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

Percentage Accurate: 86.2% → 99.4%

Time: 12.5s

Alternatives: 13

Speedup: 0.6×

• 24.1% 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: 86.2% 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: 99.4% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (- 1.0 t) (* 2.0 z))) (* 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 + ((1.0 - t) * (2.0 * z))) / (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 + ((1.0 - t) * (2.0 * z))) / (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 + ((1.0 - t) * (2.0 * z))) / (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(1.0 - t) * Float64(2.0 * z))) / 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 + ((1.0 - t) * (2.0 * z))) / (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[(1.0 - t), $MachinePrecision] * N[(2.0 * z), $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 99.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 97.7%

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

4. Final simplification 99.5%

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

Alternative 2: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+85} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+85) (not (<= (/ x y) 2e+42)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))
   (/ (+ (+ 2.0 (/ 2.0 z)) (* t (+ (/ x y) -2.0))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+85) || !((x / y) <= 2e+42)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d+85)) .or. (.not. ((x / y) <= 2d+42))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) + (t * ((x / y) + (-2.0d0)))) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+85) || !((x / y) <= 2e+42)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+85) or not ((x / y) <= 2e+42):
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	else:
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+85) || !(Float64(x / y) <= 2e+42))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) + Float64(t * Float64(Float64(x / y) + -2.0))) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+85) || ~(((x / y) <= 2e+42)))
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	else
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+85], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+42]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e85 or 2.00000000000000009e42 < (/.f64 x y)

   1. Initial program 84.2%

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

   3. Taylor expanded in t around 0 98.9%

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

   if -1e85 < (/.f64 x y) < 2.00000000000000009e42

   1. Initial program 82.5%

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

   3. Taylor expanded in t around 0 99.3%

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

      1. associate-+r+ 99.3%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+85} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -400000000 \lor \neg \left(\frac{x}{y} \leq 10000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -400000000.0) (not (<= (/ x y) 10000000.0)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))
   (/ (+ (+ 2.0 (/ 2.0 z)) (* t -2.0)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -400000000.0) || !((x / y) <= 10000000.0)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * -2.0)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-400000000.0d0)) .or. (.not. ((x / y) <= 10000000.0d0))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) + (t * (-2.0d0))) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -400000000.0) || !((x / y) <= 10000000.0)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * -2.0)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -400000000.0) or not ((x / y) <= 10000000.0):
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	else:
		tmp = ((2.0 + (2.0 / z)) + (t * -2.0)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -400000000.0) || !(Float64(x / y) <= 10000000.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) + Float64(t * -2.0)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -400000000.0) || ~(((x / y) <= 10000000.0)))
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	else
		tmp = ((2.0 + (2.0 / z)) + (t * -2.0)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -400000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 10000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] + N[(t * -2.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4e8 or 1e7 < (/.f64 x y)

   1. Initial program 86.0%

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

   3. Taylor expanded in t around 0 98.5%

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

   if -4e8 < (/.f64 x y) < 1e7

   1. Initial program 80.4%

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

   3. Taylor expanded in t around 0 99.1%

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

      1. associate-+r+ 99.1%

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

      2. associate-*r/ 99.1%

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

      3. metadata-eval 99.1%

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

      4. sub-neg 99.1%

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

      5. metadata-eval 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in x around 0 97.7%

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

      1. *-commutative 97.7%

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

   8. Simplified 97.7%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -400000000 \lor \neg \left(\frac{x}{y} \leq 10000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot -2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-97} \lor \neg \left(z \leq 7.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.9e-97) (not (<= z 7.2e-16)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ -2.0 (/ (/ 2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e-97) || !(z <= 7.2e-16)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 / z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.9d-97)) .or. (.not. (z <= 7.2d-16))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e-97) || !(z <= 7.2e-16)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.9e-97) or not (z <= 7.2e-16):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = -2.0 + ((2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.9e-97) || !(z <= 7.2e-16))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.9e-97) || ~((z <= 7.2e-16)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = -2.0 + ((2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.9e-97], N[Not[LessEqual[z, 7.2e-16]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8999999999999998e-97 or 7.19999999999999965e-16 < z

