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

Percentage Accurate: 86.8% → 99.3%

Time: 12.4s

Alternatives: 13

Speedup: 0.9×

• 23.5% 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: 86.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.4× speedup

Math

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

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 (+ (/ x y) (+ (/ 2.0 t) -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 / t) + -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 / t) + -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 / t) + -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) + Float64(Float64(2.0 / t) + -2.0));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + 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] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x y) (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (-.f64 1 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 2 (*.f64 (*.f64 z 2) (-.f64 1 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 88.9%

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

      1. associate-*r/ 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in t around 0 88.9%

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

      1. sub-neg 88.9%

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

      2. associate-*r/ 88.9%

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

      3. metadata-eval 88.9%

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

      4. metadata-eval 88.9%

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

   8. Simplified 88.9%

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

4. Final simplification 98.7%

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

Alternative 2: 79.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+90}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-19} \lor \neg \left(t \leq 650000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -3.5e+114)
     t_1
     (if (<= t -2.1e+90)
       (+ -2.0 (/ (/ 2.0 t) z))
       (if (or (<= t -5.5e-19) (not (<= t 650000.0)))
         t_1
         (/ (+ 2.0 (/ 2.0 z)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -3.5e+114) {
		tmp = t_1;
	} else if (t <= -2.1e+90) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else if ((t <= -5.5e-19) || !(t <= 650000.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-3.5d+114)) then
        tmp = t_1
    else if (t <= (-2.1d+90)) then
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    else if ((t <= (-5.5d-19)) .or. (.not. (t <= 650000.0d0))) then
        tmp = t_1
    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 t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -3.5e+114) {
		tmp = t_1;
	} else if (t <= -2.1e+90) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else if ((t <= -5.5e-19) || !(t <= 650000.0)) {
		tmp = t_1;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -3.5e+114:
		tmp = t_1
	elif t <= -2.1e+90:
		tmp = -2.0 + ((2.0 / t) / z)
	elif (t <= -5.5e-19) or not (t <= 650000.0):
		tmp = t_1
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -3.5e+114)
		tmp = t_1;
	elseif (t <= -2.1e+90)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	elseif ((t <= -5.5e-19) || !(t <= 650000.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -3.5e+114)
		tmp = t_1;
	elseif (t <= -2.1e+90)
		tmp = -2.0 + ((2.0 / t) / z);
	elseif ((t <= -5.5e-19) || ~((t <= 650000.0)))
		tmp = t_1;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	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, -3.5e+114], t$95$1, If[LessEqual[t, -2.1e+90], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -5.5e-19], N[Not[LessEqual[t, 650000.0]], $MachinePrecision]], t$95$1, N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5000000000000001e114 or -2.09999999999999981e90 < t < -5.4999999999999996e-19 or 6.5e5 < t

   1. Initial program 79.7%

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

   3. Taylor expanded in t around inf 85.1%

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

   if -3.5000000000000001e114 < t < -2.09999999999999981e90

   1. Initial program 85.5%

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

   3. Taylor expanded in t around inf 85.5%

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

      1. *-commutative 85.5%

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

      2. *-commutative 85.5%

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

      3. *-commutative 85.5%

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

      4. associate-*l* 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-/r* 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in x around 0 99.6%

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

   if -5.4999999999999996e-19 < t < 6.5e5

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 82.5%

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

      1. associate-*r/ 82.5%

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

      2. metadata-eval 82.5%

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

   5. Simplified 82.5%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+90}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-19} \lor \neg \left(t \leq 650000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-6} \lor \neg \left(t \leq 1\right):\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \left(\frac{x}{y} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.1e-6) (not (<= t 1.0)))
   (+ (/ (/ 2.0 t) z) (+ (/ x y) -2.0))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e-6) || !(t <= 1.0)) {
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	} 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 <= (-4.1d-6)) .or. (.not. (t <= 1.0d0))) then
        tmp = ((2.0d0 / t) / z) + ((x / y) + (-2.0d0))
    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 <= -4.1e-6) || !(t <= 1.0)) {
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.1e-6) or not (t <= 1.0):
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0)
	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 <= -4.1e-6) || !(t <= 1.0))
		tmp = Float64(Float64(Float64(2.0 / t) / z) + Float64(Float64(x / y) + -2.0));
	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 <= -4.1e-6) || ~((t <= 1.0)))
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	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, -4.1e-6], N[Not[LessEqual[t, 1.0]], $MachinePrecision]], N[(N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] + -2.0), $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 < -4.0999999999999997e-6 or 1 < t

