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

Percentage Accurate: 86.3% → 98.5%

Time: 10.3s

Alternatives: 14

Speedup: 0.8×

• 22.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.3% 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: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+95} \lor \neg \left(\frac{x}{y} \leq 1000000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+95) (not (<= (/ x y) 1000000000000.0)))
   (+ (/ 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) <= -2e+95) || !((x / y) <= 1000000000000.0)) {
		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) <= (-2d+95)) .or. (.not. ((x / y) <= 1000000000000.0d0))) 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) <= -2e+95) || !((x / y) <= 1000000000000.0)) {
		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) <= -2e+95) or not ((x / y) <= 1000000000000.0):
		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) <= -2e+95) || !(Float64(x / y) <= 1000000000000.0))
		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 * 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) <= -2e+95) || ~(((x / y) <= 1000000000000.0)))
		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], -2e+95], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1000000000000.0]], $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 * N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.00000000000000004e95 or 1e12 < (/.f64 x y)

   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. Taylor expanded in t around 0 97.3%

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

   if -2.00000000000000004e95 < (/.f64 x y) < 1e12

   1. Initial program 86.2%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+95} \lor \neg \left(\frac{x}{y} \leq 1000000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 0.4× speedup

Math

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

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 (+ (/ 2.0 t) (+ (/ 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 = (2.0 / t) + ((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 = (2.0 / t) + ((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 = (2.0 / t) + ((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(2.0 / t) + 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 = (2.0 / t) + ((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[(2.0 / t), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $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 z around inf 92.7%

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

      1. div-sub 92.7%

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

      2. sub-neg 92.7%

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

      3. *-inverses 92.7%

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

      4. metadata-eval 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in x around 0 92.7%

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

      1. sub-neg 92.7%

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

      2. metadata-eval 92.7%

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

      3. distribute-lft-in 92.7%

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

      4. metadata-eval 92.7%

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

      5. associate-+r+ 92.7%

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

      6. +-commutative 92.7%

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

      7. associate-*r/ 92.7%

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

      8. metadata-eval 92.7%

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

   8. Simplified 92.7%

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

4. Final simplification 98.7%

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

Alternative 3: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-242}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2000000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -200.0)
   (/ x y)
   (if (<= (/ x y) 1e-242)
     -2.0
     (if (<= (/ x y) 2000000000.0) (/ 2.0 t) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -200.0) {
		tmp = x / y;
	} else if ((x / y) <= 1e-242) {
		tmp = -2.0;
	} else if ((x / y) <= 2000000000.0) {
		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) <= (-200.0d0)) then
        tmp = x / y
    else if ((x / y) <= 1d-242) then
        tmp = -2.0d0
    else if ((x / y) <= 2000000000.0d0) 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) <= -200.0) {
		tmp = x / y;
	} else if ((x / y) <= 1e-242) {
		tmp = -2.0;
	} else if ((x / y) <= 2000000000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -200.0:
		tmp = x / y
	elif (x / y) <= 1e-242:
		tmp = -2.0
	elif (x / y) <= 2000000000.0:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -200.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1e-242)
		tmp = -2.0;
	elseif (Float64(x / y) <= 2000000000.0)
		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) <= -200.0)
		tmp = x / y;
	elseif ((x / y) <= 1e-242)
		tmp = -2.0;
	elseif ((x / y) <= 2000000000.0)
		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], -200.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-242], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 2000000000.0], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -200 or 2e9 < (/.f64 x y)

   1. Initial program 79.9%

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

   3. Taylor expanded in x around inf 73.2%

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

   if -200 < (/.f64 x y) < 1e-242

   1. Initial program 86.5%

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

   3. Taylor expanded in z around inf 65.7%

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

      1. div-sub 65.7%

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

      2. sub-neg 65.7%

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

      3. *-inverses 65.7%

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

      4. metadata-eval 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in x around 0 64.5%

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

      1. sub-neg 64.5%

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

      2. metadata-eval 64.5%

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

      3. distribute-lft-in 64.5%

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

      4. metadata-eval 64.5%

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

      5. associate-*r/ 64.5%

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

      6. metadata-eval 64.5%

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

   8. Simplified 64.5%

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

   9. Taylor expanded in t around inf 42.2%

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

   if 1e-242 < (/.f64 x y) < 2e9

   1. Initial program 91.4%

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

   3. Taylor expanded in z around inf 52.0%

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

      1. div-sub 52.1%

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

      2. sub-neg 52.1%

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

      3. *-inverses 52.1%

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

      4. metadata-eval 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in t around 0 35.6%

