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

Percentage Accurate: 86.7% → 99.5%

Time: 11.7s

Alternatives: 13

Speedup: 0.7×

• 23.3% 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: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 62.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+192}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-61}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 88000000000000 \lor \neg \left(z \leq 9.2 \cdot 10^{+154}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -1.65e+192)
     t_2
     (if (<= z -1.3e+169)
       t_1
       (if (<= z -3.6e+15)
         t_2
         (if (<= z -6.8e-109)
           t_1
           (if (<= z 3.5e-61)
             (/ 2.0 (* z t))
             (if (or (<= z 88000000000000.0) (not (<= z 9.2e+154)))
               t_1
               t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.65e+192) {
		tmp = t_2;
	} else if (z <= -1.3e+169) {
		tmp = t_1;
	} else if (z <= -3.6e+15) {
		tmp = t_2;
	} else if (z <= -6.8e-109) {
		tmp = t_1;
	} else if (z <= 3.5e-61) {
		tmp = 2.0 / (z * t);
	} else if ((z <= 88000000000000.0) || !(z <= 9.2e+154)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    t_2 = (-2.0d0) + (2.0d0 / t)
    if (z <= (-1.65d+192)) then
        tmp = t_2
    else if (z <= (-1.3d+169)) then
        tmp = t_1
    else if (z <= (-3.6d+15)) then
        tmp = t_2
    else if (z <= (-6.8d-109)) then
        tmp = t_1
    else if (z <= 3.5d-61) then
        tmp = 2.0d0 / (z * t)
    else if ((z <= 88000000000000.0d0) .or. (.not. (z <= 9.2d+154))) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.65e+192) {
		tmp = t_2;
	} else if (z <= -1.3e+169) {
		tmp = t_1;
	} else if (z <= -3.6e+15) {
		tmp = t_2;
	} else if (z <= -6.8e-109) {
		tmp = t_1;
	} else if (z <= 3.5e-61) {
		tmp = 2.0 / (z * t);
	} else if ((z <= 88000000000000.0) || !(z <= 9.2e+154)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	t_2 = -2.0 + (2.0 / t)
	tmp = 0
	if z <= -1.65e+192:
		tmp = t_2
	elif z <= -1.3e+169:
		tmp = t_1
	elif z <= -3.6e+15:
		tmp = t_2
	elif z <= -6.8e-109:
		tmp = t_1
	elif z <= 3.5e-61:
		tmp = 2.0 / (z * t)
	elif (z <= 88000000000000.0) or not (z <= 9.2e+154):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	t_2 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -1.65e+192)
		tmp = t_2;
	elseif (z <= -1.3e+169)
		tmp = t_1;
	elseif (z <= -3.6e+15)
		tmp = t_2;
	elseif (z <= -6.8e-109)
		tmp = t_1;
	elseif (z <= 3.5e-61)
		tmp = Float64(2.0 / Float64(z * t));
	elseif ((z <= 88000000000000.0) || !(z <= 9.2e+154))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	t_2 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if (z <= -1.65e+192)
		tmp = t_2;
	elseif (z <= -1.3e+169)
		tmp = t_1;
	elseif (z <= -3.6e+15)
		tmp = t_2;
	elseif (z <= -6.8e-109)
		tmp = t_1;
	elseif (z <= 3.5e-61)
		tmp = 2.0 / (z * t);
	elseif ((z <= 88000000000000.0) || ~((z <= 9.2e+154)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+192], t$95$2, If[LessEqual[z, -1.3e+169], t$95$1, If[LessEqual[z, -3.6e+15], t$95$2, If[LessEqual[z, -6.8e-109], t$95$1, If[LessEqual[z, 3.5e-61], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 88000000000000.0], N[Not[LessEqual[z, 9.2e+154]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000005e192 or -1.3e169 < z < -3.6e15 or 8.8e13 < z < 9.1999999999999999e154

   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 t around 0 95.4%

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

      1. associate-+r+ 95.4%

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

      2. associate-*r/ 95.4%

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

      3. metadata-eval 95.4%

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

      4. sub-neg 95.4%

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

      5. metadata-eval 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in y around 0 81.3%