   1. Initial program 79.6%

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

   3. Taylor expanded in t around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. *-commutative 79.2%

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

      3. *-commutative 79.2%

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

      4. associate-*l* 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in x around 0 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. metadata-eval 99.5%

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

      4. associate-/r* 99.5%

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

      5. sub-neg 99.5%

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

      6. metadata-eval 99.5%

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

   8. Simplified 99.5%

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

   if -4.0999999999999997e-6 < t < 1

   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 96.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-6} \lor \neg \left(t \leq 1\right):\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \left(\frac{x}{y} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \left(\frac{x}{y} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9) (not (<= z 1.0)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ (/ 2.0 t) z) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9) || !(z <= 1.0)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.9d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = ((2.0d0 / t) / z) + ((x / y) + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9) || !(z <= 1.0)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9) or not (z <= 1.0):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9) || !(z <= 1.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(Float64(2.0 / t) / z) + Float64(Float64(x / y) + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.9) || ~((z <= 1.0)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999991 or 1 < z

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf 99.4%

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

      1. associate-*r/ 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in t around 0 99.4%

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

      1. sub-neg 99.4%

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

      2. associate-*r/ 99.4%

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

      3. metadata-eval 99.4%

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

      4. metadata-eval 99.4%

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

   8. Simplified 99.4%

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

   if -2.89999999999999991 < z < 1

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf 96.3%

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

      1. *-commutative 96.3%

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

      2. *-commutative 96.3%

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

      3. *-commutative 96.3%

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

      4. associate-*l* 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in x around 0 96.3%

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

      1. associate--l+ 96.3%

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

      2. associate-*r/ 96.3%

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

      3. metadata-eval 96.3%

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

      4. associate-/r* 96.3%

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

      5. sub-neg 96.3%

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

      6. metadata-eval 96.3%

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

   8. Simplified 96.3%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \left(\frac{x}{y} + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -75:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.45 \cdot 10^{+92}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -75.0)
   (- (/ x y) 2.0)
   (if (<= (/ x y) 2.45e+92) (+ -2.0 (/ (/ 2.0 t) z)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -75.0) {
		tmp = (x / y) - 2.0;
	} else if ((x / y) <= 2.45e+92) {
		tmp = -2.0 + ((2.0 / t) / z);
	} 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) <= (-75.0d0)) then
        tmp = (x / y) - 2.0d0
    else if ((x / y) <= 2.45d+92) then
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    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) <= -75.0) {
		tmp = (x / y) - 2.0;
	} else if ((x / y) <= 2.45e+92) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -75.0:
		tmp = (x / y) - 2.0
	elif (x / y) <= 2.45e+92:
		tmp = -2.0 + ((2.0 / t) / z)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -75.0)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (Float64(x / y) <= 2.45e+92)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -75.0)
		tmp = (x / y) - 2.0;
	elseif ((x / y) <= 2.45e+92)
		tmp = -2.0 + ((2.0 / t) / z);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -75.0], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.45e+92], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -75

   1. Initial program 83.3%

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

   3. Taylor expanded in t around inf 70.7%

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

   if -75 < (/.f64 x y) < 2.4500000000000001e92

   1. Initial program 91.5%

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

   3. Taylor expanded in t around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. *-commutative 65.5%

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

      3. *-commutative 65.5%

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

      4. associate-*l* 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in x around 0 73.8%

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

      1. associate--l+ 73.8%

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

      2. associate-*r/ 73.8%

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

      3. metadata-eval 73.8%

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

      4. associate-/r* 73.8%

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

      5. sub-neg 73.8%

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

      6. metadata-eval 73.8%

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

   8. Simplified 73.8%

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

   9. Taylor expanded in x around 0 71.8%

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

   if 2.4500000000000001e92 < (/.f64 x y)

