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

Percentage Accurate: 86.6% → 99.5%

Time: 14.1s

Alternatives: 18

Speedup: 0.7×

• 23.7% 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: 86.6% 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

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (- 1.0 t) (* 2.0 z))) (* t z)))))
   (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))) / (t * z));
	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))) / (t * z));
	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))) / (t * z))
	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(t * z)))
	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))) / (t * z));
	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[(t * z), $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 99.9%

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

Alternative 2: 99.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 84.6%

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

3. Taylor expanded in x around 0 99.5%

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

   1. associate-+r+ 99.5%

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

   2. +-commutative 99.5%

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

   3. fma-define 99.5%

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

   4. associate-*r/ 99.5%

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

   5. metadata-eval 99.5%

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

   6. associate-/r* 99.5%

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

5. Simplified 99.5%

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

6. Final simplification 99.5%

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

Alternative 3: 91.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{\frac{2}{t}}{z} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-31}:\\ \;\;\;\;-2 + t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (+ (/ (/ 2.0 t) z) (/ x y))))
   (if (<= (/ x y) -2000.0)
     t_2
     (if (<= (/ x y) 5e-31)
       (+ -2.0 t_1)
       (if (<= (/ x y) 2e+51)
         (+ (/ x y) (+ (/ 2.0 t) -2.0))
         (if (<= (/ x y) 5e+90) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = ((2.0 / t) / z) + (x / y);
	double tmp;
	if ((x / y) <= -2000.0) {
		tmp = t_2;
	} else if ((x / y) <= 5e-31) {
		tmp = -2.0 + t_1;
	} else if ((x / y) <= 2e+51) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else if ((x / y) <= 5e+90) {
		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 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = ((2.0d0 / t) / z) + (x / y)
    if ((x / y) <= (-2000.0d0)) then
        tmp = t_2
    else if ((x / y) <= 5d-31) then
        tmp = (-2.0d0) + t_1
    else if ((x / y) <= 2d+51) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else if ((x / y) <= 5d+90) 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 = (2.0 + (2.0 / z)) / t;
	double t_2 = ((2.0 / t) / z) + (x / y);
	double tmp;
	if ((x / y) <= -2000.0) {
		tmp = t_2;
	} else if ((x / y) <= 5e-31) {
		tmp = -2.0 + t_1;
	} else if ((x / y) <= 2e+51) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else if ((x / y) <= 5e+90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = ((2.0 / t) / z) + (x / y)
	tmp = 0
	if (x / y) <= -2000.0:
		tmp = t_2
	elif (x / y) <= 5e-31:
		tmp = -2.0 + t_1
	elif (x / y) <= 2e+51:
		tmp = (x / y) + ((2.0 / t) + -2.0)
	elif (x / y) <= 5e+90:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(Float64(2.0 / t) / z) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -2000.0)
		tmp = t_2;
	elseif (Float64(x / y) <= 5e-31)
		tmp = Float64(-2.0 + t_1);
	elseif (Float64(x / y) <= 2e+51)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	elseif (Float64(x / y) <= 5e+90)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = ((2.0 / t) / z) + (x / y);
	tmp = 0.0;
	if ((x / y) <= -2000.0)
		tmp = t_2;
	elseif ((x / y) <= 5e-31)
		tmp = -2.0 + t_1;
	elseif ((x / y) <= 2e+51)
		tmp = (x / y) + ((2.0 / t) + -2.0);
	elseif ((x / y) <= 5e+90)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2000.0], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 5e-31], N[(-2.0 + t$95$1), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+51], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+90], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2e3 or 5.0000000000000004e90 < (/.f64 x y)

   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 z around 0 96.0%

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

      1. associate-/r* 96.0%

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

   5. Simplified 96.0%

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

   if -2e3 < (/.f64 x y) < 5e-31

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. div-sub 99.4%

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

      3. *-inverses 99.4%

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

      4. sub-neg 99.4%

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

      5. metadata-eval 99.4%

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

      6. distribute-lft-out 99.4%

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

      7. distribute-lft-in 99.4%

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

      8. associate-*r/ 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. +-commutative 99.4%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. associate-+l+ 99.4%

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

      15. metadata-eval 99.4%

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

      16. associate-*r/ 99.4%

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

      17. metadata-eval 99.4%

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

      18. associate-*r/ 99.4%

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

      19. associate-/r* 99.4%

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

      20. *-lft-identity 99.4%

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

      21. associate-*l/ 99.4%

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

      22. associate-*r* 99.4%

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

   8. Simplified 99.4%

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

   if 5e-31 < (/.f64 x y) < 2e51

   1. Initial program 81.7%

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

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]
   4. 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. metadata-eval 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   if 2e51 < (/.f64 x y) < 5.0000000000000004e90

