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

Percentage Accurate: 86.1% → 99.4%

Time: 11.7s

Alternatives: 17

Speedup: 1.1×

• 23.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   5. Applied rewrites 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 69.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ t_2 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+264}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+151}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z)))
        (t_2 (+ -2.0 (/ x y))))
   (if (<= t_1 -1e+264)
     (/ (/ 2.0 t) z)
     (if (<= t_1 -2e+49)
       (- (/ 2.0 t) 2.0)
       (if (<= t_1 2e+90)
         t_2
         (if (<= t_1 1e+151)
           (/ 2.0 t)
           (if (<= t_1 INFINITY) (/ 2.0 (* t z)) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_2 = -2.0 + (x / y);
	double tmp;
	if (t_1 <= -1e+264) {
		tmp = (2.0 / t) / z;
	} else if (t_1 <= -2e+49) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_1 <= 2e+90) {
		tmp = t_2;
	} else if (t_1 <= 1e+151) {
		tmp = 2.0 / t;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_2 = -2.0 + (x / y);
	double tmp;
	if (t_1 <= -1e+264) {
		tmp = (2.0 / t) / z;
	} else if (t_1 <= -2e+49) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_1 <= 2e+90) {
		tmp = t_2;
	} else if (t_1 <= 1e+151) {
		tmp = 2.0 / t;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z)
	t_2 = -2.0 + (x / y)
	tmp = 0
	if t_1 <= -1e+264:
		tmp = (2.0 / t) / z
	elif t_1 <= -2e+49:
		tmp = (2.0 / t) - 2.0
	elif t_1 <= 2e+90:
		tmp = t_2
	elif t_1 <= 1e+151:
		tmp = 2.0 / t
	elif t_1 <= math.inf:
		tmp = 2.0 / (t * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	t_2 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_1 <= -1e+264)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t_1 <= -2e+49)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif (t_1 <= 2e+90)
		tmp = t_2;
	elseif (t_1 <= 1e+151)
		tmp = Float64(2.0 / t);
	elseif (t_1 <= Inf)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	t_2 = -2.0 + (x / y);
	tmp = 0.0;
	if (t_1 <= -1e+264)
		tmp = (2.0 / t) / z;
	elseif (t_1 <= -2e+49)
		tmp = (2.0 / t) - 2.0;
	elseif (t_1 <= 2e+90)
		tmp = t_2;
	elseif (t_1 <= 1e+151)
		tmp = 2.0 / t;
	elseif (t_1 <= Inf)
		tmp = 2.0 / (t * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+264], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -2e+49], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+90], t$95$2, If[LessEqual[t$95$1, 1e+151], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000004e264

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 69.7

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

   5. Applied rewrites 69.7%

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

   if -1.00000000000000004e264 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.99999999999999989e49

   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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. associate-/l/ N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. *-lft-identity N/A

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

      10. associate-*l/ N/A

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

      11. distribute-lft-out N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 81.9

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 49.6%

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

   if -1.99999999999999989e49 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999993e90 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 71.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 87.9%

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

   if 1.99999999999999993e90 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.00000000000000002e151

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 83.4

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

   5. Applied rewrites 83.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.5%

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

   if 1.00000000000000002e151 < (/.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 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. frac-add N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 59.0

