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

Percentage Accurate: 86.7% → 99.4%

Time: 9.6s

Alternatives: 12

Speedup: 1.3×

• 23.6% 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: 99.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

2. Taylor expanded in z around 0 98.3%

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

   1. div-sub 98.3%

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

   2. sub-neg 98.3%

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

   3. *-inverses 98.3%

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

   4. metadata-eval 98.3%

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

   5. distribute-lft-in 98.3%

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

   6. associate-*r/ 98.3%

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

   7. metadata-eval 98.3%

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

   8. metadata-eval 98.3%

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

   9. associate-*r/ 98.3%

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

   10. metadata-eval 98.3%

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

4. Simplified 98.3%

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

   1. div-inv 98.2%

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

   2. fma-def 99.0%

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

6. Applied egg-rr 99.0%

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

7. Final simplification 99.0%

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

Alternative 2: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000 \lor \neg \left(\frac{x}{y} \leq 0.05\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{t} + -2\right) + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -100000000.0) (not (<= (/ x y) 0.05)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* t z)))
   (+ (+ (/ 2.0 t) -2.0) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000000.0) || !((x / y) <= 0.05)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	} else {
		tmp = ((2.0 / t) + -2.0) + (2.0 / (t * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-100000000.0d0)) .or. (.not. ((x / y) <= 0.05d0))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (t * z))
    else
        tmp = ((2.0d0 / t) + (-2.0d0)) + (2.0d0 / (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000000.0) || !((x / y) <= 0.05)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	} else {
		tmp = ((2.0 / t) + -2.0) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -100000000.0) or not ((x / y) <= 0.05):
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z))
	else:
		tmp = ((2.0 / t) + -2.0) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -100000000.0) || !(Float64(x / y) <= 0.05))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(2.0 / t) + -2.0) + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -100000000.0) || ~(((x / y) <= 0.05)))
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	else
		tmp = ((2.0 / t) + -2.0) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -100000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.05]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e8 or 0.050000000000000003 < (/.f64 x y)

   1. Initial program 83.8%

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

   2. Taylor expanded in t around 0 96.3%

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

   if -1e8 < (/.f64 x y) < 0.050000000000000003

   1. Initial program 87.8%

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

   2. Taylor expanded in z around 0 99.9%

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

      1. div-sub 99.9%

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

      2. sub-neg 99.9%

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

      3. *-inverses 99.9%

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

      4. metadata-eval 99.9%

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

      5. distribute-lft-in 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-*r/ 99.9%

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

      10. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. 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. associate-*r/ 98.4%

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

      3. metadata-eval 98.4%

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

      4. associate-*r/ 98.4%

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

      5. metadata-eval 98.4%

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

      6. metadata-eval 98.4%

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

      7. +-commutative 98.4%

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

      8. associate-+r+ 98.4%

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

      9. +-commutative 98.4%

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

   7. Simplified 98.4%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000 \lor \neg \left(\frac{x}{y} \leq 0.05\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{t} + -2\right) + \frac{2}{t \cdot z}\\ \end{array} \]

