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

Percentage Accurate: 86.7% → 99.1%

Time: 9.6s

Alternatives: 12

Speedup: 1.1×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.6%

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

3. Taylor expanded in z around 0

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

5. Applied rewrites 99.1%

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

Alternative 2: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+249} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+28} \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (or (<= t_1 -2e+249) (not (or (<= t_1 5e+28) (not (<= t_1 INFINITY)))))
     (/ 2.0 (* t z))
     (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -2e+249) || !((t_1 <= 5e+28) || !(t_1 <= ((double) INFINITY)))) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -2e+249) || !((t_1 <= 5e+28) || !(t_1 <= Double.POSITIVE_INFINITY))) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if (t_1 <= -2e+249) or not ((t_1 <= 5e+28) or not (t_1 <= math.inf)):
		tmp = 2.0 / (t * z)
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if ((t_1 <= -2e+249) || !((t_1 <= 5e+28) || !(t_1 <= Inf)))
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if ((t_1 <= -2e+249) || ~(((t_1 <= 5e+28) || ~((t_1 <= Inf)))))
		tmp = 2.0 / (t * z);
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+249], N[Not[Or[LessEqual[t$95$1, 5e+28], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]]], $MachinePrecision]], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.9999999999999998e249 or 4.99999999999999957e28 < (/.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 97.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 63.6

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

   8. Applied rewrites 63.6%

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

   if -1.9999999999999998e249 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.99999999999999957e28 or +inf.0 < (/.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 79.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 82.9%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -2 \cdot 10^{+249} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 5 \cdot 10^{+28} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right)\right):\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{+66} \lor \neg \left(\frac{x}{y} \leq 4.8 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6.6e+66) (not (<= (/ x y) 4.8e+28)))
   (+ (/ x y) (/ 2.0 t))
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.6e+66) || !((x / y) <= 4.8e+28)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-6.6d+66)) .or. (.not. ((x / y) <= 4.8d+28))) then
        tmp = (x / y) + (2.0d0 / t)
    else
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.6e+66) || !((x / y) <= 4.8e+28)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -6.6e+66) or not ((x / y) <= 4.8e+28):
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -6.6e+66) || !(Float64(x / y) <= 4.8e+28))
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -6.6e+66) || ~(((x / y) <= 4.8e+28)))
		tmp = (x / y) + (2.0 / t);
	else
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -6.6e+66], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.8e+28]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.6000000000000003e66 or 4.79999999999999962e28 < (/.f64 x y)

   1. Initial program 88.8%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l/ N/A

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

   5. Applied rewrites 98.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 81.4%

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

   if -6.6000000000000003e66 < (/.f64 x y) < 4.79999999999999962e28

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 94.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{+66} \lor \neg \left(\frac{x}{y} \leq 4.8 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{+66} \lor \neg \left(\frac{x}{y} \leq 4.8 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6.6e+66) (not (<= (/ x y) 4.8e+28)))
   (+ (/ x y) (/ 2.0 t))
   (- (/ (fma z 2.0 2.0) (* t z)) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.6e+66) || !((x / y) <= 4.8e+28)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = (fma(z, 2.0, 2.0) / (t * z)) - 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -6.6e+66) || !(Float64(x / y) <= 4.8e+28))
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	else
		tmp = Float64(Float64(fma(z, 2.0, 2.0) / Float64(t * z)) - 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -6.6e+66], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.8e+28]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.6000000000000003e66 or 4.79999999999999962e28 < (/.f64 x y)

   1. Initial program 88.8%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l/ N/A

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

   5. Applied rewrites 98.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 81.4%

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

   if -6.6000000000000003e66 < (/.f64 x y) < 4.79999999999999962e28

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 94.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 56.7%

      \[\leadsto \frac{2}{t} - 2 \]

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 93.9%

       \[\leadsto \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} - 2 \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{+66} \lor \neg \left(\frac{x}{y} \leq 4.8 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.8 \cdot 10^{+67} \lor \neg \left(\frac{x}{y} \leq 5.6 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4.8e+67) (not (<= (/ x y) 5.6e+28)))
   (/ x y)
   (- (/ (fma z 2.0 2.0) (* t z)) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4.8e+67) || !((x / y) <= 5.6e+28)) {
		tmp = x / y;
	} else {
		tmp = (fma(z, 2.0, 2.0) / (t * z)) - 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4.8e+67) || !(Float64(x / y) <= 5.6e+28))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(fma(z, 2.0, 2.0) / Float64(t * z)) - 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4.8e+67], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5.6e+28]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.80000000000000004e67 or 5.6000000000000003e28 < (/.f64 x y)