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 88.8%

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

      1. associate-*r/ 88.8%

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

      2. metadata-eval 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-31}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+90}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{t}}{z} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-31}:\\ \;\;\;\;2 \cdot \frac{\left(1 - t\right) + \frac{1}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+90}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ (/ 2.0 t) z) (/ x y))))
   (if (<= (/ x y) -2000.0)
     t_1
     (if (<= (/ x y) 5e-31)
       (* 2.0 (/ (+ (- 1.0 t) (/ 1.0 z)) t))
       (if (<= (/ x y) 2e+51)
         (+ (/ x y) (+ (/ 2.0 t) -2.0))
         (if (<= (/ x y) 5e+90) (/ (+ 2.0 (/ 2.0 z)) t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / t) / z) + (x / y);
	double tmp;
	if ((x / y) <= -2000.0) {
		tmp = t_1;
	} else if ((x / y) <= 5e-31) {
		tmp = 2.0 * (((1.0 - t) + (1.0 / z)) / t);
	} else if ((x / y) <= 2e+51) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else if ((x / y) <= 5e+90) {
		tmp = (2.0 + (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 = ((2.0d0 / t) / z) + (x / y)
    if ((x / y) <= (-2000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 5d-31) then
        tmp = 2.0d0 * (((1.0d0 - t) + (1.0d0 / z)) / t)
    else if ((x / y) <= 2d+51) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else if ((x / y) <= 5d+90) then
        tmp = (2.0d0 + (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 = ((2.0 / t) / z) + (x / y);
	double tmp;
	if ((x / y) <= -2000.0) {
		tmp = t_1;
	} else if ((x / y) <= 5e-31) {
		tmp = 2.0 * (((1.0 - t) + (1.0 / z)) / t);
	} else if ((x / y) <= 2e+51) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else if ((x / y) <= 5e+90) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / t) / z) + (x / y)
	tmp = 0
	if (x / y) <= -2000.0:
		tmp = t_1
	elif (x / y) <= 5e-31:
		tmp = 2.0 * (((1.0 - t) + (1.0 / z)) / t)
	elif (x / y) <= 2e+51:
		tmp = (x / y) + ((2.0 / t) + -2.0)
	elif (x / y) <= 5e+90:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / t) / z) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -2000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-31)
		tmp = Float64(2.0 * Float64(Float64(Float64(1.0 - t) + Float64(1.0 / z)) / t));
	elseif (Float64(x / y) <= 2e+51)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	elseif (Float64(x / y) <= 5e+90)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((2.0 / t) / z) + (x / y);
	tmp = 0.0;
	if ((x / y) <= -2000.0)
		tmp = t_1;
	elseif ((x / y) <= 5e-31)
		tmp = 2.0 * (((1.0 - t) + (1.0 / z)) / t);
	elseif ((x / y) <= 2e+51)
		tmp = (x / y) + ((2.0 / t) + -2.0);
	elseif ((x / y) <= 5e+90)
		tmp = (2.0 + (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[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-31], N[(2.0 * N[(N[(N[(1.0 - t), $MachinePrecision] + N[(1.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+51], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+90], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2e3 or 5.0000000000000004e90 < (/.f64 x y)

   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 z around 0 96.0%

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

      1. associate-/r* 96.0%

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

   5. Simplified 96.0%

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

   if -2e3 < (/.f64 x y) < 5e-31

   1. Initial program 83.3%

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

      1. +-commutative 83.3%

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

      2. remove-double-neg 83.3%

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

      3. distribute-frac-neg 83.3%

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

      4. unsub-neg 83.3%

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

      5. *-commutative 83.3%

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

      6. associate-*r* 83.3%

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

      7. distribute-rgt1-in 83.3%

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

      8. associate-/l* 83.2%

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

      9. fma-neg 83.2%

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

      10. *-commutative 83.2%

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

      11. fma-define 83.2%

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

      12. *-commutative 83.2%

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

      13. distribute-frac-neg 83.2%

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

      14. remove-double-neg 83.2%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in x around 0 82.8%

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

   6. Taylor expanded in t around 0 99.5%

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

      1. neg-mul-1 99.5%

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

      2. associate-+r+ 99.5%

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

      3. sub-neg 99.5%

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

   8. Simplified 99.5%

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

   if 5e-31 < (/.f64 x y) < 2e51

   1. Initial program 81.7%

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

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]
   4. 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. metadata-eval 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   if 2e51 < (/.f64 x y) < 5.0000000000000004e90

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 88.8%

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

      1. associate-*r/ 88.8%

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

      2. metadata-eval 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-31}:\\ \;\;\;\;2 \cdot \frac{\left(1 - t\right) + \frac{1}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+90}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{+140} \lor \neg \left(z \leq 2.6 \cdot 10^{+183}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (+ (/ x y) -2.0)))
   (if (<= z -1.05e-34)
     t_2
     (if (<= z -1.95e-53)
       t_1
       (if (<= z -1.16e-114)
         t_2
         (if (<= z 2.35e-8)
           t_1
           (if (or (<= z 1.82e+140) (not (<= z 2.6e+183)))
             t_2
             (+ (/ 2.0 t) -2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (z <= -1.05e-34) {
		tmp = t_2;
	} else if (z <= -1.95e-53) {
		tmp = t_1;
	} else if (z <= -1.16e-114) {
		tmp = t_2;
	} else if (z <= 2.35e-8) {
		tmp = t_1;
	} else if ((z <= 1.82e+140) || !(z <= 2.6e+183)) {
		tmp = t_2;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 / (t * z)
    t_2 = (x / y) + (-2.0d0)
    if (z <= (-1.05d-34)) then
        tmp = t_2
    else if (z <= (-1.95d-53)) then
        tmp = t_1
    else if (z <= (-1.16d-114)) then
        tmp = t_2
    else if (z <= 2.35d-8) then
        tmp = t_1
    else if ((z <= 1.82d+140) .or. (.not. (z <= 2.6d+183))) then
        tmp = t_2
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (z <= -1.05e-34) {
		tmp = t_2;
	} else if (z <= -1.95e-53) {
		tmp = t_1;
	} else if (z <= -1.16e-114) {
		tmp = t_2;
	} else if (z <= 2.35e-8) {
		tmp = t_1;
	} else if ((z <= 1.82e+140) || !(z <= 2.6e+183)) {
		tmp = t_2;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) + -2.0
	tmp = 0
	if z <= -1.05e-34:
		tmp = t_2
	elif z <= -1.95e-53:
		tmp = t_1
	elif z <= -1.16e-114:
		tmp = t_2
	elif z <= 2.35e-8:
		tmp = t_1
	elif (z <= 1.82e+140) or not (z <= 2.6e+183):
		tmp = t_2
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (z <= -1.05e-34)
		tmp = t_2;
	elseif (z <= -1.95e-53)
		tmp = t_1;
	elseif (z <= -1.16e-114)
		tmp = t_2;
	elseif (z <= 2.35e-8)
		tmp = t_1;
	elseif ((z <= 1.82e+140) || !(z <= 2.6e+183))
		tmp = t_2;
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (x / y) + -2.0;
	tmp = 0.0;
	if (z <= -1.05e-34)
		tmp = t_2;
	elseif (z <= -1.95e-53)
		tmp = t_1;
	elseif (z <= -1.16e-114)
		tmp = t_2;
	elseif (z <= 2.35e-8)
		tmp = t_1;
	elseif ((z <= 1.82e+140) || ~((z <= 2.6e+183)))
		tmp = t_2;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[z, -1.05e-34], t$95$2, If[LessEqual[z, -1.95e-53], t$95$1, If[LessEqual[z, -1.16e-114], t$95$2, If[LessEqual[z, 2.35e-8], t$95$1, If[Or[LessEqual[z, 1.82e+140], N[Not[LessEqual[z, 2.6e+183]], $MachinePrecision]], t$95$2, N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e-34 or -1.9500000000000001e-53 < z < -1.1599999999999999e-114 or 2.3499999999999999e-8 < z < 1.82e140 or 2.5999999999999999e183 < z