Alternative 3: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := \frac{2}{t} + -2\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+82} \lor \neg \left(z \leq 3.3 \cdot 10^{+134}\right) \land z \leq 1.25 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (+ (/ 2.0 t) -2.0)))
   (if (<= z -1.2e+77)
     t_2
     (if (<= z -1.4e-59)
       t_1
       (if (<= z 8.5e-169)
         (/ 2.0 (* t z))
         (if (or (<= z 4.4e+82) (and (not (<= z 3.3e+134)) (<= z 1.25e+196)))
           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 / t) + -2.0;
	double tmp;
	if (z <= -1.2e+77) {
		tmp = t_2;
	} else if (z <= -1.4e-59) {
		tmp = t_1;
	} else if (z <= 8.5e-169) {
		tmp = 2.0 / (t * z);
	} else if ((z <= 4.4e+82) || (!(z <= 3.3e+134) && (z <= 1.25e+196))) {
		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 / t) + (-2.0d0)
    if (z <= (-1.2d+77)) then
        tmp = t_2
    else if (z <= (-1.4d-59)) then
        tmp = t_1
    else if (z <= 8.5d-169) then
        tmp = 2.0d0 / (t * z)
    else if ((z <= 4.4d+82) .or. (.not. (z <= 3.3d+134)) .and. (z <= 1.25d+196)) 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 / t) + -2.0;
	double tmp;
	if (z <= -1.2e+77) {
		tmp = t_2;
	} else if (z <= -1.4e-59) {
		tmp = t_1;
	} else if (z <= 8.5e-169) {
		tmp = 2.0 / (t * z);
	} else if ((z <= 4.4e+82) || (!(z <= 3.3e+134) && (z <= 1.25e+196))) {
		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 / t) + -2.0
	tmp = 0
	if z <= -1.2e+77:
		tmp = t_2
	elif z <= -1.4e-59:
		tmp = t_1
	elif z <= 8.5e-169:
		tmp = 2.0 / (t * z)
	elif (z <= 4.4e+82) or (not (z <= 3.3e+134) and (z <= 1.25e+196)):
		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(Float64(2.0 / t) + -2.0)
	tmp = 0.0
	if (z <= -1.2e+77)
		tmp = t_2;
	elseif (z <= -1.4e-59)
		tmp = t_1;
	elseif (z <= 8.5e-169)
		tmp = Float64(2.0 / Float64(t * z));
	elseif ((z <= 4.4e+82) || (!(z <= 3.3e+134) && (z <= 1.25e+196)))
		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 / t) + -2.0;
	tmp = 0.0;
	if (z <= -1.2e+77)
		tmp = t_2;
	elseif (z <= -1.4e-59)
		tmp = t_1;
	elseif (z <= 8.5e-169)
		tmp = 2.0 / (t * z);
	elseif ((z <= 4.4e+82) || (~((z <= 3.3e+134)) && (z <= 1.25e+196)))
		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[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[z, -1.2e+77], t$95$2, If[LessEqual[z, -1.4e-59], t$95$1, If[LessEqual[z, 8.5e-169], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.4e+82], And[N[Not[LessEqual[z, 3.3e+134]], $MachinePrecision], LessEqual[z, 1.25e+196]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1999999999999999e77 or 4.4000000000000002e82 < z < 3.3e134 or 1.2499999999999999e196 < z

   1. Initial program 70.7%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. div-sub 100.0%

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

      2. sub-neg 100.0%

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

      3. *-inverses 100.0%

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

      4. metadata-eval 100.0%

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

      5. distribute-lft-in 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

      1. div-inv 99.9%

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

      2. fma-def 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 76.2%

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

      1. sub-neg 76.2%

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

      2. associate-*r/ 76.2%

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

      3. metadata-eval 76.2%

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

      4. metadata-eval 76.2%

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

   9. Simplified 76.2%

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

   if -1.1999999999999999e77 < z < -1.3999999999999999e-59 or 8.50000000000000054e-169 < z < 4.4000000000000002e82 or 3.3e134 < z < 1.2499999999999999e196

   1. Initial program 89.3%

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

   2. Taylor expanded in t around inf 67.2%

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

   if -1.3999999999999999e-59 < z < 8.50000000000000054e-169

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 96.4%

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

      1. div-sub 96.4%

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

      2. sub-neg 96.4%

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

      3. *-inverses 96.4%

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

      4. metadata-eval 96.4%

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

      5. distribute-lft-in 96.4%

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

      6. associate-*r/ 96.4%

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

      7. metadata-eval 96.4%

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

      8. metadata-eval 96.4%

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

      9. associate-*r/ 96.4%

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

      10. metadata-eval 96.4%

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

   4. Simplified 96.4%

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

   5. Taylor expanded in z around 0 75.0%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+82} \lor \neg \left(z \leq 3.3 \cdot 10^{+134}\right) \land z \leq 1.25 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]