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 75.6

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

   5. Applied rewrites 75.6%

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

   if -4.80000000000000004e67 < (/.f64 x y) < 5.6000000000000003e28

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 94.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 56.7%

      \[\leadsto \frac{2}{t} - 2 \]

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 93.9%

       \[\leadsto \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} - 2 \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.8 \cdot 10^{+67} \lor \neg \left(\frac{x}{y} \leq 5.6 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -17000 \lor \neg \left(z \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{\frac{2}{z}}{t} - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -17000.0) (not (<= z 1.4e-18)))
   (+ (/ x y) (- -2.0 (/ -2.0 t)))
   (+ (/ x y) (- (/ (/ 2.0 z) t) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -17000.0) || !(z <= 1.4e-18)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (x / y) + (((2.0 / z) / t) - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-17000.0d0)) .or. (.not. (z <= 1.4d-18))) then
        tmp = (x / y) + ((-2.0d0) - ((-2.0d0) / t))
    else
        tmp = (x / y) + (((2.0d0 / z) / t) - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -17000.0) || !(z <= 1.4e-18)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (x / y) + (((2.0 / z) / t) - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -17000.0) or not (z <= 1.4e-18):
		tmp = (x / y) + (-2.0 - (-2.0 / t))
	else:
		tmp = (x / y) + (((2.0 / z) / t) - 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -17000.0) || !(z <= 1.4e-18))
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(Float64(2.0 / z) / t) - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -17000.0) || ~((z <= 1.4e-18)))
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	else
		tmp = (x / y) + (((2.0 / z) / t) - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -17000.0], N[Not[LessEqual[z, 1.4e-18]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -17000 or 1.40000000000000006e-18 < z

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. remove-double-neg N/A

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

      9. mul-1-neg N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower-/.f64 99.7

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

   5. Applied rewrites 99.7%

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

   if -17000 < z < 1.40000000000000006e-18

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 98.1%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000 \lor \neg \left(z \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{\frac{2}{z}}{t} - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -17000 \lor \neg \left(z \leq 2.5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -17000.0) (not (<= z 2.5e-19)))
   (+ (/ x y) (- -2.0 (/ -2.0 t)))
   (+ (/ x y) (/ (/ 2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -17000.0) || !(z <= 2.5e-19)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} 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 <= (-17000.0d0)) .or. (.not. (z <= 2.5d-19))) then
        tmp = (x / y) + ((-2.0d0) - ((-2.0d0) / t))
    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 <= -17000.0) || !(z <= 2.5e-19)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -17000.0) or not (z <= 2.5e-19):
		tmp = (x / y) + (-2.0 - (-2.0 / t))
	else:
		tmp = (x / y) + ((2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -17000.0) || !(z <= 2.5e-19))
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -17000.0) || ~((z <= 2.5e-19)))
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	else
		tmp = (x / y) + ((2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -17000.0], N[Not[LessEqual[z, 2.5e-19]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -17000 or 2.5000000000000002e-19 < z

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. remove-double-neg N/A

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

      9. mul-1-neg N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower-/.f64 99.7

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

   5. Applied rewrites 99.7%

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

   if -17000 < z < 2.5000000000000002e-19

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l/ N/A

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

   5. Applied rewrites 89.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 89.4%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000 \lor \neg \left(z \leq 2.5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.9 \cdot 10^{+44} \lor \neg \left(\frac{x}{y} \leq 1000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.9e+44) (not (<= (/ x y) 1000.0)))
   (/ x y)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.9e+44) || !((x / y) <= 1000.0)) {
		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) <= (-1.9d+44)) .or. (.not. ((x / y) <= 1000.0d0))) 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) <= -1.9e+44) || !((x / y) <= 1000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.9e+44) or not ((x / y) <= 1000.0):
		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) <= -1.9e+44) || !(Float64(x / y) <= 1000.0))
		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) <= -1.9e+44) || ~(((x / y) <= 1000.0)))
		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], -1.9e+44], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1000.0]], $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) < -1.9000000000000001e44 or 1e3 < (/.f64 x y)