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

      1. associate--l+ 81.3%

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

      2. associate-*r/ 81.3%

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

      3. metadata-eval 81.3%

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

      4. fmm-def 81.3%

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

      5. *-commutative 81.3%

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

      6. metadata-eval 81.3%

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

      7. fma-define 81.3%

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

      8. associate-*r/ 81.3%

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

      9. metadata-eval 81.3%

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

      10. associate-/r* 81.3%

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

   8. Simplified 81.3%

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

   9. Taylor expanded in x around 0 79.7%

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

       1. sub-neg 79.7%

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

       2. metadata-eval 79.7%

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

       3. associate-/r* 79.7%

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

       4. associate-*r/ 79.7%

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

       5. associate-*l/ 79.7%

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

       6. distribute-rgt-in 79.7%

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

       7. associate-*l/ 79.7%

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

       8. associate-*r/ 79.7%

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

       9. *-lft-identity 79.7%

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

       10. +-commutative 79.7%

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

   11. Simplified 79.7%

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

   12. Taylor expanded in z around inf 79.7%

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

       1. associate-*r/ 79.7%

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

       2. metadata-eval 79.7%

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

       3. sub-neg 79.7%

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

       4. metadata-eval 79.7%

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

       5. +-commutative 79.7%

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

   14. Simplified 79.7%

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

   if -1.65000000000000005e192 < z < -1.3e169 or -3.6e15 < z < -6.80000000000000023e-109 or 3.5000000000000003e-61 < z < 8.8e13 or 9.1999999999999999e154 < z

   1. Initial program 78.6%

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

   3. Taylor expanded in t around inf 76.6%

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

   if -6.80000000000000023e-109 < z < 3.5000000000000003e-61

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 93.0%

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

      1. associate-+r+ 93.0%

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

      2. associate-*r/ 93.0%

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

      3. metadata-eval 93.0%

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

      4. sub-neg 93.0%

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

      5. metadata-eval 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in z around 0 76.3%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+192}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-61}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 88000000000000 \lor \neg \left(z \leq 9.2 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.35 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-319}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.3 \cdot 10^{-272}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.35e+22)
   (/ x y)
   (if (<= (/ x y) -1e-319)
     -2.0
     (if (<= (/ x y) 2.3e-272) (/ 2.0 t) (if (<= (/ x y) 2.0) -2.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.35e+22) {
		tmp = x / y;
	} else if ((x / y) <= -1e-319) {
		tmp = -2.0;
	} else if ((x / y) <= 2.3e-272) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} 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) <= (-2.35d+22)) then
        tmp = x / y
    else if ((x / y) <= (-1d-319)) then
        tmp = -2.0d0
    else if ((x / y) <= 2.3d-272) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2.0d0) then
        tmp = -2.0d0
    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) <= -2.35e+22) {
		tmp = x / y;
	} else if ((x / y) <= -1e-319) {
		tmp = -2.0;
	} else if ((x / y) <= 2.3e-272) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.35e+22:
		tmp = x / y
	elif (x / y) <= -1e-319:
		tmp = -2.0
	elif (x / y) <= 2.3e-272:
		tmp = 2.0 / t
	elif (x / y) <= 2.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.35e+22)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -1e-319)
		tmp = -2.0;
	elseif (Float64(x / y) <= 2.3e-272)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2.35e+22)
		tmp = x / y;
	elseif ((x / y) <= -1e-319)
		tmp = -2.0;
	elseif ((x / y) <= 2.3e-272)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.35e+22], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1e-319], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 2.3e-272], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.0], -2.0, N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.3500000000000001e22 or 2 < (/.f64 x y)

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf 65.0%

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

   if -2.3500000000000001e22 < (/.f64 x y) < -9.99989e-320 or 2.29999999999999989e-272 < (/.f64 x y) < 2