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

   7. Applied rewrites 59.0%

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

   9. Applied rewrites 59.0%

      \[\leadsto \frac{2}{\color{blue}{z \cdot t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -1 \cdot 10^{+264}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 10^{+151}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ t_2 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+264}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+151}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z)))
        (t_2 (+ -2.0 (/ x y))))
   (if (<= t_1 -1e+264)
     (/ (/ 2.0 z) t)
     (if (<= t_1 -2e+49)
       (- (/ 2.0 t) 2.0)
       (if (<= t_1 2e+90)
         t_2
         (if (<= t_1 1e+151)
           (/ 2.0 t)
           (if (<= t_1 INFINITY) (/ 2.0 (* t z)) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_2 = -2.0 + (x / y);
	double tmp;
	if (t_1 <= -1e+264) {
		tmp = (2.0 / z) / t;
	} else if (t_1 <= -2e+49) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_1 <= 2e+90) {
		tmp = t_2;
	} else if (t_1 <= 1e+151) {
		tmp = 2.0 / t;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_2 = -2.0 + (x / y);
	double tmp;
	if (t_1 <= -1e+264) {
		tmp = (2.0 / z) / t;
	} else if (t_1 <= -2e+49) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_1 <= 2e+90) {
		tmp = t_2;
	} else if (t_1 <= 1e+151) {
		tmp = 2.0 / t;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z)
	t_2 = -2.0 + (x / y)
	tmp = 0
	if t_1 <= -1e+264:
		tmp = (2.0 / z) / t
	elif t_1 <= -2e+49:
		tmp = (2.0 / t) - 2.0
	elif t_1 <= 2e+90:
		tmp = t_2
	elif t_1 <= 1e+151:
		tmp = 2.0 / t
	elif t_1 <= math.inf:
		tmp = 2.0 / (t * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	t_2 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_1 <= -1e+264)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif (t_1 <= -2e+49)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif (t_1 <= 2e+90)
		tmp = t_2;
	elseif (t_1 <= 1e+151)
		tmp = Float64(2.0 / t);
	elseif (t_1 <= Inf)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	t_2 = -2.0 + (x / y);
	tmp = 0.0;
	if (t_1 <= -1e+264)
		tmp = (2.0 / z) / t;
	elseif (t_1 <= -2e+49)
		tmp = (2.0 / t) - 2.0;
	elseif (t_1 <= 2e+90)
		tmp = t_2;
	elseif (t_1 <= 1e+151)
		tmp = 2.0 / t;
	elseif (t_1 <= Inf)
		tmp = 2.0 / (t * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+264], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, -2e+49], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+90], t$95$2, If[LessEqual[t$95$1, 1e+151], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000004e264

   1. Initial program 94.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 85.4

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

   5. Applied rewrites 85.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 69.7%

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

   if -1.00000000000000004e264 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.99999999999999989e49

   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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. associate-/l/ N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. *-lft-identity N/A

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

      10. associate-*l/ N/A

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

      11. distribute-lft-out N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 81.9

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 49.6%

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

   if -1.99999999999999989e49 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999993e90 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 71.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 87.9%

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

   if 1.99999999999999993e90 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.00000000000000002e151

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 83.4

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

   5. Applied rewrites 83.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.5%

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

   if 1.00000000000000002e151 < (/.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 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. frac-add N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 59.0

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

   7. Applied rewrites 59.0%

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

   9. Applied rewrites 59.0%

      \[\leadsto \frac{2}{\color{blue}{z \cdot t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -1 \cdot 10^{+264}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 10^{+151}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ t_3 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+90}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+151}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z)))
        (t_3 (+ -2.0 (/ x y))))
   (if (<= t_2 -1e+264)
     t_1
     (if (<= t_2 -2e+49)
       (- (/ 2.0 t) 2.0)
       (if (<= t_2 2e+90)
         t_3
         (if (<= t_2 1e+151) (/ 2.0 t) (if (<= t_2 INFINITY) t_1 t_3)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -1e+264) {
		tmp = t_1;
	} else if (t_2 <= -2e+49) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_2 <= 2e+90) {
		tmp = t_3;
	} else if (t_2 <= 1e+151) {
		tmp = 2.0 / t;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -1e+264) {
		tmp = t_1;
	} else if (t_2 <= -2e+49) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_2 <= 2e+90) {
		tmp = t_3;
	} else if (t_2 <= 1e+151) {
		tmp = 2.0 / t;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z)
	t_3 = -2.0 + (x / y)
	tmp = 0
	if t_2 <= -1e+264:
		tmp = t_1
	elif t_2 <= -2e+49:
		tmp = (2.0 / t) - 2.0
	elif t_2 <= 2e+90:
		tmp = t_3
	elif t_2 <= 1e+151:
		tmp = 2.0 / t
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	t_3 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_2 <= -1e+264)
		tmp = t_1;
	elseif (t_2 <= -2e+49)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif (t_2 <= 2e+90)
		tmp = t_3;
	elseif (t_2 <= 1e+151)
		tmp = Float64(2.0 / t);
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	t_3 = -2.0 + (x / y);
	tmp = 0.0;
	if (t_2 <= -1e+264)
		tmp = t_1;
	elseif (t_2 <= -2e+49)
		tmp = (2.0 / t) - 2.0;
	elseif (t_2 <= 2e+90)
		tmp = t_3;
	elseif (t_2 <= 1e+151)
		tmp = 2.0 / t;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	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[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+264], t$95$1, If[LessEqual[t$95$2, -2e+49], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t$95$2, 2e+90], t$95$3, If[LessEqual[t$95$2, 1e+151], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000004e264 or 1.00000000000000002e151 < (/.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 98.3%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. frac-add N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 78.3%