   1. Initial program 74.2%

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

   3. Taylor expanded in t around inf 73.2%

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

   if -1.05e-34 < z < -1.9500000000000001e-53 or -1.1599999999999999e-114 < z < 2.3499999999999999e-8

   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 x around 0 98.9%

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

      1. associate-+r+ 98.9%

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

      2. +-commutative 98.9%

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

      3. fma-define 98.9%

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

      4. associate-*r/ 98.9%

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

      5. metadata-eval 98.9%

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

      6. associate-/r* 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around 0 70.2%

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

      1. *-commutative 70.2%

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

   8. Simplified 70.2%

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

   if 1.82e140 < z < 2.5999999999999999e183

   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 z around inf 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]
   4. 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. metadata-eval 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 46.4%

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

      1. sub-neg 46.4%

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

      2. associate-*r/ 46.4%

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

      3. metadata-eval 46.4%

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

      4. metadata-eval 46.4%

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

      5. +-commutative 46.4%

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

   8. Simplified 46.4%

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

   9. Taylor expanded in x around 0 100.0%

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

       1. sub-neg 100.0%

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

       2. associate-*r/ 100.0%

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

       3. metadata-eval 100.0%

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

       4. metadata-eval 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-53}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-8}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{+140} \lor \neg \left(z \leq 2.6 \cdot 10^{+183}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-54}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-8}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+140} \lor \neg \left(z \leq 1.3 \cdot 10^{+182}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= z -1.32e-34)
     t_1
     (if (<= z -9e-54)
       (/ (/ 2.0 z) t)
       (if (<= z -9e-114)
         t_1
         (if (<= z 2.35e-8)
           (/ 2.0 (* t z))
           (if (or (<= z 1.32e+140) (not (<= z 1.3e+182)))
             t_1
             (+ (/ 2.0 t) -2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -1.32e-34) {
		tmp = t_1;
	} else if (z <= -9e-54) {
		tmp = (2.0 / z) / t;
	} else if (z <= -9e-114) {
		tmp = t_1;
	} else if (z <= 2.35e-8) {
		tmp = 2.0 / (t * z);
	} else if ((z <= 1.32e+140) || !(z <= 1.3e+182)) {
		tmp = t_1;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (z <= (-1.32d-34)) then
        tmp = t_1
    else if (z <= (-9d-54)) then
        tmp = (2.0d0 / z) / t
    else if (z <= (-9d-114)) then
        tmp = t_1
    else if (z <= 2.35d-8) then
        tmp = 2.0d0 / (t * z)
    else if ((z <= 1.32d+140) .or. (.not. (z <= 1.3d+182))) then
        tmp = t_1
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -1.32e-34) {
		tmp = t_1;
	} else if (z <= -9e-54) {
		tmp = (2.0 / z) / t;
	} else if (z <= -9e-114) {
		tmp = t_1;
	} else if (z <= 2.35e-8) {
		tmp = 2.0 / (t * z);
	} else if ((z <= 1.32e+140) || !(z <= 1.3e+182)) {
		tmp = t_1;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if z <= -1.32e-34:
		tmp = t_1
	elif z <= -9e-54:
		tmp = (2.0 / z) / t
	elif z <= -9e-114:
		tmp = t_1
	elif z <= 2.35e-8:
		tmp = 2.0 / (t * z)
	elif (z <= 1.32e+140) or not (z <= 1.3e+182):
		tmp = t_1
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (z <= -1.32e-34)
		tmp = t_1;
	elseif (z <= -9e-54)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif (z <= -9e-114)
		tmp = t_1;
	elseif (z <= 2.35e-8)
		tmp = Float64(2.0 / Float64(t * z));
	elseif ((z <= 1.32e+140) || !(z <= 1.3e+182))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (z <= -1.32e-34)
		tmp = t_1;
	elseif (z <= -9e-54)
		tmp = (2.0 / z) / t;
	elseif (z <= -9e-114)
		tmp = t_1;
	elseif (z <= 2.35e-8)
		tmp = 2.0 / (t * z);
	elseif ((z <= 1.32e+140) || ~((z <= 1.3e+182)))
		tmp = t_1;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[z, -1.32e-34], t$95$1, If[LessEqual[z, -9e-54], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -9e-114], t$95$1, If[LessEqual[z, 2.35e-8], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.32e+140], N[Not[LessEqual[z, 1.3e+182]], $MachinePrecision]], t$95$1, N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.32e-34 or -8.9999999999999997e-54 < z < -8.99999999999999937e-114 or 2.3499999999999999e-8 < z < 1.3200000000000001e140 or 1.3e182 < z

   1. Initial program 74.2%

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

   3. Taylor expanded in t around inf 73.2%

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

   if -1.32e-34 < z < -8.9999999999999997e-54

   1. Initial program 99.4%

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

   3. Taylor expanded in t around 0 99.4%

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

      1. associate-+r+ 99.4%

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

      2. associate-*r/ 99.4%

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

      3. metadata-eval 99.4%

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

      4. sub-neg 99.4%

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

      5. metadata-eval 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in z around 0 92.2%

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

   if -8.99999999999999937e-114 < z < 2.3499999999999999e-8

   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 x around 0 98.9%

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

      1. associate-+r+ 98.9%

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

      2. +-commutative 98.9%

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

      3. fma-define 98.9%

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

      4. associate-*r/ 98.9%

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

      5. metadata-eval 98.9%

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

      6. associate-/r* 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around 0 69.1%

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

      1. *-commutative 69.1%

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

   8. Simplified 69.1%

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

   if 1.3200000000000001e140 < z < 1.3e182

   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 z around inf 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]
   4. 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. metadata-eval 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 46.4%