Alternative 4: 98.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((2.0 / t) + -2.0) + (2.0 / (t * z))) + (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 / t) + (-2.0d0)) + (2.0d0 / (t * z))) + (x / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

2. Taylor expanded in z around 0 98.3%

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

   1. div-sub 98.3%

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

   2. sub-neg 98.3%

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

   3. *-inverses 98.3%

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

   4. metadata-eval 98.3%

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

   5. distribute-lft-in 98.3%

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

   6. associate-*r/ 98.3%

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

   7. metadata-eval 98.3%

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

   8. metadata-eval 98.3%

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

   9. associate-*r/ 98.3%

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

   10. metadata-eval 98.3%

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

4. Simplified 98.3%

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

5. Final simplification 98.3%

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

Alternative 5: 67.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t} + \frac{x}{y}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-169}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 t) (/ x y))))
   (if (<= z -1.4e-58)
     t_1
     (if (<= z 8e-169)
       (/ 2.0 (* t z))
       (if (<= z 3.6e+16) (- (/ x y) 2.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + (x / y);
	double tmp;
	if (z <= -1.4e-58) {
		tmp = t_1;
	} else if (z <= 8e-169) {
		tmp = 2.0 / (t * z);
	} else if (z <= 3.6e+16) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / t) + (x / y)
    if (z <= (-1.4d-58)) then
        tmp = t_1
    else if (z <= 8d-169) then
        tmp = 2.0d0 / (t * z)
    else if (z <= 3.6d+16) then
        tmp = (x / y) - 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + (x / y);
	double tmp;
	if (z <= -1.4e-58) {
		tmp = t_1;
	} else if (z <= 8e-169) {
		tmp = 2.0 / (t * z);
	} else if (z <= 3.6e+16) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) + (x / y)
	tmp = 0
	if z <= -1.4e-58:
		tmp = t_1
	elif z <= 8e-169:
		tmp = 2.0 / (t * z)
	elif z <= 3.6e+16:
		tmp = (x / y) - 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) + Float64(x / y))
	tmp = 0.0
	if (z <= -1.4e-58)
		tmp = t_1;
	elseif (z <= 8e-169)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (z <= 3.6e+16)
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) + (x / y);
	tmp = 0.0;
	if (z <= -1.4e-58)
		tmp = t_1;
	elseif (z <= 8e-169)
		tmp = 2.0 / (t * z);
	elseif (z <= 3.6e+16)
		tmp = (x / y) - 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-58], t$95$1, If[LessEqual[z, 8e-169], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+16], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e-58 or 3.6e16 < z

   1. Initial program 75.9%

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

   2. Taylor expanded in t around 0 80.1%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate-*r/ 77.5%

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

      2. metadata-eval 77.5%

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

      3. +-commutative 77.5%

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

   5. Simplified 77.5%

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

   if -1.4e-58 < z < 8.00000000000000016e-169

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 96.4%

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

      1. div-sub 96.4%

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

      2. sub-neg 96.4%

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

      3. *-inverses 96.4%

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

      4. metadata-eval 96.4%

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

      5. distribute-lft-in 96.4%

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

      6. associate-*r/ 96.4%

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

      7. metadata-eval 96.4%

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

      8. metadata-eval 96.4%

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

      9. associate-*r/ 96.4%

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

      10. metadata-eval 96.4%

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

   4. Simplified 96.4%

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

   5. Taylor expanded in z around 0 75.0%

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

   if 8.00000000000000016e-169 < z < 3.6e16

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 62.6%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-58}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-169}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \end{array} \]