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

   5. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 61.9

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

   7. Applied rewrites 61.9%

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

   9. Applied rewrites 61.9%

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

   if -1.00000000000000004e264 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.99999999999999989e49

   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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. associate-/l/ N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. *-lft-identity N/A

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

      10. associate-*l/ N/A

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

      11. distribute-lft-out N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 81.9

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 49.6%

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

   if -1.99999999999999989e49 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999993e90 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 71.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 87.9%

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

   if 1.99999999999999993e90 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.00000000000000002e151

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 83.4

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

   5. Applied rewrites 83.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -1 \cdot 10^{+264}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 2 \cdot 10^{+90}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 10^{+151}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ t_3 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_2 \leq -2000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1.99998:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+131}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t))
        (t_2 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z)))
        (t_3 (+ -2.0 (/ x y))))
   (if (<= t_2 -2000000000.0)
     t_1
     (if (<= t_2 -1.99998)
       t_3
       (if (<= t_2 5e+131)
         (+ (/ 2.0 t) (/ x y))
         (if (<= t_2 INFINITY) t_1 t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -2000000000.0) {
		tmp = t_1;
	} else if (t_2 <= -1.99998) {
		tmp = t_3;
	} else if (t_2 <= 5e+131) {
		tmp = (2.0 / t) + (x / y);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -2000000000.0) {
		tmp = t_1;
	} else if (t_2 <= -1.99998) {
		tmp = t_3;
	} else if (t_2 <= 5e+131) {
		tmp = (2.0 / t) + (x / y);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / z) - -2.0) / t
	t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z)
	t_3 = -2.0 + (x / y)
	tmp = 0
	if t_2 <= -2000000000.0:
		tmp = t_1
	elif t_2 <= -1.99998:
		tmp = t_3
	elif t_2 <= 5e+131:
		tmp = (2.0 / t) + (x / y)
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / z) - -2.0) / t)
	t_2 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	t_3 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_2 <= -2000000000.0)
		tmp = t_1;
	elseif (t_2 <= -1.99998)
		tmp = t_3;
	elseif (t_2 <= 5e+131)
		tmp = Float64(Float64(2.0 / t) + Float64(x / y));
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((2.0 / z) - -2.0) / t;
	t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	t_3 = -2.0 + (x / y);
	tmp = 0.0;
	if (t_2 <= -2000000000.0)
		tmp = t_1;
	elseif (t_2 <= -1.99998)
		tmp = t_3;
	elseif (t_2 <= 5e+131)
		tmp = (2.0 / t) + (x / y);
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2000000000.0], t$95$1, If[LessEqual[t$95$2, -1.99998], t$95$3, If[LessEqual[t$95$2, 5e+131], N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2e9 or 4.99999999999999995e131 < (/.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 99.0%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -2e9 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.99998000000000009 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 61.3%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 97.7%

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

   if -1.99998000000000009 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.99999999999999995e131