   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 0 99.8%

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

      1. associate-+r+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 82.7%

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

      1. associate--l+ 82.7%

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

      2. associate-*r/ 82.7%

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

      3. metadata-eval 82.7%

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

      4. fmm-def 82.7%

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

      5. *-commutative 82.7%

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

      6. metadata-eval 82.7%

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

      7. fma-define 82.7%

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

      8. associate-*r/ 82.7%

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

      9. metadata-eval 82.7%

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

      10. associate-/r* 82.7%

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

   8. Simplified 82.7%

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

   9. Taylor expanded in x around 0 99.4%

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

       1. sub-neg 99.4%

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

       2. metadata-eval 99.4%

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

       3. associate-/r* 99.4%

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

       4. associate-*r/ 99.4%

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

       5. associate-*l/ 99.3%

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

       6. distribute-rgt-in 99.3%

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

       7. associate-*l/ 99.3%

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

       8. associate-*r/ 99.3%

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

       9. *-lft-identity 99.3%

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

       10. +-commutative 99.3%

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

   11. Simplified 99.3%

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

   12. Taylor expanded in t around inf 39.9%

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

   if -9.99989e-320 < (/.f64 x y) < 2.29999999999999989e-272

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 83.1%

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

      1. associate-*r/ 83.1%

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

      2. metadata-eval 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in z around inf 38.9%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.35 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-319}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.3 \cdot 10^{-272}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+81} \lor \neg \left(\frac{x}{y} \leq 100000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+81) (not (<= (/ x y) 100000000000.0)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))
   (/ (+ (+ 2.0 (/ 2.0 z)) (* t (+ (/ x y) -2.0))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+81) || !((x / y) <= 100000000000.0)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d+81)) .or. (.not. ((x / y) <= 100000000000.0d0))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) + (t * ((x / y) + (-2.0d0)))) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+81) || !((x / y) <= 100000000000.0)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+81) or not ((x / y) <= 100000000000.0):
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	else:
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+81) || !(Float64(x / y) <= 100000000000.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) + Float64(t * Float64(Float64(x / y) + -2.0))) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+81) || ~(((x / y) <= 100000000000.0)))
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	else
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+81], N[Not[LessEqual[N[(x / y), $MachinePrecision], 100000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999921e80 or 1e11 < (/.f64 x y)

   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 t around 0 98.9%

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

   if -9.99999999999999921e80 < (/.f64 x y) < 1e11

   1. Initial program 89.7%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+81} \lor \neg \left(\frac{x}{y} \leq 100000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1000.0) (not (<= (/ x y) 5e-13)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))
   (+ -2.0 (* (+ 2.0 (/ 2.0 z)) (/ 1.0 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1000.0) || !((x / y) <= 5e-13)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) * (1.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1000.0d0)) .or. (.not. ((x / y) <= 5d-13))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) * (1.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1000.0) || !((x / y) <= 5e-13)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) * (1.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1000.0) or not ((x / y) <= 5e-13):
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) * (1.0 / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1000.0) || !(Float64(x / y) <= 5e-13))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) * Float64(1.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1000.0) || ~(((x / y) <= 5e-13)))
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) * (1.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-13]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e3 or 4.9999999999999999e-13 < (/.f64 x y)

   1. Initial program 85.1%

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

   3. Taylor expanded in t around 0 98.4%

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

   if -1e3 < (/.f64 x y) < 4.9999999999999999e-13

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. associate-+r+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 75.3%

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

      1. associate--l+ 75.3%

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

      2. associate-*r/ 75.3%

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

      3. metadata-eval 75.3%

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

      4. fmm-def 75.3%

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

      5. *-commutative 75.3%

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

      6. metadata-eval 75.3%

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

      7. fma-define 75.3%

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

      8. associate-*r/ 75.3%

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

      9. metadata-eval 75.3%

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

      10. associate-/r* 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in x around 0 99.6%

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

       1. sub-neg 99.6%

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

       2. associate-/r* 99.5%

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

       3. associate-*r/ 99.5%

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

       4. associate-*l/ 99.5%

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

       5. distribute-rgt-in 99.5%

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

       6. metadata-eval 99.5%

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

   11. Simplified 99.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.02 \cdot 10^{+24} \lor \neg \left(\frac{x}{y} \leq 7.5 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.02e+24) (not (<= (/ x y) 7.5e+66)))
   (+ (/ x y) (/ 2.0 t))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.02e+24) || !((x / y) <= 7.5e+66)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1.02d+24)) .or. (.not. ((x / y) <= 7.5d+66))) then
        tmp = (x / y) + (2.0d0 / t)
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.02e+24) || !((x / y) <= 7.5e+66)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.02e+24) or not ((x / y) <= 7.5e+66):
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.02e+24) || !(Float64(x / y) <= 7.5e+66))
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.02e+24) || ~(((x / y) <= 7.5e+66)))
		tmp = (x / y) + (2.0 / t);
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.02e+24], N[Not[LessEqual[N[(x / y), $MachinePrecision], 7.5e+66]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.02000000000000004e24 or 7.50000000000000024e66 < (/.f64 x y)