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 73.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -75:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.45 \cdot 10^{+92}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-61} \lor \neg \left(z \leq 5.5 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.2e-61) (not (<= z 5.5e-45)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ -2.0 (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-61) || !(z <= 5.5e-45)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.2d-61)) .or. (.not. (z <= 5.5d-45))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-61) || !(z <= 5.5e-45)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.2e-61) or not (z <= 5.5e-45):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = -2.0 + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.2e-61) || !(z <= 5.5e-45))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.2e-61) || ~((z <= 5.5e-45)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = -2.0 + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.2e-61], N[Not[LessEqual[z, 5.5e-45]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1999999999999998e-61 or 5.5000000000000003e-45 < z

   1. Initial program 83.4%

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

   3. Taylor expanded in z around inf 94.8%

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

      1. associate-*r/ 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in t around 0 94.8%

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

      1. sub-neg 94.8%

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

      2. associate-*r/ 94.8%

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

      3. metadata-eval 94.8%

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

      4. metadata-eval 94.8%

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

   8. Simplified 94.8%

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

   if -4.1999999999999998e-61 < z < 5.5000000000000003e-45

   1. Initial program 96.4%

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

   3. Taylor expanded in t around inf 96.4%

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

      1. *-commutative 96.4%

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

      2. *-commutative 96.4%

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

      3. *-commutative 96.4%

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

      4. associate-*l* 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in x around 0 96.4%

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

      1. associate--l+ 96.4%

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

      2. associate-*r/ 96.4%

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

      3. metadata-eval 96.4%

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

      4. associate-/r* 96.4%

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

      5. sub-neg 96.4%

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

      6. metadata-eval 96.4%

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

   8. Simplified 96.4%

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

   9. Taylor expanded in x around 0 78.2%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-61} \lor \neg \left(z \leq 5.5 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-8} \lor \neg \left(z \leq 3 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7e-8) (not (<= z 3e-7)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7e-8) || !(z <= 3e-7)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (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 <= (-7d-8)) .or. (.not. (z <= 3d-7))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (x / y) + (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 <= -7e-8) || !(z <= 3e-7)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7e-8) or not (z <= 3e-7):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7e-8) || !(z <= 3e-7))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7e-8) || ~((z <= 3e-7)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7e-8], N[Not[LessEqual[z, 3e-7]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000048e-8 or 2.9999999999999999e-7 < z

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf 98.6%

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

      1. associate-*r/ 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in t around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. associate-*r/ 98.6%

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

      3. metadata-eval 98.6%

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

      4. metadata-eval 98.6%

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

   8. Simplified 98.6%

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

   if -7.00000000000000048e-8 < z < 2.9999999999999999e-7

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 89.6%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-8} \lor \neg \left(z \leq 3 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-11} \lor \neg \left(z \leq 0.00029\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e-11) (not (<= z 0.00029)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-11) || !(z <= 0.00029)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9d-11)) .or. (.not. (z <= 0.00029d0))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-11) || !(z <= 0.00029)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e-11) or not (z <= 0.00029):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e-11) || !(z <= 0.00029))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9e-11) || ~((z <= 0.00029)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e-11], N[Not[LessEqual[z, 0.00029]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.9999999999999999e-11 or 2.9e-4 < z

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf 98.6%

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

      1. associate-*r/ 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in t around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. associate-*r/ 98.6%

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

      3. metadata-eval 98.6%

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

      4. metadata-eval 98.6%

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

   8. Simplified 98.6%

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

   if -8.9999999999999999e-11 < z < 2.9e-4

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 89.6%

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

      1. associate-/r* 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-11} \lor \neg \left(z \leq 0.00029\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-64} \lor \neg \left(z \leq 2.9 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.6e-64) (not (<= z 2.9e-37)))
   (- (/ x y) 2.0)
   (/ 2.0 (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.6e-64) || !(z <= 2.9e-37)) {
		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 <= (-9.6d-64)) .or. (.not. (z <= 2.9d-37))) 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 <= -9.6e-64) || !(z <= 2.9e-37)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.6e-64) or not (z <= 2.9e-37):
		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 <= -9.6e-64) || !(z <= 2.9e-37))
		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 <= -9.6e-64) || ~((z <= 2.9e-37)))
		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, -9.6e-64], N[Not[LessEqual[z, 2.9e-37]], $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 < -9.59999999999999994e-64 or 2.90000000000000005e-37 < z