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf 95.8%

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

      1. associate-*r/ 95.1%

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

   5. Simplified 95.1%

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

   6. Taylor expanded in x around 0 95.8%

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

      1. +-commutative 95.8%

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

      2. div-sub 95.8%

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

      3. *-inverses 95.8%

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

      4. sub-neg 95.8%

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

      5. metadata-eval 95.8%

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

      6. distribute-lft-in 95.8%

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

      7. metadata-eval 95.8%

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

      8. associate-*r/ 95.8%

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

      9. metadata-eval 95.8%

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

   8. Simplified 95.8%

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

   if -3.8999999999999998e-97 < z < 7.19999999999999965e-16

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 90.7%

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

      1. associate-+r+ 90.7%

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

      2. associate-*r/ 90.7%

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

      3. metadata-eval 90.7%

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

      4. sub-neg 90.7%

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

      5. metadata-eval 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in z around 0 90.6%

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

   7. Taylor expanded in x around 0 80.3%

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

   8. Taylor expanded in z around inf 81.2%

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

      1. sub-neg 81.2%

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

      2. associate-*r/ 81.2%

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

      3. metadata-eval 81.2%

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

      4. *-commutative 81.2%

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

      5. associate-/r* 81.1%

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

      6. metadata-eval 81.1%

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

   10. Simplified 81.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-97} \lor \neg \left(z \leq 7.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -8500000 \lor \neg \left(\frac{x}{y} \leq 1.9 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -8500000.0) (not (<= (/ x y) 1.9e-12)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -8500000.0) || !((x / y) <= 1.9e-12)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-8500000.0d0)) .or. (.not. ((x / y) <= 1.9d-12))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -8500000.0) || !((x / y) <= 1.9e-12)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -8500000.0) or not ((x / y) <= 1.9e-12):
		tmp = (x / y) - 2.0
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -8500000.0) || !(Float64(x / y) <= 1.9e-12))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -8500000.0) || ~(((x / y) <= 1.9e-12)))
		tmp = (x / y) - 2.0;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -8500000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.9e-12]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -8.5e6 or 1.89999999999999998e-12 < (/.f64 x y)

   1. Initial program 85.2%

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

   3. Taylor expanded in t around inf 66.7%

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

   if -8.5e6 < (/.f64 x y) < 1.89999999999999998e-12

   1. Initial program 81.0%

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

   3. Taylor expanded in z around inf 66.7%

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

      1. associate-*r/ 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in x around 0 66.4%

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

      1. div-sub 66.4%

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

      2. *-inverses 66.4%

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

      3. sub-neg 66.4%

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

      4. metadata-eval 66.4%

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

      5. distribute-lft-in 66.4%

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

      6. associate-*r/ 66.4%

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

      7. metadata-eval 66.4%

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

      8. metadata-eval 66.4%

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

   8. Simplified 66.4%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -8500000 \lor \neg \left(\frac{x}{y} \leq 1.9 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6200000 \lor \neg \left(\frac{x}{y} \leq 270000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6200000.0) (not (<= (/ x y) 270000000.0)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6200000.0) || !((x / y) <= 270000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-6200000.0d0)) .or. (.not. ((x / y) <= 270000000.0d0))) then
        tmp = x / y
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6200000.0) || !((x / y) <= 270000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -6200000.0) or not ((x / y) <= 270000000.0):
		tmp = x / y
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -6200000.0) || !(Float64(x / y) <= 270000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -6200000.0) || ~(((x / y) <= 270000000.0)))
		tmp = x / y;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -6200000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 270000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.2e6 or 2.7e8 < (/.f64 x y)

   1. Initial program 85.8%

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

   3. Taylor expanded in x around inf 68.7%

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

   if -6.2e6 < (/.f64 x y) < 2.7e8

   1. Initial program 80.7%

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

   3. Taylor expanded in z around inf 65.3%

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

      1. associate-*r/ 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in x around 0 64.0%