   1. Initial program 85.0%

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

   3. Taylor expanded in t around 0 79.1%

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

      1. associate-+r+ 79.1%

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

      2. associate-*r/ 79.1%

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

      3. metadata-eval 79.1%

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

      4. sub-neg 79.1%

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

      5. metadata-eval 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in z around inf 63.0%

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

   7. Taylor expanded in x around inf 59.8%

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

      1. associate-*l/ 60.9%

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

      2. *-commutative 60.9%

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

   9. Simplified 60.9%

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

   10. Taylor expanded in x around 0 83.8%

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

       1. associate-*r/ 83.8%

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

       2. metadata-eval 83.8%

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

       3. +-commutative 83.8%

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

   12. Simplified 83.8%

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

   if -1.02000000000000004e24 < (/.f64 x y) < 7.50000000000000024e66

   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 0 99.3%

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

      1. associate-+r+ 99.3%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in y around 0 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-*r/ 78.5%

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

      3. metadata-eval 78.5%

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

      4. fmm-def 78.5%

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

      5. *-commutative 78.5%

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

      6. metadata-eval 78.5%

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

      7. fma-define 78.5%

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

      8. associate-*r/ 78.5%

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

      9. metadata-eval 78.5%

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

      10. associate-/r* 78.5%

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

   8. Simplified 78.5%

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

   9. Taylor expanded in x around 0 95.3%

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

       1. sub-neg 95.3%

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

       2. metadata-eval 95.3%

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

       3. associate-/r* 95.3%

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

       4. associate-*r/ 95.3%

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

       5. associate-*l/ 95.3%

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

       6. distribute-rgt-in 95.3%

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

       7. associate-*l/ 95.3%

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

       8. associate-*r/ 95.3%

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

       9. *-lft-identity 95.3%

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

       10. +-commutative 95.3%

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

   11. Simplified 95.3%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.02 \cdot 10^{+24} \lor \neg \left(\frac{x}{y} \leq 7.5 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+58} \lor \neg \left(\frac{x}{y} \leq 100000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+58) (not (<= (/ x y) 100000000000.0)))
   (+ (/ x y) (/ 2.0 (* z t)))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+58) || !((x / y) <= 100000000000.0)) {
		tmp = (x / y) + (2.0 / (z * t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d+58)) .or. (.not. ((x / y) <= 100000000000.0d0))) then
        tmp = (x / y) + (2.0d0 / (z * t))
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+58) || !((x / y) <= 100000000000.0)) {
		tmp = (x / y) + (2.0 / (z * t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+58) or not ((x / y) <= 100000000000.0):
		tmp = (x / y) + (2.0 / (z * t))
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+58) || !(Float64(x / y) <= 100000000000.0))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+58) || ~(((x / y) <= 100000000000.0)))
		tmp = (x / y) + (2.0 / (z * t));
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+58], N[Not[LessEqual[N[(x / y), $MachinePrecision], 100000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999944e57 or 1e11 < (/.f64 x y)