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

Alternative 4: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+14} \lor \neg \left(t \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{z \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e+14) (not (<= t 1.0)))
   (+ (/ x y) (- -2.0 (/ -2.0 (* z t))))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e+14) || !(t <= 1.0)) {
		tmp = (x / y) + (-2.0 - (-2.0 / (z * t)));
	} else {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.2d+14)) .or. (.not. (t <= 1.0d0))) then
        tmp = (x / y) + ((-2.0d0) - ((-2.0d0) / (z * t)))
    else
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e+14) || !(t <= 1.0)) {
		tmp = (x / y) + (-2.0 - (-2.0 / (z * t)));
	} else {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.2e+14) or not (t <= 1.0):
		tmp = (x / y) + (-2.0 - (-2.0 / (z * t)))
	else:
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.2e+14) || !(t <= 1.0))
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / Float64(z * t))));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.2e+14) || ~((t <= 1.0)))
		tmp = (x / y) + (-2.0 - (-2.0 / (z * t)));
	else
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.2e+14], N[Not[LessEqual[t, 1.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2e14 or 1 < t

   1. Initial program 71.6%

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

   3. Taylor expanded in t around 0 80.2%

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

      1. associate-+r+ 80.2%

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

      2. associate-*r/ 80.2%

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

      3. metadata-eval 80.2%

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

      4. sub-neg 80.2%

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

      5. metadata-eval 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in z around 0 90.7%

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

   7. Taylor expanded in t around inf 90.2%

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

   8. Taylor expanded in z around inf 99.4%

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

      1. sub-neg 99.4%

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

      2. +-commutative 99.4%

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

      3. associate-*r/ 99.4%

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

      4. metadata-eval 99.4%

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

      5. *-commutative 99.4%

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

      6. metadata-eval 99.4%

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

      7. associate-+l+ 99.4%

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

      8. +-commutative 99.4%

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

      9. associate-/r* 99.4%

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

      10. remove-double-neg 99.4%

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

      11. distribute-neg-frac2 99.4%

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

      12. unsub-neg 99.4%

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

      13. distribute-frac-neg2 99.4%

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

      14. distribute-neg-frac 99.4%

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

      15. distribute-neg-frac 99.4%

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

      16. metadata-eval 99.4%

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

      17. associate-/l/ 99.4%

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

   10. Simplified 99.4%

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

   if -3.2e14 < t < 1

   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 t around 0 96.8%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+14} \lor \neg \left(t \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{z \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-225}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -1.15e-55)
     t_1
     (if (<= t 2.5e-225)
       (/ (/ 2.0 t) z)
       (if (<= t 1.0) (+ (/ x y) (/ 2.0 t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.15e-55) {
		tmp = t_1;
	} else if (t <= 2.5e-225) {
		tmp = (2.0 / t) / z;
	} else if (t <= 1.0) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-1.15d-55)) then
        tmp = t_1
    else if (t <= 2.5d-225) then
        tmp = (2.0d0 / t) / z
    else if (t <= 1.0d0) then
        tmp = (x / y) + (2.0d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.15e-55) {
		tmp = t_1;
	} else if (t <= 2.5e-225) {
		tmp = (2.0 / t) / z;
	} else if (t <= 1.0) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -1.15e-55:
		tmp = t_1
	elif t <= 2.5e-225:
		tmp = (2.0 / t) / z
	elif t <= 1.0:
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.15e-55)
		tmp = t_1;
	elseif (t <= 2.5e-225)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t <= 1.0)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.15e-55)
		tmp = t_1;
	elseif (t <= 2.5e-225)
		tmp = (2.0 / t) / z;
	elseif (t <= 1.0)
		tmp = (x / y) + (2.0 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.15e-55], t$95$1, If[LessEqual[t, 2.5e-225], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.0], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15000000000000006e-55 or 1 < t

   1. Initial program 74.1%

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

   3. Taylor expanded in t around inf 85.2%

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

   if -1.15000000000000006e-55 < t < 2.5e-225

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0 95.3%

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

      1. associate-+r+ 95.3%

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

      2. associate-*r/ 95.3%

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

      3. metadata-eval 95.3%

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

      4. sub-neg 95.3%

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

      5. metadata-eval 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in z around 0 71.3%

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

   7. Taylor expanded in z around 0 58.1%

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

      1. associate-/r* 58.2%

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

   9. Simplified 58.2%

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

   if 2.5e-225 < t < 1

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 66.9%

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

      1. div-sub 67.0%

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

      2. sub-neg 67.0%

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

      3. *-inverses 67.0%

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

      4. metadata-eval 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around 0 47.6%