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

      1. div-sub 63.9%

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

      2. *-inverses 63.9%

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

      3. sub-neg 63.9%

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

      4. metadata-eval 63.9%

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

      5. distribute-lft-in 63.9%

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

      6. associate-*r/ 63.9%

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

      7. metadata-eval 63.9%

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

      8. metadata-eval 63.9%

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

   8. Simplified 63.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6200000 \lor \neg \left(\frac{x}{y} \leq 270000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{y} + \frac{2 \cdot \left(1 - t\right)}{t}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-16}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e-97)
   (+ (/ x y) (/ (* 2.0 (- 1.0 t)) t))
   (if (<= z 7.4e-16)
     (+ -2.0 (/ (/ 2.0 z) t))
     (+ (/ x y) (+ -2.0 (/ 2.0 t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e-97) {
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	} else if (z <= 7.4e-16) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.8d-97)) then
        tmp = (x / y) + ((2.0d0 * (1.0d0 - t)) / t)
    else if (z <= 7.4d-16) then
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    else
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e-97) {
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	} else if (z <= 7.4e-16) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e-97:
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t)
	elif z <= 7.4e-16:
		tmp = -2.0 + ((2.0 / z) / t)
	else:
		tmp = (x / y) + (-2.0 + (2.0 / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e-97)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 * Float64(1.0 - t)) / t));
	elseif (z <= 7.4e-16)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	else
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e-97)
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	elseif (z <= 7.4e-16)
		tmp = -2.0 + ((2.0 / z) / t);
	else
		tmp = (x / y) + (-2.0 + (2.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e-97], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-16], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000001e-97

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf 92.9%

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

      1. associate-*r/ 92.9%

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

   5. Simplified 92.9%

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

   if -3.8000000000000001e-97 < z < 7.3999999999999999e-16

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 90.7%

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

      1. associate-+r+ 90.7%

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

      2. associate-*r/ 90.7%

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

      3. metadata-eval 90.7%

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

      4. sub-neg 90.7%

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

      5. metadata-eval 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in z around 0 90.6%

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

   7. Taylor expanded in x around 0 80.3%

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

   8. Taylor expanded in z around inf 81.2%

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

      1. sub-neg 81.2%

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

      2. associate-*r/ 81.2%

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

      3. metadata-eval 81.2%

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

      4. *-commutative 81.2%

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

      5. associate-/r* 81.1%

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

      6. metadata-eval 81.1%

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

   10. Simplified 81.1%

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

   if 7.3999999999999999e-16 < z

   1. Initial program 65.0%

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

   3. Taylor expanded in z around inf 99.2%

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

      1. associate-*r/ 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in x around 0 99.2%

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

      1. +-commutative 99.2%

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

      2. div-sub 99.2%

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

      3. *-inverses 99.2%

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

      4. sub-neg 99.2%

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

      5. metadata-eval 99.2%

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

      6. distribute-lft-in 99.2%

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

      7. metadata-eval 99.2%

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

      8. associate-*r/ 99.2%

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

      9. metadata-eval 99.2%

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

   8. Simplified 99.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{y} + \frac{2 \cdot \left(1 - t\right)}{t}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-16}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-90} \lor \neg \left(t \leq 1.75 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e-90) (not (<= t 1.75e+44)))
   (- (/ 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 <= -8.5e-90) || !(t <= 1.75e+44)) {
		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 <= (-8.5d-90)) .or. (.not. (t <= 1.75d+44))) 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 <= -8.5e-90) || !(t <= 1.75e+44)) {
		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 <= -8.5e-90) or not (t <= 1.75e+44):
		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 <= -8.5e-90) || !(t <= 1.75e+44))
		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 <= -8.5e-90) || ~((t <= 1.75e+44)))
		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, -8.5e-90], N[Not[LessEqual[t, 1.75e+44]], $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 < -8.5000000000000001e-90 or 1.75e44 < t

   1. Initial program 72.8%

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

   3. Taylor expanded in t around inf 85.9%

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

   if -8.5000000000000001e-90 < t < 1.75e44

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0 82.9%

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

      1. associate-*r/ 82.9%

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

      2. metadata-eval 82.9%

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

   5. Simplified 82.9%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-90} \lor \neg \left(t \leq 1.75 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-97} \lor \neg \left(z \leq 2.55 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.9e-97) (not (<= z 2.55e-15)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ (/ 2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e-97) || !(z <= 2.55e-15)) {
		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 ((z <= (-3.9d-97)) .or. (.not. (z <= 2.55d-15))) 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 ((z <= -3.9e-97) || !(z <= 2.55e-15)) {
		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 (z <= -3.9e-97) or not (z <= 2.55e-15):
		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 ((z <= -3.9e-97) || !(z <= 2.55e-15))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.9e-97) || ~((z <= 2.55e-15)))
		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[z, -3.9e-97], N[Not[LessEqual[z, 2.55e-15]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8999999999999998e-97 or 2.55e-15 < z