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 88.9%

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

   if -9.99999999999999944e57 < (/.f64 x y) < 1e11

   1. Initial program 90.0%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 76.8%

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

      1. associate--l+ 76.8%

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

      2. associate-*r/ 76.8%

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

      3. metadata-eval 76.8%

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

      4. fmm-def 76.8%

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

      5. *-commutative 76.8%

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

      6. metadata-eval 76.8%

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

      7. fma-define 76.8%

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

      8. associate-*r/ 76.8%

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

      9. metadata-eval 76.8%

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

      10. associate-/r* 76.8%

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

   8. Simplified 76.8%

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

   9. Taylor expanded in x around 0 97.7%

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

       1. sub-neg 97.7%

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

       2. metadata-eval 97.7%

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

       3. associate-/r* 97.7%

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

       4. associate-*r/ 97.7%

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

       5. associate-*l/ 97.7%

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

       6. distribute-rgt-in 97.7%

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

       7. associate-*l/ 97.7%

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

       8. associate-*r/ 97.7%

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

       9. *-lft-identity 97.7%

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

       10. +-commutative 97.7%

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

   11. Simplified 97.7%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+58} \lor \neg \left(\frac{x}{y} \leq 100000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-26}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= z -2.05e+46)
     t_1
     (if (<= z -2.05e-109)
       (- (/ x y) 2.0)
       (if (<= z 1.4e-26) (/ 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if (z <= -2.05e+46) {
		tmp = t_1;
	} else if (z <= -2.05e-109) {
		tmp = (x / y) - 2.0;
	} else if (z <= 1.4e-26) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (2.0d0 / t)
    if (z <= (-2.05d+46)) then
        tmp = t_1
    else if (z <= (-2.05d-109)) then
        tmp = (x / y) - 2.0d0
    else if (z <= 1.4d-26) then
        tmp = 2.0d0 / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if (z <= -2.05e+46) {
		tmp = t_1;
	} else if (z <= -2.05e-109) {
		tmp = (x / y) - 2.0;
	} else if (z <= 1.4e-26) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / t)
	tmp = 0
	if z <= -2.05e+46:
		tmp = t_1
	elif z <= -2.05e-109:
		tmp = (x / y) - 2.0
	elif z <= 1.4e-26:
		tmp = 2.0 / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -2.05e+46)
		tmp = t_1;
	elseif (z <= -2.05e-109)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (z <= 1.4e-26)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if (z <= -2.05e+46)
		tmp = t_1;
	elseif (z <= -2.05e-109)
		tmp = (x / y) - 2.0;
	elseif (z <= 1.4e-26)
		tmp = 2.0 / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+46], t$95$1, If[LessEqual[z, -2.05e-109], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[z, 1.4e-26], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e46 or 1.4000000000000001e-26 < z

   1. Initial program 76.0%

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

   3. Taylor expanded in t around 0 90.8%

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

      1. associate-+r+ 90.8%

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

      2. associate-*r/ 90.8%

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

      3. metadata-eval 90.8%

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

      4. sub-neg 90.8%

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

      5. metadata-eval 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in z around inf 90.1%

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

   7. Taylor expanded in x around inf 67.0%

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

      1. associate-*l/ 66.9%

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

      2. *-commutative 66.9%

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

   9. Simplified 66.9%

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

   10. Taylor expanded in x around 0 78.6%

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

       1. associate-*r/ 78.6%

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

       2. metadata-eval 78.6%

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

       3. +-commutative 78.6%

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

   12. Simplified 78.6%

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

   if -2.05e46 < z < -2.0500000000000001e-109

   1. Initial program 96.5%

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

   3. Taylor expanded in t around inf 71.6%

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

   if -2.0500000000000001e-109 < z < 1.4000000000000001e-26

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 93.4%

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

      1. associate-+r+ 93.4%

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

      2. associate-*r/ 93.4%

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

      3. metadata-eval 93.4%

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

      4. sub-neg 93.4%

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

      5. metadata-eval 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in z around 0 74.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-26}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.6 \cdot 10^{+51} \lor \neg \left(\frac{x}{y} \leq 4000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3.6e+51) (not (<= (/ x y) 4000000.0)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3.6e+51) || !((x / y) <= 4000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-3.6d+51)) .or. (.not. ((x / y) <= 4000000.0d0))) then
        tmp = x / y
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3.6e+51) || !((x / y) <= 4000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3.6e+51) or not ((x / y) <= 4000000.0):
		tmp = x / y
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -3.6e+51) || !(Float64(x / y) <= 4000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -3.6e+51) || ~(((x / y) <= 4000000.0)))
		tmp = x / y;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -3.6e+51], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.60000000000000011e51 or 4e6 < (/.f64 x y)