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

      1. sub-neg 46.4%

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

      2. associate-*r/ 46.4%

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

      3. metadata-eval 46.4%

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

      4. metadata-eval 46.4%

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

      5. +-commutative 46.4%

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

   8. Simplified 46.4%

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

   9. Taylor expanded in x around 0 100.0%

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

       1. sub-neg 100.0%

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

       2. associate-*r/ 100.0%

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

       3. metadata-eval 100.0%

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

       4. metadata-eval 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-54}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-8}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+140} \lor \neg \left(z \leq 1.3 \cdot 10^{+182}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.5 \cdot 10^{-96}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.24 \cdot 10^{-48}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0)
   (/ x y)
   (if (<= (/ x y) 4.5e-96)
     -2.0
     (if (<= (/ x y) 1.24e-48) (/ 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) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 4.5e-96) {
		tmp = -2.0;
	} else if ((x / y) <= 1.24e-48) {
		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) <= (-2.0d0)) then
        tmp = x / y
    else if ((x / y) <= 4.5d-96) then
        tmp = -2.0d0
    else if ((x / y) <= 1.24d-48) 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) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 4.5e-96) {
		tmp = -2.0;
	} else if ((x / y) <= 1.24e-48) {
		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) <= -2.0:
		tmp = x / y
	elif (x / y) <= 4.5e-96:
		tmp = -2.0
	elif (x / y) <= 1.24e-48:
		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) <= -2.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4.5e-96)
		tmp = -2.0;
	elseif (Float64(x / y) <= 1.24e-48)
		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) <= -2.0)
		tmp = x / y;
	elseif ((x / y) <= 4.5e-96)
		tmp = -2.0;
	elseif ((x / y) <= 1.24e-48)
		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], -2.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.5e-96], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 1.24e-48], 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 or 2 < (/.f64 x y)

   1. Initial program 85.9%

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

   3. Taylor expanded in x around inf 70.4%

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

   if -2 < (/.f64 x y) < 4.5e-96 or 1.24e-48 < (/.f64 x y) < 2

   1. Initial program 82.3%

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

      1. +-commutative 82.3%

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

      2. remove-double-neg 82.3%

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

      3. distribute-frac-neg 82.3%

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

      4. unsub-neg 82.3%

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

      5. *-commutative 82.3%

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

      6. associate-*r* 82.3%

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

      7. distribute-rgt1-in 82.3%

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

      8. associate-/l* 82.3%

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

      9. fma-neg 82.3%

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

      10. *-commutative 82.3%

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

      11. fma-define 82.3%

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

      12. *-commutative 82.3%

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

      13. distribute-frac-neg 82.3%

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

      14. remove-double-neg 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in x around 0 81.1%

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

   6. Taylor expanded in t around inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. *-commutative 59.3%

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

      3. distribute-rgt-neg-in 59.3%

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

   8. Simplified 59.3%

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

   9. Taylor expanded in z around inf 41.3%

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

   if 4.5e-96 < (/.f64 x y) < 1.24e-48

   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

   3. Taylor expanded in t around 0 93.6%

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

      1. associate-*r/ 93.6%

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

      2. metadata-eval 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in z around inf 57.5%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.5 \cdot 10^{-96}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.24 \cdot 10^{-48}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+122} \lor \neg \left(\frac{x}{y} \leq 0.02\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+122) (not (<= (/ x y) 0.02)))
   (+ (/ x y) (+ (/ 2.0 t) (/ (/ 2.0 z) t)))
   (/ (+ (+ 2.0 (/ 2.0 z)) (* t (+ (/ x y) -2.0))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+122) || !((x / y) <= 0.02)) {
		tmp = (x / y) + ((2.0 / t) + ((2.0 / z) / t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d+122)) .or. (.not. ((x / y) <= 0.02d0))) then
        tmp = (x / y) + ((2.0d0 / t) + ((2.0d0 / z) / t))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) + (t * ((x / y) + (-2.0d0)))) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+122) || !((x / y) <= 0.02)) {
		tmp = (x / y) + ((2.0 / t) + ((2.0 / z) / t));
	} else {
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+122) or not ((x / y) <= 0.02):
		tmp = (x / y) + ((2.0 / t) + ((2.0 / z) / t))
	else:
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+122) || !(Float64(x / y) <= 0.02))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + Float64(Float64(2.0 / z) / t)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) + Float64(t * Float64(Float64(x / y) + -2.0))) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+122) || ~(((x / y) <= 0.02)))
		tmp = (x / y) + ((2.0 / t) + ((2.0 / z) / t));
	else
		tmp = ((2.0 + (2.0 / z)) + (t * ((x / y) + -2.0))) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+122], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.02]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.00000000000000003e122 or 0.0200000000000000004 < (/.f64 x y)

   1. Initial program 84.0%

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

   3. Taylor expanded in x around 0 99.0%

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

      1. associate-+r+ 99.0%

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

      2. +-commutative 99.0%

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

      3. fma-define 99.0%

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

      4. associate-*r/ 99.0%

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

      5. metadata-eval 99.0%

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

      6. associate-/r* 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in t around 0 99.0%

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

      1. fma-undefine 99.0%

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

      2. div-inv 99.0%

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

      3. +-commutative 99.0%

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

      4. associate-/l/ 99.0%

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

      5. associate-/r* 99.0%

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

   8. Applied egg-rr 99.0%

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

   if -2.00000000000000003e122 < (/.f64 x y) < 0.0200000000000000004

   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 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+122} \lor \neg \left(\frac{x}{y} \leq 0.02\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t} + \frac{x}{y}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -5 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 29500000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 t) (/ x y))) (t_2 (+ (/ x y) -2.0)))
   (if (<= t -5e+14)
     t_2
     (if (<= t -1e-191)
       t_1
       (if (<= t -2.5e-275)
         (/ 2.0 (* t z))
         (if (<= t 29500000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + (x / y);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t <= -5e+14) {
		tmp = t_2;
	} else if (t <= -1e-191) {
		tmp = t_1;
	} else if (t <= -2.5e-275) {
		tmp = 2.0 / (t * z);
	} else if (t <= 29500000000000.0) {
		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 = (2.0d0 / t) + (x / y)
    t_2 = (x / y) + (-2.0d0)
    if (t <= (-5d+14)) then
        tmp = t_2
    else if (t <= (-1d-191)) then
        tmp = t_1
    else if (t <= (-2.5d-275)) then
        tmp = 2.0d0 / (t * z)
    else if (t <= 29500000000000.0d0) 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 = (2.0 / t) + (x / y);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t <= -5e+14) {
		tmp = t_2;
	} else if (t <= -1e-191) {
		tmp = t_1;
	} else if (t <= -2.5e-275) {
		tmp = 2.0 / (t * z);
	} else if (t <= 29500000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) + (x / y)
	t_2 = (x / y) + -2.0
	tmp = 0
	if t <= -5e+14:
		tmp = t_2
	elif t <= -1e-191:
		tmp = t_1
	elif t <= -2.5e-275:
		tmp = 2.0 / (t * z)
	elif t <= 29500000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) + Float64(x / y))
	t_2 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -5e+14)
		tmp = t_2;
	elseif (t <= -1e-191)
		tmp = t_1;
	elseif (t <= -2.5e-275)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t <= 29500000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) + (x / y);
	t_2 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -5e+14)
		tmp = t_2;
	elseif (t <= -1e-191)
		tmp = t_1;
	elseif (t <= -2.5e-275)
		tmp = 2.0 / (t * z);
	elseif (t <= 29500000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -5e+14], t$95$2, If[LessEqual[t, -1e-191], t$95$1, If[LessEqual[t, -2.5e-275], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 29500000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5e14 or 2.95e13 < t