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 71.6

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

   5. Applied rewrites 71.6%

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

   if -1.9000000000000001e44 < (/.f64 x y) < 1e3

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 61.7%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.9 \cdot 10^{+44} \lor \neg \left(\frac{x}{y} \leq 1000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 38:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.9e+44)
   (/ x y)
   (if (<= (/ x y) 38.0) (- (/ 2.0 t) 2.0) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.9e+44) {
		tmp = x / y;
	} else if ((x / y) <= 38.0) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.9d+44)) then
        tmp = x / y
    else if ((x / y) <= 38.0d0) then
        tmp = (2.0d0 / t) - 2.0d0
    else
        tmp = (x / y) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.9e+44) {
		tmp = x / y;
	} else if ((x / y) <= 38.0) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.9e+44:
		tmp = x / y
	elif (x / y) <= 38.0:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.9e+44)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 38.0)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.9e+44)
		tmp = x / y;
	elseif ((x / y) <= 38.0)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.9e+44], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 38.0], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.9000000000000001e44

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 77.2

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

   5. Applied rewrites 77.2%

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

   if -1.9000000000000001e44 < (/.f64 x y) < 38

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 61.7%

      \[\leadsto \frac{2}{t} - 2 \]

   if 38 < (/.f64 x y)

   1. Initial program 87.2%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 67.6%

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

Alternative 10: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -17000 \lor \neg \left(z \leq 2.5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -17000.0) (not (<= z 2.5e-19)))
   (+ (/ x y) (- -2.0 (/ -2.0 t)))
   (+ (/ x y) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -17000.0) || !(z <= 2.5e-19)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} 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 <= (-17000.0d0)) .or. (.not. (z <= 2.5d-19))) then
        tmp = (x / y) + ((-2.0d0) - ((-2.0d0) / t))
    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 <= -17000.0) || !(z <= 2.5e-19)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -17000.0) or not (z <= 2.5e-19):
		tmp = (x / y) + (-2.0 - (-2.0 / t))
	else:
		tmp = (x / y) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -17000.0) || !(z <= 2.5e-19))
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -17000.0) || ~((z <= 2.5e-19)))
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	else
		tmp = (x / y) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -17000.0], N[Not[LessEqual[z, 2.5e-19]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -17000 or 2.5000000000000002e-19 < z

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. remove-double-neg N/A

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

      9. mul-1-neg N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower-/.f64 99.7

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

   5. Applied rewrites 99.7%

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

   if -17000 < z < 2.5000000000000002e-19

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 89.4%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000 \lor \neg \left(z \leq 2.5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-103} \lor \neg \left(z \leq 1.02 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e-103) (not (<= z 1.02e-27)))
   (+ (/ x y) (- -2.0 (/ -2.0 t)))
   (- (/ (fma z 2.0 2.0) (* t z)) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e-103) || !(z <= 1.02e-27)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (fma(z, 2.0, 2.0) / (t * z)) - 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e-103) || !(z <= 1.02e-27))
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / t)));
	else
		tmp = Float64(Float64(fma(z, 2.0, 2.0) / Float64(t * z)) - 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e-103], N[Not[LessEqual[z, 1.02e-27]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000003e-103 or 1.02000000000000002e-27 < z

   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 z around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. remove-double-neg N/A

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

      9. mul-1-neg N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower-/.f64 95.0

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

   5. Applied rewrites 95.0%

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

   if -6.2000000000000003e-103 < z < 1.02000000000000002e-27

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 77.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 10.7%

      \[\leadsto \frac{2}{t} - 2 \]

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 77.2%

       \[\leadsto \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} - 2 \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-103} \lor \neg \left(z \leq 1.02 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.2% accurate, 3.9× 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 86.6%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{x}{y}} \]
4. Step-by-step derivation

   1. lower-/.f64 40.8

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

5. Applied rewrites 40.8%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
6. Add Preprocessing

Developer Target 1: 99.1% accurate, 1.1× 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 2024318 
(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))))