Alternative 6: 80.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-59} \lor \neg \left(z \leq 2.8 \cdot 10^{-169}\right):\\ \;\;\;\;\left(\frac{2}{t} + -2\right) + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e-59) (not (<= z 2.8e-169)))
   (+ (+ (/ 2.0 t) -2.0) (/ x y))
   (/ 2.0 (* t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-59) || !(z <= 2.8e-169)) {
		tmp = ((2.0 / t) + -2.0) + (x / y);
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.2d-59)) .or. (.not. (z <= 2.8d-169))) then
        tmp = ((2.0d0 / t) + (-2.0d0)) + (x / y)
    else
        tmp = 2.0d0 / (t * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-59) || !(z <= 2.8e-169)) {
		tmp = ((2.0 / t) + -2.0) + (x / y);
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e-59) or not (z <= 2.8e-169):
		tmp = ((2.0 / t) + -2.0) + (x / y)
	else:
		tmp = 2.0 / (t * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e-59) || !(z <= 2.8e-169))
		tmp = Float64(Float64(Float64(2.0 / t) + -2.0) + Float64(x / y));
	else
		tmp = Float64(2.0 / Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e-59) || ~((z <= 2.8e-169)))
		tmp = ((2.0 / t) + -2.0) + (x / y);
	else
		tmp = 2.0 / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e-59], N[Not[LessEqual[z, 2.8e-169]], $MachinePrecision]], N[(N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.19999999999999996e-59 or 2.79999999999999988e-169 < z

   1. Initial program 80.1%

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

   2. Taylor expanded in z around inf 90.6%

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

      1. div-sub 90.6%

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

      2. sub-neg 90.6%

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

      3. *-inverses 90.6%

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

      4. metadata-eval 90.6%

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

      5. distribute-lft-in 90.6%

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

      6. associate-*r/ 90.6%

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

      7. metadata-eval 90.6%

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

      8. metadata-eval 90.6%

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

   4. Simplified 90.6%

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

   if -5.19999999999999996e-59 < z < 2.79999999999999988e-169

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 96.4%

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

      1. div-sub 96.4%

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

      2. sub-neg 96.4%

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

      3. *-inverses 96.4%

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

      4. metadata-eval 96.4%

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

      5. distribute-lft-in 96.4%

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

      6. associate-*r/ 96.4%

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

      7. metadata-eval 96.4%

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

      8. metadata-eval 96.4%

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

      9. associate-*r/ 96.4%

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

      10. metadata-eval 96.4%

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

   4. Simplified 96.4%

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

   5. Taylor expanded in z around 0 75.0%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-59} \lor \neg \left(z \leq 2.8 \cdot 10^{-169}\right):\\ \;\;\;\;\left(\frac{2}{t} + -2\right) + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]

Alternative 7: 90.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-7} \lor \neg \left(z \leq 2.7 \cdot 10^{-87}\right):\\ \;\;\;\;\left(\frac{2}{t} + -2\right) + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e-7) (not (<= z 2.7e-87)))
   (+ (+ (/ 2.0 t) -2.0) (/ x y))
   (+ (/ 2.0 (* t z)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e-7) || !(z <= 2.7e-87)) {
		tmp = ((2.0 / t) + -2.0) + (x / y);
	} else {
		tmp = (2.0 / (t * z)) + (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 ((z <= (-7.5d-7)) .or. (.not. (z <= 2.7d-87))) then
        tmp = ((2.0d0 / t) + (-2.0d0)) + (x / y)
    else
        tmp = (2.0d0 / (t * z)) + (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e-7) || !(z <= 2.7e-87)) {
		tmp = ((2.0 / t) + -2.0) + (x / y);
	} else {
		tmp = (2.0 / (t * z)) + (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e-7) or not (z <= 2.7e-87):
		tmp = ((2.0 / t) + -2.0) + (x / y)
	else:
		tmp = (2.0 / (t * z)) + (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e-7) || !(z <= 2.7e-87))
		tmp = Float64(Float64(Float64(2.0 / t) + -2.0) + Float64(x / y));
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e-7) || ~((z <= 2.7e-87)))
		tmp = ((2.0 / t) + -2.0) + (x / y);
	else
		tmp = (2.0 / (t * z)) + (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e-7], N[Not[LessEqual[z, 2.7e-87]], $MachinePrecision]], N[(N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5000000000000002e-7 or 2.69999999999999984e-87 < z