   1. Initial program 66.9%

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

   3. Taylor expanded in t around inf 86.2%

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

   if -5e14 < t < -1e-191 or -2.49999999999999992e-275 < t < 2.95e13

   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 x around 0 99.0%

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

      1. associate-+r+ 99.0%

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

      2. +-commutative 99.0%

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

      3. fma-define 99.0%

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

      4. associate-*r/ 99.0%

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

      5. metadata-eval 99.0%

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

      6. associate-/r* 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in t around 0 98.3%

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

   7. Taylor expanded in z around inf 64.8%

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

      1. associate-*r/ 64.8%

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

      2. metadata-eval 64.8%

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

      3. +-commutative 64.8%

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

   9. Simplified 64.8%

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

   if -1e-191 < t < -2.49999999999999992e-275

   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

   3. Taylor expanded in x around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 73.4%

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

      1. *-commutative 73.4%

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

   8. Simplified 73.4%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-191}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 29500000000000:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -1 \cdot 10^{-17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-191}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;t \leq 85000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (+ (/ x y) -2.0)))
   (if (<= t -1e-17)
     t_2
     (if (<= t -8e-45)
       t_1
       (if (<= t -5.2e-191)
         (+ (/ 2.0 t) (/ x y))
         (if (<= t 85000000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t <= -1e-17) {
		tmp = t_2;
	} else if (t <= -8e-45) {
		tmp = t_1;
	} else if (t <= -5.2e-191) {
		tmp = (2.0 / t) + (x / y);
	} else if (t <= 85000000000000.0) {
		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 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = (x / y) + (-2.0d0)
    if (t <= (-1d-17)) then
        tmp = t_2
    else if (t <= (-8d-45)) then
        tmp = t_1
    else if (t <= (-5.2d-191)) then
        tmp = (2.0d0 / t) + (x / y)
    else if (t <= 85000000000000.0d0) 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 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t <= -1e-17) {
		tmp = t_2;
	} else if (t <= -8e-45) {
		tmp = t_1;
	} else if (t <= -5.2e-191) {
		tmp = (2.0 / t) + (x / y);
	} else if (t <= 85000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) + -2.0
	tmp = 0
	if t <= -1e-17:
		tmp = t_2
	elif t <= -8e-45:
		tmp = t_1
	elif t <= -5.2e-191:
		tmp = (2.0 / t) + (x / y)
	elif t <= 85000000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -1e-17)
		tmp = t_2;
	elseif (t <= -8e-45)
		tmp = t_1;
	elseif (t <= -5.2e-191)
		tmp = Float64(Float64(2.0 / t) + Float64(x / y));
	elseif (t <= 85000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -1e-17)
		tmp = t_2;
	elseif (t <= -8e-45)
		tmp = t_1;
	elseif (t <= -5.2e-191)
		tmp = (2.0 / t) + (x / y);
	elseif (t <= 85000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -1e-17], t$95$2, If[LessEqual[t, -8e-45], t$95$1, If[LessEqual[t, -5.2e-191], N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 85000000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.00000000000000007e-17 or 8.5e13 < t

   1. Initial program 68.8%

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

   3. Taylor expanded in t around inf 86.1%

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

   if -1.00000000000000007e-17 < t < -7.99999999999999987e-45 or -5.19999999999999972e-191 < t < 8.5e13

   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 80.9%

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

      1. associate-*r/ 80.9%

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

      2. metadata-eval 80.9%

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

   5. Simplified 80.9%

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

   if -7.99999999999999987e-45 < t < -5.19999999999999972e-191

   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 x around 0 100.0%

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

      1. associate-+r+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/r* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 100.0%

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

   7. Taylor expanded in z around inf 79.5%

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

      1. associate-*r/ 79.5%

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

      2. metadata-eval 79.5%

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

      3. +-commutative 79.5%

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

   9. Simplified 79.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-45}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-191}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;t \leq 85000000000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-45}:\\ \;\;\;\;2 \cdot \frac{1 + z}{t \cdot z}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-190}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;t \leq 31000000000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= t -3.6e-16)
     t_1
     (if (<= t -6.6e-45)
       (* 2.0 (/ (+ 1.0 z) (* t z)))
       (if (<= t -3e-190)
         (+ (/ 2.0 t) (/ x y))
         (if (<= t 31000000000000.0) (/ (+ 2.0 (/ 2.0 z)) t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -3.6e-16) {
		tmp = t_1;
	} else if (t <= -6.6e-45) {
		tmp = 2.0 * ((1.0 + z) / (t * z));
	} else if (t <= -3e-190) {
		tmp = (2.0 / t) + (x / y);
	} else if (t <= 31000000000000.0) {
		tmp = (2.0 + (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)
    if (t <= (-3.6d-16)) then
        tmp = t_1
    else if (t <= (-6.6d-45)) then
        tmp = 2.0d0 * ((1.0d0 + z) / (t * z))
    else if (t <= (-3d-190)) then
        tmp = (2.0d0 / t) + (x / y)
    else if (t <= 31000000000000.0d0) then
        tmp = (2.0d0 + (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;
	double tmp;
	if (t <= -3.6e-16) {
		tmp = t_1;
	} else if (t <= -6.6e-45) {
		tmp = 2.0 * ((1.0 + z) / (t * z));
	} else if (t <= -3e-190) {
		tmp = (2.0 / t) + (x / y);
	} else if (t <= 31000000000000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if t <= -3.6e-16:
		tmp = t_1
	elif t <= -6.6e-45:
		tmp = 2.0 * ((1.0 + z) / (t * z))
	elif t <= -3e-190:
		tmp = (2.0 / t) + (x / y)
	elif t <= 31000000000000.0:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -3.6e-16)
		tmp = t_1;
	elseif (t <= -6.6e-45)
		tmp = Float64(2.0 * Float64(Float64(1.0 + z) / Float64(t * z)));
	elseif (t <= -3e-190)
		tmp = Float64(Float64(2.0 / t) + Float64(x / y));
	elseif (t <= 31000000000000.0)
		tmp = Float64(Float64(2.0 + Float64(2.0 / 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;
	tmp = 0.0;
	if (t <= -3.6e-16)
		tmp = t_1;
	elseif (t <= -6.6e-45)
		tmp = 2.0 * ((1.0 + z) / (t * z));
	elseif (t <= -3e-190)
		tmp = (2.0 / t) + (x / y);
	elseif (t <= 31000000000000.0)
		tmp = (2.0 + (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] + -2.0), $MachinePrecision]}, If[LessEqual[t, -3.6e-16], t$95$1, If[LessEqual[t, -6.6e-45], N[(2.0 * N[(N[(1.0 + z), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e-190], N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 31000000000000.0], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.59999999999999983e-16 or 3.1e13 < t