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

      1. *-commutative 47.6%

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

      2. *-inverses 47.6%

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

      3. div-sub 47.5%

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

      4. associate-*r* 47.5%

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

      5. *-commutative 47.5%

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

      6. div-sub 47.6%

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

      7. *-inverses 47.6%

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

      8. sub-neg 47.6%

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

      9. metadata-eval 47.6%

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

      10. distribute-lft-in 47.6%

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

      11. associate-*r/ 47.6%

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

      12. metadata-eval 47.6%

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

      13. metadata-eval 47.6%

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

   8. Simplified 47.6%

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

   9. Taylor expanded in t around 0 46.5%

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

       1. associate-*r/ 46.5%

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

       2. associate-*l/ 46.5%

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

       3. *-commutative 46.5%

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

   11. Simplified 46.5%

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

   12. Taylor expanded in x around 0 65.7%

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

       1. associate-*r/ 65.7%

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

       2. metadata-eval 65.7%

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

       3. +-commutative 65.7%

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

   14. Simplified 65.7%

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

Alternative 6: 97.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -29000000000 \lor \neg \left(z \leq 8.2 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{2}{t} + \left(\frac{x}{y} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{z \cdot t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -29000000000.0) (not (<= z 8.2e-21)))
   (+ (/ 2.0 t) (+ (/ x y) -2.0))
   (+ (/ x y) (- -2.0 (/ -2.0 (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -29000000000.0) || !(z <= 8.2e-21)) {
		tmp = (2.0 / t) + ((x / y) + -2.0);
	} else {
		tmp = (x / y) + (-2.0 - (-2.0 / (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-29000000000.0d0)) .or. (.not. (z <= 8.2d-21))) then
        tmp = (2.0d0 / t) + ((x / y) + (-2.0d0))
    else
        tmp = (x / y) + ((-2.0d0) - ((-2.0d0) / (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -29000000000.0) || !(z <= 8.2e-21)) {
		tmp = (2.0 / t) + ((x / y) + -2.0);
	} else {
		tmp = (x / y) + (-2.0 - (-2.0 / (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -29000000000.0) or not (z <= 8.2e-21):
		tmp = (2.0 / t) + ((x / y) + -2.0)
	else:
		tmp = (x / y) + (-2.0 - (-2.0 / (z * t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -29000000000.0) || !(z <= 8.2e-21))
		tmp = Float64(Float64(2.0 / t) + Float64(Float64(x / y) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -29000000000.0) || ~((z <= 8.2e-21)))
		tmp = (2.0 / t) + ((x / y) + -2.0);
	else
		tmp = (x / y) + (-2.0 - (-2.0 / (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -29000000000.0], N[Not[LessEqual[z, 8.2e-21]], $MachinePrecision]], N[(N[(2.0 / t), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e10 or 8.19999999999999988e-21 < z

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf 99.5%

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

      1. div-sub 99.5%

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

      2. sub-neg 99.5%

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

      3. *-inverses 99.5%

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

      4. metadata-eval 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in x around 0 99.5%

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

      1. sub-neg 99.5%

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

      2. metadata-eval 99.5%

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

      3. distribute-lft-in 99.5%

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

      4. metadata-eval 99.5%

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

      5. associate-+r+ 99.5%

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

      6. +-commutative 99.5%

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

      7. associate-*r/ 99.5%

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

      8. metadata-eval 99.5%

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

   8. Simplified 99.5%

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

   if -2.9e10 < z < 8.19999999999999988e-21

   1. Initial program 97.2%

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

   3. Taylor expanded in t around 0 87.6%

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

      1. associate-+r+ 87.6%

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

      2. associate-*r/ 87.6%

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

      3. metadata-eval 87.6%

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

      4. sub-neg 87.6%

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

      5. metadata-eval 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in z around 0 97.3%