   1. Initial program 84.5%

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

   3. Taylor expanded in x around inf 67.7%

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

   if -3.60000000000000011e51 < (/.f64 x y) < 4e6

   1. Initial program 89.9%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 76.5%

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

      1. associate--l+ 76.5%

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

      2. associate-*r/ 76.5%

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

      3. metadata-eval 76.5%

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

      4. fmm-def 76.5%

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

      5. *-commutative 76.5%

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

      6. metadata-eval 76.5%

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

      7. fma-define 76.5%

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

      8. associate-*r/ 76.5%

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

      9. metadata-eval 76.5%

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

      10. associate-/r* 76.5%

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

   8. Simplified 76.5%

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

   9. Taylor expanded in x around 0 97.7%

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

       1. sub-neg 97.7%

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

       2. metadata-eval 97.7%

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

       3. associate-/r* 97.7%

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

       4. associate-*r/ 97.7%

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

       5. associate-*l/ 97.7%

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

       6. distribute-rgt-in 97.7%

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

       7. associate-*l/ 97.7%

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

       8. associate-*r/ 97.7%

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

       9. *-lft-identity 97.7%

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

       10. +-commutative 97.7%

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

   11. Simplified 97.7%

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

   12. Taylor expanded in z around inf 59.9%

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

       1. associate-*r/ 59.9%

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

       2. metadata-eval 59.9%

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

       3. sub-neg 59.9%

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

       4. metadata-eval 59.9%

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

       5. +-commutative 59.9%

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

   14. Simplified 59.9%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.6 \cdot 10^{+51} \lor \neg \left(\frac{x}{y} \leq 4000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 240:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.5e+54)
   (/ x y)
   (if (<= (/ x y) 240.0) (+ -2.0 (/ 2.0 t)) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.5e+54) {
		tmp = x / y;
	} else if ((x / y) <= 240.0) {
		tmp = -2.0 + (2.0 / t);
	} 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) <= (-1.5d+54)) then
        tmp = x / y
    else if ((x / y) <= 240.0d0) then
        tmp = (-2.0d0) + (2.0d0 / t)
    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) <= -1.5e+54) {
		tmp = x / y;
	} else if ((x / y) <= 240.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.5e+54:
		tmp = x / y
	elif (x / y) <= 240.0:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.5e+54)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 240.0)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	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) <= -1.5e+54)
		tmp = x / y;
	elseif ((x / y) <= 240.0)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.5e+54], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 240.0], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.4999999999999999e54

   1. Initial program 80.3%

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

   3. Taylor expanded in x around inf 76.5%

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

   if -1.4999999999999999e54 < (/.f64 x y) < 240

   1. Initial program 90.4%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-*r/ 76.2%

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

      3. metadata-eval 76.2%

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

      4. fmm-def 76.2%

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

      5. *-commutative 76.2%

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

      6. metadata-eval 76.2%

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

      7. fma-define 76.2%

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

      8. associate-*r/ 76.2%

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

      9. metadata-eval 76.2%

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

      10. associate-/r* 76.1%

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

   8. Simplified 76.1%

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

   9. Taylor expanded in x around 0 98.4%

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

       1. sub-neg 98.4%

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

       2. metadata-eval 98.4%

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

       3. associate-/r* 98.3%

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

       4. associate-*r/ 98.3%

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

       5. associate-*l/ 98.3%

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

       6. distribute-rgt-in 98.3%

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

       7. associate-*l/ 98.3%

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

       8. associate-*r/ 98.3%

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

       9. *-lft-identity 98.3%

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

       10. +-commutative 98.3%

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

   11. Simplified 98.3%

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

   12. Taylor expanded in z around inf 60.0%

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

       1. associate-*r/ 60.0%

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

       2. metadata-eval 60.0%

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

       3. sub-neg 60.0%

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

       4. metadata-eval 60.0%

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

       5. +-commutative 60.0%

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

   14. Simplified 60.0%

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

   if 240 < (/.f64 x y)

   1. Initial program 87.1%

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

   3. Taylor expanded in t around inf 59.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 240:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+25} \lor \neg \left(t \leq 4.5 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.5e+25) (not (<= t 4.5e+17)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.5e+25) || !(t <= 4.5e+17)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-6.5d+25)) .or. (.not. (t <= 4.5d+17))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.5e+25) || !(t <= 4.5e+17)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.5e+25) or not (t <= 4.5e+17):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.5e+25) || !(t <= 4.5e+17))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.5e+25) || ~((t <= 4.5e+17)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.5e+25], N[Not[LessEqual[t, 4.5e+17]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.50000000000000005e25 or 4.5e17 < t