   1. Initial program 68.8%

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

   3. Taylor expanded in t around inf 86.1%

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

   if -3.59999999999999983e-16 < t < -6.6000000000000001e-45

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-*r* 100.0%

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

      7. distribute-rgt1-in 100.0%

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

      8. associate-/l* 100.0%

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

      9. fma-neg 100.0%

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

      10. *-commutative 100.0%

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

      11. fma-define 100.0%

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

      12. *-commutative 100.0%

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

      13. distribute-frac-neg 100.0%

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

      14. remove-double-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 97.1%

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

   if -6.6000000000000001e-45 < t < -2.9999999999999998e-190

   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 x around 0 100.0%

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

      1. associate-+r+ 100.0%

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

      2. +-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/r* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 100.0%

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

   7. Taylor expanded in z around inf 79.5%

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

      1. associate-*r/ 79.5%

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

      2. metadata-eval 79.5%

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

      3. +-commutative 79.5%

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

   9. Simplified 79.5%

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

   if -2.9999999999999998e-190 < t < 3.1e13

   1. Initial program 98.8%

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

   3. Taylor expanded in t around 0 79.8%

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

      1. associate-*r/ 79.8%

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

      2. metadata-eval 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-45}:\\ \;\;\;\;2 \cdot \frac{1 + z}{t \cdot z}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-190}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;t \leq 31000000000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+17} \lor \neg \left(\frac{x}{y} \leq 0.02\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\left(1 - t\right) + \frac{1}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+17) (not (<= (/ x y) 0.02)))
   (+ (/ x y) (+ (/ 2.0 t) (/ (/ 2.0 z) t)))
   (* 2.0 (/ (+ (- 1.0 t) (/ 1.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+17) || !((x / y) <= 0.02)) {
		tmp = (x / y) + ((2.0 / t) + ((2.0 / z) / t));
	} else {
		tmp = 2.0 * (((1.0 - t) + (1.0 / 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+17)) .or. (.not. ((x / y) <= 0.02d0))) then
        tmp = (x / y) + ((2.0d0 / t) + ((2.0d0 / z) / t))
    else
        tmp = 2.0d0 * (((1.0d0 - t) + (1.0d0 / 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+17) || !((x / y) <= 0.02)) {
		tmp = (x / y) + ((2.0 / t) + ((2.0 / z) / t));
	} else {
		tmp = 2.0 * (((1.0 - t) + (1.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+17) or not ((x / y) <= 0.02):
		tmp = (x / y) + ((2.0 / t) + ((2.0 / z) / t))
	else:
		tmp = 2.0 * (((1.0 - t) + (1.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+17) || !(Float64(x / y) <= 0.02))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + Float64(Float64(2.0 / z) / t)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(1.0 - t) + Float64(1.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+17) || ~(((x / y) <= 0.02)))
		tmp = (x / y) + ((2.0 / t) + ((2.0 / z) / t));
	else
		tmp = 2.0 * (((1.0 - t) + (1.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+17], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.02]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(1.0 - t), $MachinePrecision] + N[(1.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e17 or 0.0200000000000000004 < (/.f64 x y)

   1. Initial program 85.6%

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

   3. Taylor expanded in x around 0 99.2%

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

      1. associate-+r+ 99.2%

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

      2. +-commutative 99.2%

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

      3. fma-define 99.2%

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

      4. associate-*r/ 99.2%

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

      5. metadata-eval 99.2%

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

      6. associate-/r* 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in t around 0 99.1%

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

      1. fma-undefine 99.1%

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

      2. div-inv 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-/l/ 99.2%

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

      5. associate-/r* 99.1%

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

   8. Applied egg-rr 99.1%

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

   if -1e17 < (/.f64 x y) < 0.0200000000000000004

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. remove-double-neg 83.7%

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

      3. distribute-frac-neg 83.7%

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

      4. unsub-neg 83.7%

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

      5. *-commutative 83.7%

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

      6. associate-*r* 83.7%

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

      7. distribute-rgt1-in 83.7%

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

      8. associate-/l* 83.6%

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

      9. fma-neg 83.6%

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

      10. *-commutative 83.6%

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

      11. fma-define 83.6%

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

      12. *-commutative 83.6%

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

      13. distribute-frac-neg 83.6%

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

      14. remove-double-neg 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in x around 0 82.5%