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

   7. Taylor expanded in t around inf 96.1%

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

   8. Taylor expanded in z around inf 96.0%

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

      1. sub-neg 96.0%

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

      2. +-commutative 96.0%

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

      3. associate-*r/ 96.0%

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

      4. metadata-eval 96.0%

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

      5. *-commutative 96.0%

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

      6. metadata-eval 96.0%

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

      7. associate-+l+ 96.0%

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

      8. +-commutative 96.0%

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

      9. associate-/r* 96.0%

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

      10. remove-double-neg 96.0%

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

      11. distribute-neg-frac2 96.0%

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

      12. unsub-neg 96.0%

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

      13. distribute-frac-neg2 96.0%

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

      14. distribute-neg-frac 96.0%

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

      15. distribute-neg-frac 96.0%

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

      16. metadata-eval 96.0%

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

      17. associate-/l/ 96.0%

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

   10. Simplified 96.0%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -29000000000 \lor \neg \left(z \leq 8.2 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{2}{t} + \left(\frac{x}{y} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{z \cdot t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-225}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 65:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -2.1e-55)
     t_1
     (if (<= t 4.8e-225)
       (/ (/ 2.0 t) z)
       (if (<= t 65.0) (+ (/ 2.0 t) -2.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.1e-55) {
		tmp = t_1;
	} else if (t <= 4.8e-225) {
		tmp = (2.0 / t) / z;
	} else if (t <= 65.0) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-2.1d-55)) then
        tmp = t_1
    else if (t <= 4.8d-225) then
        tmp = (2.0d0 / t) / z
    else if (t <= 65.0d0) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.1e-55) {
		tmp = t_1;
	} else if (t <= 4.8e-225) {
		tmp = (2.0 / t) / z;
	} else if (t <= 65.0) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -2.1e-55:
		tmp = t_1
	elif t <= 4.8e-225:
		tmp = (2.0 / t) / z
	elif t <= 65.0:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -2.1e-55)
		tmp = t_1;
	elseif (t <= 4.8e-225)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t <= 65.0)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -2.1e-55)
		tmp = t_1;
	elseif (t <= 4.8e-225)
		tmp = (2.0 / t) / z;
	elseif (t <= 65.0)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -2.1e-55], t$95$1, If[LessEqual[t, 4.8e-225], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 65.0], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1000000000000002e-55 or 65 < t

   1. Initial program 73.9%

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

   3. Taylor expanded in t around inf 85.6%

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

   if -2.1000000000000002e-55 < t < 4.79999999999999992e-225

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0 95.3%

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

      1. associate-+r+ 95.3%

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

      2. associate-*r/ 95.3%

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

      3. metadata-eval 95.3%

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

      4. sub-neg 95.3%

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

      5. metadata-eval 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in z around 0 71.3%

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

   7. Taylor expanded in z around 0 58.1%

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

      1. associate-/r* 58.2%

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

   9. Simplified 58.2%

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

   if 4.79999999999999992e-225 < t < 65

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 67.7%

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

      1. div-sub 67.7%

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

      2. sub-neg 67.7%

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

      3. *-inverses 67.7%

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

      4. metadata-eval 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in x around 0 48.4%

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

      1. sub-neg 48.4%

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

      2. metadata-eval 48.4%

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

      3. distribute-lft-in 48.4%

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

      4. metadata-eval 48.4%

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

      5. associate-*r/ 48.4%

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

      6. metadata-eval 48.4%

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

   8. Simplified 48.4%

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

Alternative 8: 61.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-221}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 65:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -2.4e-60)
     t_1
     (if (<= t 1.1e-221)
       (/ 2.0 (* z t))
       (if (<= t 65.0) (+ (/ 2.0 t) -2.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.4e-60) {
		tmp = t_1;
	} else if (t <= 1.1e-221) {
		tmp = 2.0 / (z * t);
	} else if (t <= 65.0) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-2.4d-60)) then
        tmp = t_1
    else if (t <= 1.1d-221) then
        tmp = 2.0d0 / (z * t)
    else if (t <= 65.0d0) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.4e-60) {
		tmp = t_1;
	} else if (t <= 1.1e-221) {
		tmp = 2.0 / (z * t);
	} else if (t <= 65.0) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -2.4e-60:
		tmp = t_1
	elif t <= 1.1e-221:
		tmp = 2.0 / (z * t)
	elif t <= 65.0:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -2.4e-60)
		tmp = t_1;
	elseif (t <= 1.1e-221)
		tmp = Float64(2.0 / Float64(z * t));
	elseif (t <= 65.0)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -2.4e-60)
		tmp = t_1;
	elseif (t <= 1.1e-221)
		tmp = 2.0 / (z * t);
	elseif (t <= 65.0)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -2.4e-60], t$95$1, If[LessEqual[t, 1.1e-221], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 65.0], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.40000000000000009e-60 or 65 < t