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf 63.1%

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

   if -9.59999999999999994e-64 < z < 2.90000000000000005e-37

   1. Initial program 96.4%

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

   3. Taylor expanded in t around inf 96.4%

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

      1. *-commutative 96.4%

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

      2. *-commutative 96.4%

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

      3. *-commutative 96.4%

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

      4. associate-*l* 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in x around 0 96.4%

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

      1. associate--l+ 96.4%

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

      2. associate-*r/ 96.4%

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

      3. metadata-eval 96.4%

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

      4. associate-/r* 96.4%

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

      5. sub-neg 96.4%

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

      6. metadata-eval 96.4%

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

   8. Simplified 96.4%

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

   9. Taylor expanded in t around 0 72.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-64} \lor \neg \left(z \leq 2.9 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-66} \lor \neg \left(z \leq 3.4 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e-66) (not (<= z 3.4e-37)))
   (- (/ x y) 2.0)
   (/ (/ 2.0 t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e-66) || !(z <= 3.4e-37)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.5d-66)) .or. (.not. (z <= 3.4d-37))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 / t) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e-66) || !(z <= 3.4e-37)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e-66) or not (z <= 3.4e-37):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e-66) || !(z <= 3.4e-37))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 / t) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e-66) || ~((z <= 3.4e-37)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 / t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e-66], N[Not[LessEqual[z, 3.4e-37]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000053e-66 or 3.40000000000000018e-37 < z

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf 63.1%

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

   if -5.50000000000000053e-66 < z < 3.40000000000000018e-37

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 90.2%

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

      1. associate-/r* 90.2%

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

   5. Simplified 90.2%

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

      1. frac-add 78.1%

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

      2. div-inv 77.7%

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

      3. fma-define 77.7%

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

   7. Applied egg-rr 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*l/ 77.6%

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

      3. *-commutative 77.6%

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

   9. Simplified 77.6%

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

   10. Taylor expanded in x around 0 64.3%

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

       1. associate-*r/ 64.3%

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

   12. Simplified 64.3%

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

   13. Taylor expanded in y around 0 72.1%

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

       1. associate-/r* 72.2%

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

   15. Simplified 72.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-66} \lor \neg \left(z \leq 3.4 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-66} \lor \neg \left(z \leq 4.2 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e-66) (not (<= z 4.2e-37)))
   (- (/ x y) 2.0)
   (/ (/ 2.0 z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e-66) || !(z <= 4.2e-37)) {
		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 <= (-2.9d-66)) .or. (.not. (z <= 4.2d-37))) 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 <= -2.9e-66) || !(z <= 4.2e-37)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9e-66) or not (z <= 4.2e-37):
		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 <= -2.9e-66) || !(z <= 4.2e-37))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 / z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.9e-66) || ~((z <= 4.2e-37)))
		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, -2.9e-66], N[Not[LessEqual[z, 4.2e-37]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.90000000000000011e-66 or 4.2000000000000002e-37 < z

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf 63.1%

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

   if -2.90000000000000011e-66 < z < 4.2000000000000002e-37

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 90.2%

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

      1. associate-/r* 90.2%

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

   5. Simplified 90.2%

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

      1. frac-add 78.1%

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

      2. div-inv 77.7%

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

      3. fma-define 77.7%

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

   7. Applied egg-rr 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*l/ 77.6%

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

      3. *-commutative 77.6%

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

   9. Simplified 77.6%

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

   10. Taylor expanded in x around 0 64.3%

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

       1. associate-*r/ 64.3%

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

   12. Simplified 64.3%

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

   13. Taylor expanded in y around 0 72.1%

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

       1. *-commutative 72.1%

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

       2. associate-/r* 72.2%

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

   15. Simplified 72.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-66} \lor \neg \left(z \leq 4.2 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} - 2 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in t around inf 48.4%

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

4. Final simplification 48.4%

   \[\leadsto \frac{x}{y} - 2 \]
5. Add Preprocessing

Alternative 13: 35.5% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t) {
	return 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 = x / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in x around inf 32.8%

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

4. Final simplification 32.8%

   \[\leadsto \frac{x}{y} \]
5. Add Preprocessing

Developer target: 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 2024034 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

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