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

   6. Taylor expanded in t around 0 98.3%

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

      1. neg-mul-1 98.3%

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

      2. associate-+r+ 98.3%

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

      3. sub-neg 98.3%

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

   8. Simplified 98.3%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+17} \lor \neg \left(\frac{x}{y} \leq 0.02\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\left(1 - t\right) + \frac{1}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.5 \cdot 10^{+80} \lor \neg \left(\frac{x}{y} \leq 1.2 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.5e+80) (not (<= (/ x y) 1.2e+14)))
   (+ (/ 2.0 t) (/ x y))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.5e+80) || !((x / y) <= 1.2e+14)) {
		tmp = (2.0 / t) + (x / y);
	} 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) <= (-1.5d+80)) .or. (.not. ((x / y) <= 1.2d+14))) then
        tmp = (2.0d0 / t) + (x / y)
    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) <= -1.5e+80) || !((x / y) <= 1.2e+14)) {
		tmp = (2.0 / t) + (x / y);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.5e+80) or not ((x / y) <= 1.2e+14):
		tmp = (2.0 / t) + (x / y)
	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) <= -1.5e+80) || !(Float64(x / y) <= 1.2e+14))
		tmp = Float64(Float64(2.0 / t) + Float64(x / y));
	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) <= -1.5e+80) || ~(((x / y) <= 1.2e+14)))
		tmp = (2.0 / t) + (x / y);
	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], -1.5e+80], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.2e+14]], $MachinePrecision]], N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $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) < -1.49999999999999993e80 or 1.2e14 < (/.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 x around 0 99.1%

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

      1. associate-+r+ 99.1%

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

      2. +-commutative 99.1%

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

      3. fma-define 99.1%

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

      4. associate-*r/ 99.1%

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

      5. metadata-eval 99.1%

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

      6. associate-/r* 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in t around 0 99.1%

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

   7. Taylor expanded in z around inf 80.1%

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

      1. associate-*r/ 80.1%

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

      2. metadata-eval 80.1%

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

      3. +-commutative 80.1%

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

   9. Simplified 80.1%

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

   if -1.49999999999999993e80 < (/.f64 x y) < 1.2e14

   1. Initial program 84.3%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 95.2%

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

      1. distribute-lft-out 95.2%

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

      2. div-sub 95.2%

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

      3. *-inverses 95.2%

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

      4. sub-neg 95.2%

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

      5. metadata-eval 95.2%

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

      6. distribute-lft-out 95.2%

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

      7. distribute-lft-in 95.2%

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

      8. associate-*r/ 95.2%

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

      9. metadata-eval 95.2%

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

      10. metadata-eval 95.2%

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

      11. +-commutative 95.2%

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

      12. associate-*r/ 95.2%

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

      13. metadata-eval 95.2%

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

      14. associate-+l+ 95.2%

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

      15. metadata-eval 95.2%

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

      16. associate-*r/ 95.2%

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

      17. metadata-eval 95.2%

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

      18. associate-*r/ 95.2%

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

      19. associate-/r* 95.2%

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

      20. *-lft-identity 95.2%

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

      21. associate-*l/ 95.1%

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

      22. associate-*r* 95.1%

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

   8. Simplified 95.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.5 \cdot 10^{+80} \lor \neg \left(\frac{x}{y} \leq 1.2 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 88.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.6 \cdot 10^{+81}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-29}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.6e+81)
   (+ (/ 2.0 t) (/ x y))
   (if (<= (/ x y) 2e-29)
     (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
     (+ (/ x y) (+ (/ 2.0 t) -2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.6e+81) {
		tmp = (2.0 / t) + (x / y);
	} else if ((x / y) <= 2e-29) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2.6d+81)) then
        tmp = (2.0d0 / t) + (x / y)
    else if ((x / y) <= 2d-29) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.6e+81) {
		tmp = (2.0 / t) + (x / y);
	} else if ((x / y) <= 2e-29) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.6e+81:
		tmp = (2.0 / t) + (x / y)
	elif (x / y) <= 2e-29:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (x / y) + ((2.0 / t) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.6e+81)
		tmp = Float64(Float64(2.0 / t) + Float64(x / y));
	elseif (Float64(x / y) <= 2e-29)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2.6e+81)
		tmp = (2.0 / t) + (x / y);
	elseif ((x / y) <= 2e-29)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (x / y) + ((2.0 / t) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.6e+81], N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-29], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.59999999999999992e81

   1. Initial program 86.5%

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

   3. Taylor expanded in x around 0 98.0%

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

      1. associate-+r+ 98.0%

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

      2. +-commutative 98.0%

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

      3. fma-define 98.0%

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

      4. associate-*r/ 98.0%

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

      5. metadata-eval 98.0%

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

      6. associate-/r* 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in t around 0 98.0%

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

   7. Taylor expanded in z around inf 83.4%

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

      1. associate-*r/ 83.4%

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

      2. metadata-eval 83.4%

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

      3. +-commutative 83.4%

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

   9. Simplified 83.4%

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

   if -2.59999999999999992e81 < (/.f64 x y) < 1.99999999999999989e-29

   1. Initial program 84.3%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 96.1%

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

      1. distribute-lft-out 96.1%

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

      2. div-sub 96.1%

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

      3. *-inverses 96.1%

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

      4. sub-neg 96.1%

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

      5. metadata-eval 96.1%

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

      6. distribute-lft-out 96.1%

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

      7. distribute-lft-in 96.1%

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

      8. associate-*r/ 96.1%

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

      9. metadata-eval 96.1%

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

      10. metadata-eval 96.1%

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

      11. +-commutative 96.1%

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

      12. associate-*r/ 96.1%

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

      13. metadata-eval 96.1%

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

      14. associate-+l+ 96.1%

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

      15. metadata-eval 96.1%

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

      16. associate-*r/ 96.1%

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

      17. metadata-eval 96.1%

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

      18. associate-*r/ 96.1%

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

      19. associate-/r* 96.0%

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

      20. *-lft-identity 96.0%

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

      21. associate-*l/ 96.0%

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

      22. associate-*r* 96.0%

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

   8. Simplified 96.0%

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

   if 1.99999999999999989e-29 < (/.f64 x y)

   1. Initial program 83.9%

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

   3. Taylor expanded in z around inf 79.7%

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

      1. div-sub 79.7%

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

      2. sub-neg 79.7%

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

      3. *-inverses 79.7%

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

      4. metadata-eval 79.7%

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

      5. distribute-lft-in 79.7%

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

      6. metadata-eval 79.7%

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

      7. associate-*r/ 79.7%

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

      8. metadata-eval 79.7%

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

   5. Simplified 79.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.6 \cdot 10^{+81}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-29}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2600 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2600.0) (not (<= (/ x y) 4e+90)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2600.0) || !((x / y) <= 4e+90)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2600.0d0)) .or. (.not. ((x / y) <= 4d+90))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2600.0) || !((x / y) <= 4e+90)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2600.0) or not ((x / y) <= 4e+90):
		tmp = x / y
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2600.0) || !(Float64(x / y) <= 4e+90))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2600.0) || ~(((x / y) <= 4e+90)))
		tmp = x / y;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2600.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+90]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2600 or 3.99999999999999987e90 < (/.f64 x y)