   1. Initial program 73.9%

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

   3. Taylor expanded in t around inf 85.6%

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

   if -2.40000000000000009e-60 < t < 1.10000000000000001e-221

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0 58.1%

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

   if 1.10000000000000001e-221 < t < 65

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 67.7%

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

      1. div-sub 67.7%

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

      2. sub-neg 67.7%

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

      3. *-inverses 67.7%

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

      4. metadata-eval 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in x around 0 48.4%

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

      1. sub-neg 48.4%

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

      2. metadata-eval 48.4%

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

      3. distribute-lft-in 48.4%

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

      4. metadata-eval 48.4%

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

      5. associate-*r/ 48.4%

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

      6. metadata-eval 48.4%

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

   8. Simplified 48.4%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-221}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 65:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-61} \lor \neg \left(t \leq 3.9 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{2}{t} + \left(\frac{x}{y} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.45e-61) (not (<= t 3.9e-57)))
   (+ (/ 2.0 t) (+ (/ 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 <= -1.45e-61) || !(t <= 3.9e-57)) {
		tmp = (2.0 / t) + ((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 <= (-1.45d-61)) .or. (.not. (t <= 3.9d-57))) then
        tmp = (2.0d0 / t) + ((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 <= -1.45e-61) || !(t <= 3.9e-57)) {
		tmp = (2.0 / t) + ((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 <= -1.45e-61) or not (t <= 3.9e-57):
		tmp = (2.0 / t) + ((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 <= -1.45e-61) || !(t <= 3.9e-57))
		tmp = Float64(Float64(2.0 / t) + 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 <= -1.45e-61) || ~((t <= 3.9e-57)))
		tmp = (2.0 / t) + ((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, -1.45e-61], N[Not[LessEqual[t, 3.9e-57]], $MachinePrecision]], N[(N[(2.0 / t), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45e-61 or 3.90000000000000006e-57 < t

   1. Initial program 75.7%

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

   3. Taylor expanded in z around inf 87.1%

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

      1. div-sub 87.2%

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

      2. sub-neg 87.2%

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

      3. *-inverses 87.2%

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

      4. metadata-eval 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in x around 0 87.2%

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

      1. sub-neg 87.2%

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

      2. metadata-eval 87.2%

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

      3. distribute-lft-in 87.2%

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

      4. metadata-eval 87.2%

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

      5. associate-+r+ 87.2%

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

      6. +-commutative 87.2%

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

      7. associate-*r/ 87.2%

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

      8. metadata-eval 87.2%

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

   8. Simplified 87.2%

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

   if -1.45e-61 < t < 3.90000000000000006e-57

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0 89.1%

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

      1. associate-*r/ 89.1%

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

      2. metadata-eval 89.1%

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

   5. Simplified 89.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-61} \lor \neg \left(t \leq 3.9 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{2}{t} + \left(\frac{x}{y} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-31} \lor \neg \left(\frac{x}{y} \leq 2000000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e-31) (not (<= (/ x y) 2000000000.0)))
   (- (/ x y) 2.0)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-31) || !((x / y) <= 2000000000.0)) {
		tmp = (x / y) - 2.0;
	} 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) <= (-2d-31)) .or. (.not. ((x / y) <= 2000000000.0d0))) then
        tmp = (x / y) - 2.0d0
    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) <= -2e-31) || !((x / y) <= 2000000000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e-31) or not ((x / y) <= 2000000000.0):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e-31) || !(Float64(x / y) <= 2000000000.0))
		tmp = Float64(Float64(x / y) - 2.0);
	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) <= -2e-31) || ~(((x / y) <= 2000000000.0)))
		tmp = (x / y) - 2.0;
	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], -2e-31], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e-31 or 2e9 < (/.f64 x y)

   1. Initial program 79.3%

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

   3. Taylor expanded in t around inf 74.9%

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

   if -2e-31 < (/.f64 x y) < 2e9

   1. Initial program 88.9%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. div-sub 60.7%

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

      2. sub-neg 60.7%

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

      3. *-inverses 60.7%

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

      4. metadata-eval 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in x around 0 60.7%

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

      1. sub-neg 60.7%

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

      2. metadata-eval 60.7%

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

      3. distribute-lft-in 60.7%

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

      4. metadata-eval 60.7%

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

      5. associate-*r/ 60.7%

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

      6. metadata-eval 60.7%

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

   8. Simplified 60.7%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-31} \lor \neg \left(\frac{x}{y} \leq 2000000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+43} \lor \neg \left(\frac{x}{y} \leq 2000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+43) (not (<= (/ x y) 2000000000.0)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+43) || !((x / y) <= 2000000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d+43)) .or. (.not. ((x / y) <= 2000000000.0d0))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+43) || !((x / y) <= 2000000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+43) or not ((x / y) <= 2000000000.0):
		tmp = x / y
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+43) || !(Float64(x / y) <= 2000000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e+43) || ~(((x / y) <= 2000000000.0)))
		tmp = x / y;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+43], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2000000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.0000000000000004e43 or 2e9 < (/.f64 x y)