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 96.4%

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

      1. div-sub 96.4%

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

      2. sub-neg 96.4%

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

      3. *-inverses 96.4%

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

      4. metadata-eval 96.4%

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

      5. distribute-lft-in 96.4%

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

      6. associate-*r/ 96.4%

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

      7. metadata-eval 96.4%

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

      8. metadata-eval 96.4%

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

   4. Simplified 96.4%

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

   if -7.5000000000000002e-7 < z < 2.69999999999999984e-87

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 88.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-7} \lor \neg \left(z \leq 2.7 \cdot 10^{-87}\right):\\ \;\;\;\;\left(\frac{2}{t} + -2\right) + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \]

Alternative 8: 64.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.85 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4150000000:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.85e+23)
   (/ x y)
   (if (<= (/ x y) 4150000000.0) (+ (/ 2.0 t) -2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.85e+23) {
		tmp = x / y;
	} else if ((x / y) <= 4150000000.0) {
		tmp = (2.0 / t) + -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) <= (-1.85d+23)) then
        tmp = x / y
    else if ((x / y) <= 4150000000.0d0) then
        tmp = (2.0d0 / t) + (-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) <= -1.85e+23) {
		tmp = x / y;
	} else if ((x / y) <= 4150000000.0) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.85e+23:
		tmp = x / y
	elif (x / y) <= 4150000000.0:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.85e+23)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4150000000.0)
		tmp = Float64(Float64(2.0 / t) + -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) <= -1.85e+23)
		tmp = x / y;
	elseif ((x / y) <= 4150000000.0)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.85e+23], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4150000000.0], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.85000000000000006e23 or 4.15e9 < (/.f64 x y)

   1. Initial program 83.6%

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

   2. Taylor expanded in x around inf 65.4%

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

   if -1.85000000000000006e23 < (/.f64 x y) < 4.15e9

   1. Initial program 87.7%

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

   2. Taylor expanded in z around inf 62.5%

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

      1. div-sub 62.5%

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

      2. sub-neg 62.5%

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

      3. *-inverses 62.5%

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

      4. metadata-eval 62.5%

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

      5. distribute-lft-in 62.5%

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

      6. associate-*r/ 62.5%

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

      7. metadata-eval 62.5%

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

      8. metadata-eval 62.5%

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

   4. Simplified 62.5%

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

      1. div-inv 62.5%

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

      2. fma-def 62.5%

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

   6. Applied egg-rr 62.5%

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

   7. Taylor expanded in x around 0 60.4%

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

      1. sub-neg 60.4%

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

      2. associate-*r/ 60.4%

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

      3. metadata-eval 60.4%

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

      4. metadata-eval 60.4%

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

   9. Simplified 60.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.85 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4150000000:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 9: 65.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.8e+23)
   (/ x y)
   (if (<= (/ x y) 3.5e-7) (+ (/ 2.0 t) -2.0) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.8e+23) {
		tmp = x / y;
	} else if ((x / y) <= 3.5e-7) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.8d+23)) then
        tmp = x / y
    else if ((x / y) <= 3.5d-7) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.8e+23) {
		tmp = x / y;
	} else if ((x / y) <= 3.5e-7) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.8e+23:
		tmp = x / y
	elif (x / y) <= 3.5e-7:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.8e+23)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 3.5e-7)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.8e+23)
		tmp = x / y;
	elseif ((x / y) <= 3.5e-7)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.8e+23], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3.5e-7], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.7999999999999999e23