   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 x around inf 73.7%

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

   if -2600 < (/.f64 x y) < 3.99999999999999987e90

   1. Initial program 83.9%

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

   3. Taylor expanded in z around inf 66.0%

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

      1. div-sub 66.0%

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

      2. sub-neg 66.0%

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

      3. *-inverses 66.0%

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

      4. metadata-eval 66.0%

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

      5. distribute-lft-in 66.0%

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

      6. metadata-eval 66.0%

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

      7. associate-*r/ 66.0%

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

      8. metadata-eval 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in y around 0 59.2%

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

      1. sub-neg 59.2%

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

      2. associate-*r/ 59.2%

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

      3. metadata-eval 59.2%

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

      4. metadata-eval 59.2%

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

      5. +-commutative 59.2%

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

   8. Simplified 59.2%

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

   9. Taylor expanded in x around 0 61.9%

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

       1. sub-neg 61.9%

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

       2. associate-*r/ 61.9%

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

       3. metadata-eval 61.9%

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

       4. metadata-eval 61.9%

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

   11. Simplified 61.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2600 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.7 \cdot 10^{-6} \lor \neg \left(\frac{x}{y} \leq 4.5 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.7e-6) (not (<= (/ x y) 4.5e-15)))
   (+ (/ x y) -2.0)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.7e-6) || !((x / y) <= 4.5e-15)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1.7d-6)) .or. (.not. ((x / y) <= 4.5d-15))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.7e-6) || !((x / y) <= 4.5e-15)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.7e-6) or not ((x / y) <= 4.5e-15):
		tmp = (x / y) + -2.0
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.7e-6) || !(Float64(x / y) <= 4.5e-15))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.7e-6) || ~(((x / y) <= 4.5e-15)))
		tmp = (x / y) + -2.0;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.7e-6], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.5e-15]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.70000000000000003e-6 or 4.4999999999999998e-15 < (/.f64 x y)

   1. Initial program 85.6%

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

   3. Taylor expanded in t around inf 71.5%

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

   if -1.70000000000000003e-6 < (/.f64 x y) < 4.4999999999999998e-15

   1. Initial program 83.5%

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

   3. Taylor expanded in z around inf 63.4%

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

      1. div-sub 63.4%

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

      2. sub-neg 63.4%

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

      3. *-inverses 63.4%

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

      4. metadata-eval 63.4%

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

      5. distribute-lft-in 63.4%

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

      6. metadata-eval 63.4%

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

      7. associate-*r/ 63.4%

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

      8. metadata-eval 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in y around 0 57.2%

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

      1. sub-neg 57.2%

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

      2. associate-*r/ 57.2%

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

      3. metadata-eval 57.2%

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

      4. metadata-eval 57.2%

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

      5. +-commutative 57.2%

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

   8. Simplified 57.2%

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

   9. Taylor expanded in x around 0 63.4%

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

       1. sub-neg 63.4%

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

       2. associate-*r/ 63.4%

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

       3. metadata-eval 63.4%

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

       4. metadata-eval 63.4%

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

   11. Simplified 63.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.7 \cdot 10^{-6} \lor \neg \left(\frac{x}{y} \leq 4.5 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 29500000000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 29500000000000.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 29500000000000.0) {
		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 <= (-1.0d0)) then
        tmp = -2.0d0
    else if (t <= 29500000000000.0d0) 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 <= -1.0) {
		tmp = -2.0;
	} else if (t <= 29500000000000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.0:
		tmp = -2.0
	elif t <= 29500000000000.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 29500000000000.0)
		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 <= -1.0)
		tmp = -2.0;
	elseif (t <= 29500000000000.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.0], -2.0, If[LessEqual[t, 29500000000000.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 2.95e13 < t

   1. Initial program 67.7%

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

      1. +-commutative 67.7%

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

      2. remove-double-neg 67.7%

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

      3. distribute-frac-neg 67.7%

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

      4. unsub-neg 67.7%

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

      5. *-commutative 67.7%

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

      6. associate-*r* 67.7%

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

      7. distribute-rgt1-in 67.7%

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

      8. associate-/l* 67.7%

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

      9. fma-neg 67.7%

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

      10. *-commutative 67.7%

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

      11. fma-define 67.7%

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

      12. *-commutative 67.7%

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

      13. distribute-frac-neg 67.7%

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

      14. remove-double-neg 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in x around 0 37.6%

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

   6. Taylor expanded in t around inf 37.6%

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

      1. mul-1-neg 37.6%

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

      2. *-commutative 37.6%

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

      3. distribute-rgt-neg-in 37.6%

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

   8. Simplified 37.6%

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

   9. Taylor expanded in z around inf 42.1%

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

   if -1 < t < 2.95e13

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 74.4%

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

      1. associate-*r/ 74.4%

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

      2. metadata-eval 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in z around inf 30.1%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 29500000000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 19.9% 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 84.6%

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

   1. +-commutative 84.6%

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

   2. remove-double-neg 84.6%

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

   3. distribute-frac-neg 84.6%

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

   4. unsub-neg 84.6%

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

   5. *-commutative 84.6%

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

   6. associate-*r* 84.6%

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

   7. distribute-rgt1-in 84.6%

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

   8. associate-/l* 84.6%

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

   9. fma-neg 84.6%

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

   10. *-commutative 84.6%

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

   11. fma-define 84.6%

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

   12. *-commutative 84.6%

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

   13. distribute-frac-neg 84.6%

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

   14. remove-double-neg 84.6%

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

3. Simplified 84.6%

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

5. Taylor expanded in x around 0 57.7%

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

6. Taylor expanded in t around inf 42.6%

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

   1. mul-1-neg 42.6%

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

   2. *-commutative 42.6%

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

   3. distribute-rgt-neg-in 42.6%

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

8. Simplified 42.6%

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

9. Taylor expanded in z around inf 20.7%

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

10. Final simplification 20.7%

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

Developer target: 99.2% 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 2024071 
(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))))