   1. Initial program 80.5%

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

   3. Taylor expanded in x around inf 75.7%

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

   if -5.0000000000000004e43 < (/.f64 x y) < 2e9

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 62.8%

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

      1. div-sub 62.8%

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

      2. sub-neg 62.8%

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

      3. *-inverses 62.8%

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

      4. metadata-eval 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in x around 0 59.9%

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

      1. sub-neg 59.9%

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

      2. metadata-eval 59.9%

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

      3. distribute-lft-in 59.9%

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

      4. metadata-eval 59.9%

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

      5. associate-*r/ 59.9%

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

      6. metadata-eval 59.9%

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

   8. Simplified 59.9%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+43} \lor \neg \left(\frac{x}{y} \leq 2000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-55} \lor \neg \left(t \leq 0.0048\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2e-55) (not (<= t 0.0048)))
   (- (/ 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 <= -2e-55) || !(t <= 0.0048)) {
		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 <= (-2d-55)) .or. (.not. (t <= 0.0048d0))) 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 <= -2e-55) || !(t <= 0.0048)) {
		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 <= -2e-55) or not (t <= 0.0048):
		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 <= -2e-55) || !(t <= 0.0048))
		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 <= -2e-55) || ~((t <= 0.0048)))
		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, -2e-55], N[Not[LessEqual[t, 0.0048]], $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 < -1.99999999999999999e-55 or 0.00479999999999999958 < t

   1. Initial program 74.1%

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

   3. Taylor expanded in t around inf 85.2%

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

   if -1.99999999999999999e-55 < t < 0.00479999999999999958

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. metadata-eval 86.1%

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

   5. Simplified 86.1%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-55} \lor \neg \left(t \leq 0.0048\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.2e+14) -2.0 (if (<= t 1.4e-5) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e+14) {
		tmp = -2.0;
	} else if (t <= 1.4e-5) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.2d+14)) then
        tmp = -2.0d0
    else if (t <= 1.4d-5) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e+14) {
		tmp = -2.0;
	} else if (t <= 1.4e-5) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.2e+14:
		tmp = -2.0
	elif t <= 1.4e-5:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.2e+14)
		tmp = -2.0;
	elseif (t <= 1.4e-5)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.2e+14)
		tmp = -2.0;
	elseif (t <= 1.4e-5)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.2e+14], -2.0, If[LessEqual[t, 1.4e-5], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2e14 or 1.39999999999999998e-5 < t

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. div-sub 87.8%

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

      2. sub-neg 87.8%

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

      3. *-inverses 87.8%

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

      4. metadata-eval 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in x around 0 34.2%

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

      1. sub-neg 34.2%

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

      2. metadata-eval 34.2%

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

      3. distribute-lft-in 34.2%

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

      4. metadata-eval 34.2%

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

      5. associate-*r/ 34.2%

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

      6. metadata-eval 34.2%

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

   8. Simplified 34.2%

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

   9. Taylor expanded in t around inf 33.6%

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

   if -3.2e14 < t < 1.39999999999999998e-5

   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 inf 56.1%

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

      1. div-sub 56.1%

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

      2. sub-neg 56.1%

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

      3. *-inverses 56.1%

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

      4. metadata-eval 56.1%

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

   5. Simplified 56.1%

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

   6. Taylor expanded in t around 0 36.6%

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

Alternative 14: 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 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 z around inf 72.7%

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

   1. div-sub 72.7%

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

   2. sub-neg 72.7%

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

   3. *-inverses 72.7%

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

   4. metadata-eval 72.7%

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

5. Simplified 72.7%

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

6. Taylor expanded in x around 0 35.6%

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

   1. sub-neg 35.6%

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

   2. metadata-eval 35.6%

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

   3. distribute-lft-in 35.6%

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

   4. metadata-eval 35.6%

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

   5. associate-*r/ 35.6%

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

   6. metadata-eval 35.6%

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

8. Simplified 35.6%

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

9. Taylor expanded in t around inf 18.8%

   \[\leadsto \color{blue}{-2} \]
10. 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 2024180 
(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))))