   1. Initial program 72.5%

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

   3. Taylor expanded in t around inf 87.0%

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

   if -6.50000000000000005e25 < t < 4.5e17

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 82.1%

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

      1. associate-*r/ 82.1%

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

      2. metadata-eval 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+25} \lor \neg \left(t \leq 4.5 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5600000:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5600000.0) -2.0 (if (<= t 2.8e-11) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5600000.0) {
		tmp = -2.0;
	} else if (t <= 2.8e-11) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5600000.0d0)) then
        tmp = -2.0d0
    else if (t <= 2.8d-11) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5600000.0) {
		tmp = -2.0;
	} else if (t <= 2.8e-11) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5600000.0:
		tmp = -2.0
	elif t <= 2.8e-11:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5600000.0)
		tmp = -2.0;
	elseif (t <= 2.8e-11)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5600000.0)
		tmp = -2.0;
	elseif (t <= 2.8e-11)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5600000.0], -2.0, If[LessEqual[t, 2.8e-11], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -5.6e6 or 2.8e-11 < t

   1. Initial program 75.1%

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

   3. Taylor expanded in t around 0 82.9%

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

      1. associate-+r+ 82.9%

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

      2. associate-*r/ 82.9%

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

      3. metadata-eval 82.9%

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

      4. sub-neg 82.9%

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

      5. metadata-eval 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in y around 0 93.6%

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

      1. associate--l+ 93.6%

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

      2. associate-*r/ 93.6%

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

      3. metadata-eval 93.6%

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

      4. fmm-def 93.6%

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

      5. *-commutative 93.6%

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

      6. metadata-eval 93.6%

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

      7. fma-define 93.6%

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

      8. associate-*r/ 93.6%

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

      9. metadata-eval 93.6%

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

      10. associate-/r* 93.6%

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

   8. Simplified 93.6%

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

   9. Taylor expanded in x around 0 56.1%

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

       1. sub-neg 56.1%

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

       2. metadata-eval 56.1%

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

       3. associate-/r* 56.1%

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

       4. associate-*r/ 56.1%

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

       5. associate-*l/ 56.1%

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

       6. distribute-rgt-in 56.1%

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

       7. associate-*l/ 56.1%

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

       8. associate-*r/ 56.1%

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

       9. *-lft-identity 56.1%

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

       10. +-commutative 56.1%

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

   11. Simplified 56.1%

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

   12. Taylor expanded in t around inf 38.8%

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

   if -5.6e6 < t < 2.8e-11

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 85.0%

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

      1. associate-*r/ 85.0%

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

      2. metadata-eval 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in z around inf 39.5%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5600000:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 19.0% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.7%

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

3. Taylor expanded in t around 0 91.9%

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

   1. associate-+r+ 91.9%

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

   2. associate-*r/ 91.9%

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

   3. metadata-eval 91.9%

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

   4. sub-neg 91.9%

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

   5. metadata-eval 91.9%

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

5. Simplified 91.9%

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

6. Taylor expanded in y around 0 84.9%

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

   1. associate--l+ 84.9%

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

   2. associate-*r/ 84.9%

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

   3. metadata-eval 84.9%

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

   4. fmm-def 84.9%

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

   5. *-commutative 84.9%

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

   6. metadata-eval 84.9%

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

   7. fma-define 84.9%

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

   8. associate-*r/ 84.9%

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

   9. metadata-eval 84.9%

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

   10. associate-/r* 84.9%

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

8. Simplified 84.9%

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

9. Taylor expanded in x around 0 71.5%

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

    1. sub-neg 71.5%

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

    2. metadata-eval 71.5%

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

    3. associate-/r* 71.5%

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

    4. associate-*r/ 71.5%

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

    5. associate-*l/ 71.5%

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

    6. distribute-rgt-in 71.5%

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

    7. associate-*l/ 71.5%

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

    8. associate-*r/ 71.5%

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

    9. *-lft-identity 71.5%

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

    10. +-commutative 71.5%

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

11. Simplified 71.5%

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

12. Taylor expanded in t around inf 19.8%

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

13. Final simplification 19.8%

    \[\leadsto -2 \]
14. Add Preprocessing

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024115 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

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