 0.00022) (/ (/ 2.0 t) z) (+ (/ 2.0 t) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e-85) {
		tmp = (x / y) - 2.0;
	} else if (z <= 0.00022) {
		tmp = (2.0 / t) / z;
	} 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 (z <= (-2.7d-85)) then
        tmp = (x / y) - 2.0d0
    else if (z <= 0.00022d0) then
        tmp = (2.0d0 / t) / z
    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 (z <= -2.7e-85) {
		tmp = (x / y) - 2.0;
	} else if (z <= 0.00022) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e-85:
		tmp = (x / y) - 2.0
	elif z <= 0.00022:
		tmp = (2.0 / t) / z
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e-85)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (z <= 0.00022)
		tmp = Float64(Float64(2.0 / t) / z);
	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 (z <= -2.7e-85)
		tmp = (x / y) - 2.0;
	elseif (z <= 0.00022)
		tmp = (2.0 / t) / z;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e-85], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[z, 0.00022], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000001e-85

   1. Initial program 79.4%

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

   3. Taylor expanded in t around inf 73.0%

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

   if -2.7000000000000001e-85 < z < 2.20000000000000008e-4

   1. Initial program 97.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing
   3. 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. associate-/r* 97.3%

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

      3. frac-add 84.1%

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

      4. +-commutative 84.1%

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

      5. fma-define 84.1%

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

      6. *-commutative 84.1%

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

   4. Applied egg-rr 84.1%

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

   5. Taylor expanded in z around 0 73.2%

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

      1. associate-*r/ 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in y around inf 73.2%

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

      1. associate-/r* 73.3%

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

   10. Simplified 73.3%

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

   if 2.20000000000000008e-4 < z

   1. Initial program 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-/r* 53.0%

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

      3. frac-add 40.5%

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

      4. +-commutative 40.5%

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

      5. fma-define 40.5%

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

      6. *-commutative 40.5%

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

   4. Applied egg-rr 40.5%

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

   5. Taylor expanded in y around -inf 54.1%

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

   6. Taylor expanded in z around inf 58.6%

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

      1. div-sub 58.6%

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

      2. sub-neg 58.6%

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

      3. *-inverses 58.6%

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

      4. metadata-eval 58.6%

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

      5. distribute-lft-in 58.6%

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

      6. metadata-eval 58.6%

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

      7. associate-*r/ 58.6%

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

      8. metadata-eval 58.6%

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

   8. Simplified 58.6%

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

Alternative 8: 62.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 0.00115:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.2e-84)
   (- (/ x y) 2.0)
   (if (<= z 0.00115) (/ 2.0 (* z t)) (+ (/ 2.0 t) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.2e-84) {
		tmp = (x / y) - 2.0;
	} else if (z <= 0.00115) {
		tmp = 2.0 / (z * t);
	} 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 (z <= (-3.2d-84)) then
        tmp = (x / y) - 2.0d0
    else if (z <= 0.00115d0) then
        tmp = 2.0d0 / (z * t)
    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 (z <= -3.2e-84) {
		tmp = (x / y) - 2.0;
	} else if (z <= 0.00115) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.2e-84:
		tmp = (x / y) - 2.0
	elif z <= 0.00115:
		tmp = 2.0 / (z * t)
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.2e-84)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (z <= 0.00115)
		tmp = Float64(2.0 / Float64(z * t));
	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 (z <= -3.2e-84)
		tmp = (x / y) - 2.0;
	elseif (z <= 0.00115)
		tmp = 2.0 / (z * t);
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.2e-84], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[z, 0.00115], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1999999999999999e-84

   1. Initial program 79.4%

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

   3. Taylor expanded in t around inf 73.0%

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

   if -3.1999999999999999e-84 < z < 0.00115

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 86.3%

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

      1. associate-/r* 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in x around 0 73.2%

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

   if 0.00115 < z

   1. Initial program 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-/r* 53.0%

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

      3. frac-add 40.5%

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

      4. +-commutative 40.5%

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

      5. fma-define 40.5%

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

      6. *-commutative 40.5%

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

   4. Applied egg-rr 40.5%

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

   5. Taylor expanded in y around -inf 54.1%

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

   6. Taylor expanded in z around inf 58.6%

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

      1. div-sub 58.6%

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

      2. sub-neg 58.6%

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

      3. *-inverses 58.6%

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

      4. metadata-eval 58.6%

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

      5. distribute-lft-in 58.6%

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

      6. metadata-eval 58.6%

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

      7. associate-*r/ 58.6%

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

      8. metadata-eval 58.6%

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

   8. Simplified 58.6%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 0.00115:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 27000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 27000000.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 27000000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.0d0)) then
        tmp = -2.0d0
    else if (t <= 27000000.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 27000000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.0:
		tmp = -2.0
	elif t <= 27000000.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 27000000.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 27000000.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.0], -2.0, If[LessEqual[t, 27000000.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 2.7e7 < t

   1. Initial program 76.0%

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

      1. +-commutative 76.0%

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

      2. associate-/r* 81.7%

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

      3. frac-add 62.8%

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

      4. +-commutative 62.8%

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

      5. fma-define 62.8%

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

      6. *-commutative 62.8%

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

   4. Applied egg-rr 62.8%

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

   5. Taylor expanded in y around -inf 47.3%

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

   6. Taylor expanded in t around inf 35.2%

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

   if -1 < t < 2.7e7

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0 76.1%

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

      1. associate-*r/ 76.1%

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

      2. metadata-eval 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in z around inf 29.8%

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

Alternative 10: 20.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.1%

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

   1. +-commutative 88.1%

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

   2. associate-/r* 77.8%

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

   3. frac-add 63.9%

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

   4. +-commutative 63.9%

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

   5. fma-define 63.9%

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

   6. *-commutative 63.9%

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

4. Applied egg-rr 63.9%

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

5. Taylor expanded in y around -inf 64.1%

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

6. Taylor expanded in t around inf 17.0%

   \[\leadsto \color{blue}{-2} \]
7. 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 2024100 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

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