   1. Initial program 70.5%

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

   3. Taylor expanded in t around inf 76.7%

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

   if -3.8999999999999998e-97 < z < 2.55e-15

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 90.7%

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

      1. associate-+r+ 90.7%

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

      2. associate-*r/ 90.7%

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

      3. metadata-eval 90.7%

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

      4. sub-neg 90.7%

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

      5. metadata-eval 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in z around 0 90.6%

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

   7. Taylor expanded in x around 0 80.3%

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

   8. Taylor expanded in z around inf 81.2%

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

      1. sub-neg 81.2%

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

      2. associate-*r/ 81.2%

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

      3. metadata-eval 81.2%

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

      4. *-commutative 81.2%

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

      5. associate-/r* 81.1%

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

      6. metadata-eval 81.1%

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

   10. Simplified 81.1%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-97} \lor \neg \left(z \leq 2.55 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \lor \neg \left(\frac{x}{y} \leq 170000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.0) (not (<= (/ x y) 170000000.0))) (/ x y) -2.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.0) || !((x / y) <= 170000000.0)) {
		tmp = x / y;
	} 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 (((x / y) <= (-2.0d0)) .or. (.not. ((x / y) <= 170000000.0d0))) then
        tmp = x / y
    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 (((x / y) <= -2.0) || !((x / y) <= 170000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.0) or not ((x / y) <= 170000000.0):
		tmp = x / y
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.0) || !(Float64(x / y) <= 170000000.0))
		tmp = Float64(x / y);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.0) || ~(((x / y) <= 170000000.0)))
		tmp = x / y;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 170000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2 or 1.7e8 < (/.f64 x y)

   1. Initial program 85.9%

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

   3. Taylor expanded in x around inf 68.2%

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

   if -2 < (/.f64 x y) < 1.7e8

   1. Initial program 80.6%

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

   3. Taylor expanded in t around 0 99.2%

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

      1. associate-+r+ 99.2%

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

      2. associate-*r/ 99.2%

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

      3. metadata-eval 99.2%

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

      4. sub-neg 99.2%

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

      5. metadata-eval 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in z around 0 84.5%

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

   7. Taylor expanded in x around 0 83.3%

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

   8. Taylor expanded in z around inf 49.7%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \lor \neg \left(\frac{x}{y} \leq 170000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-129} \lor \neg \left(z \leq 2.4 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.35e-129) (not (<= z 2.4e-98)))
   (- (/ x y) 2.0)
   (/ 2.0 (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.35e-129) || !(z <= 2.4e-98)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.35d-129)) .or. (.not. (z <= 2.4d-98))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 / (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.35e-129) || !(z <= 2.4e-98)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.35e-129) or not (z <= 2.4e-98):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.35e-129) || !(z <= 2.4e-98))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.35e-129) || ~((z <= 2.4e-98)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.35e-129], N[Not[LessEqual[z, 2.4e-98]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3500000000000001e-129 or 2.40000000000000005e-98 < z

   1. Initial program 75.6%

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

   3. Taylor expanded in t around inf 74.6%

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

   if -2.3500000000000001e-129 < z < 2.40000000000000005e-98

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 76.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-129} \lor \neg \left(z \leq 2.4 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if t < -1 or 1 < t

   1. Initial program 71.0%

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

   3. Taylor expanded in t around 0 85.0%

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

      1. associate-+r+ 85.0%

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

      2. associate-*r/ 85.0%

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

      3. metadata-eval 85.0%

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

      4. sub-neg 85.0%

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

      5. metadata-eval 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in z around 0 84.8%

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

   7. Taylor expanded in x around 0 61.3%

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

   8. Taylor expanded in z around inf 46.8%

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

   if -1 < t < 1

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 51.1%

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

      1. associate-*r/ 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in t around 0 25.6%

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

Alternative 13: 20.5% 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 83.1%

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

3. Taylor expanded in t around 0 91.0%

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

   1. associate-+r+ 91.0%

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

   2. associate-*r/ 91.0%

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

   3. metadata-eval 91.0%

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

   4. sub-neg 91.0%

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

   5. metadata-eval 91.0%

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

5. Simplified 91.0%

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

6. Taylor expanded in z around 0 79.7%

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

7. Taylor expanded in x around 0 57.6%

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

8. Taylor expanded in z around inf 27.5%

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

Developer Target 1: 99.0% 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 2024181 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

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