   1. Initial program 88.2%

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

   2. Taylor expanded in x around inf 62.1%

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

   if -1.7999999999999999e23 < (/.f64 x y) < 3.49999999999999984e-7

   1. Initial program 87.1%

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

   2. Taylor expanded in z around inf 63.7%

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

      1. div-sub 63.7%

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

      2. sub-neg 63.7%

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

      3. *-inverses 63.7%

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

      4. metadata-eval 63.7%

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

      5. distribute-lft-in 63.7%

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

      6. associate-*r/ 63.7%

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

      7. metadata-eval 63.7%

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

      8. metadata-eval 63.7%

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

   4. Simplified 63.7%

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

      1. div-inv 63.7%

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

      2. fma-def 63.7%

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

   6. Applied egg-rr 63.7%

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

   7. Taylor expanded in x around 0 62.6%

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

      1. sub-neg 62.6%

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

      2. associate-*r/ 62.6%

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

      3. metadata-eval 62.6%

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

      4. metadata-eval 62.6%

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

   9. Simplified 62.6%

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

   if 3.49999999999999984e-7 < (/.f64 x y)

   1. Initial program 81.0%

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

   2. Taylor expanded in t around inf 66.1%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 10: 80.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -11 \lor \neg \left(t \leq 0.00088\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -11.0) (not (<= t 0.00088)))
   (- (/ 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 <= -11.0) || !(t <= 0.00088)) {
		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 <= (-11.0d0)) .or. (.not. (t <= 0.00088d0))) 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 <= -11.0) || !(t <= 0.00088)) {
		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 <= -11.0) or not (t <= 0.00088):
		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 <= -11.0) || !(t <= 0.00088))
		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 <= -11.0) || ~((t <= 0.00088)))
		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, -11.0], N[Not[LessEqual[t, 0.00088]], $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 < -11 or 8.80000000000000031e-4 < t

   1. Initial program 74.1%

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

   2. Taylor expanded in t around inf 79.5%

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

   if -11 < t < 8.80000000000000031e-4

   1. Initial program 96.7%

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

   2. Taylor expanded in t around 0 86.4%

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

      1. associate-*r/ 86.4%

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

      2. metadata-eval 86.4%

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

   4. Simplified 86.4%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -11 \lor \neg \left(t \leq 0.00088\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 11: 47.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.65 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 16800000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.65e+23)
   (/ x y)
   (if (<= (/ x y) 16800000000.0) (/ 2.0 t) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.65e+23) {
		tmp = x / y;
	} else if ((x / y) <= 16800000000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.65d+23)) then
        tmp = x / y
    else if ((x / y) <= 16800000000.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.65e+23) {
		tmp = x / y;
	} else if ((x / y) <= 16800000000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.65e+23:
		tmp = x / y
	elif (x / y) <= 16800000000.0:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.65e+23)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 16800000000.0)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.65e+23)
		tmp = x / y;
	elseif ((x / y) <= 16800000000.0)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.65e+23], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 16800000000.0], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.65000000000000015e23 or 1.68e10 < (/.f64 x y)

   1. Initial program 83.6%

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

   2. Taylor expanded in x around inf 65.4%

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

   if -1.65000000000000015e23 < (/.f64 x y) < 1.68e10

   1. Initial program 87.7%

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

   2. Taylor expanded in z around inf 62.5%

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

      1. div-sub 62.5%

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

      2. sub-neg 62.5%

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

      3. *-inverses 62.5%

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

      4. metadata-eval 62.5%

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

      5. distribute-lft-in 62.5%

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

      6. associate-*r/ 62.5%

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

      7. metadata-eval 62.5%

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

      8. metadata-eval 62.5%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in t around 0 33.4%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.65 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 16800000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 12: 19.0% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \frac{2}{t} \end{array} \]

FPCore

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

C

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

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 / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

2. Taylor expanded in z around inf 69.0%

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

   1. div-sub 69.0%

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

   2. sub-neg 69.0%

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

   3. *-inverses 69.0%

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

   4. metadata-eval 69.0%

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

   5. distribute-lft-in 69.0%

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

   6. associate-*r/ 69.0%

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

   7. metadata-eval 69.0%

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

   8. metadata-eval 69.0%

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

4. Simplified 69.0%

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

5. Taylor expanded in t around 0 23.3%

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

6. Final simplification 23.3%

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

Developer target: 99.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

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