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l/ N/A

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 78.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -2000000000:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -1.99998:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 5 \cdot 10^{+131}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ t_3 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_2 \leq -2000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+35}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t))
        (t_2 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z)))
        (t_3 (+ -2.0 (/ x y))))
   (if (<= t_2 -2000000000.0)
     t_1
     (if (<= t_2 1e+35) t_3 (if (<= t_2 INFINITY) t_1 t_3)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -2000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+35) {
		tmp = t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -2000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+35) {
		tmp = t_3;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / z) - -2.0) / t
	t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z)
	t_3 = -2.0 + (x / y)
	tmp = 0
	if t_2 <= -2000000000.0:
		tmp = t_1
	elif t_2 <= 1e+35:
		tmp = t_3
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / z) - -2.0) / t)
	t_2 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	t_3 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_2 <= -2000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+35)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((2.0 / z) - -2.0) / t;
	t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	t_3 = -2.0 + (x / y);
	tmp = 0.0;
	if (t_2 <= -2000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+35)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2000000000.0], t$95$1, If[LessEqual[t$95$2, 1e+35], t$95$3, If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2e9 or 9.9999999999999997e34 < (/.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 99.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 80.9

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

   5. Applied rewrites 80.9%

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

   if -2e9 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.9999999999999997e34 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 66.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 96.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -2000000000:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 10^{+35}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ t_2 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ t_3 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_2 \leq -2000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+35}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (fma z 2.0 2.0) (* t z)))
        (t_2 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z)))
        (t_3 (+ -2.0 (/ x y))))
   (if (<= t_2 -2000000000.0)
     t_1
     (if (<= t_2 1e+35) t_3 (if (<= t_2 INFINITY) t_1 t_3)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(z, 2.0, 2.0) / (t * z);
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -2000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+35) {
		tmp = t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(z, 2.0, 2.0) / Float64(t * z))
	t_2 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	t_3 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_2 <= -2000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+35)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2000000000.0], t$95$1, If[LessEqual[t$95$2, 1e+35], t$95$3, If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2e9 or 9.9999999999999997e34 < (/.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 99.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 62.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. lift-/.f64 N/A

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

      7. frac-add N/A

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

      8. lower-/.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 51.2

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

   7. Applied rewrites 51.2%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 80.7%

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

   if -2e9 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.9999999999999997e34 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 66.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 96.0%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -2000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 10^{+35}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -35000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -4.3 \cdot 10^{-32}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-321}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 53000000000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -35000000.0)
   (/ x y)
   (if (<= (/ x y) -4.3e-32)
     (/ 2.0 t)
     (if (<= (/ x y) -5e-321)
       -2.0
       (if (<= (/ x y) 53000000000.0) (/ 2.0 t) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -35000000.0) {
		tmp = x / y;
	} else if ((x / y) <= -4.3e-32) {
		tmp = 2.0 / t;
	} else if ((x / y) <= -5e-321) {
		tmp = -2.0;
	} else if ((x / y) <= 53000000000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-35000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= (-4.3d-32)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= (-5d-321)) then
        tmp = -2.0d0
    else if ((x / y) <= 53000000000.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -35000000.0) {
		tmp = x / y;
	} else if ((x / y) <= -4.3e-32) {
		tmp = 2.0 / t;
	} else if ((x / y) <= -5e-321) {
		tmp = -2.0;
	} else if ((x / y) <= 53000000000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -35000000.0:
		tmp = x / y
	elif (x / y) <= -4.3e-32:
		tmp = 2.0 / t
	elif (x / y) <= -5e-321:
		tmp = -2.0
	elif (x / y) <= 53000000000.0:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -35000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -4.3e-32)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= -5e-321)
		tmp = -2.0;
	elseif (Float64(x / y) <= 53000000000.0)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -35000000.0)
		tmp = x / y;
	elseif ((x / y) <= -4.3e-32)
		tmp = 2.0 / t;
	elseif ((x / y) <= -5e-321)
		tmp = -2.0;
	elseif ((x / y) <= 53000000000.0)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -35000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -4.3e-32], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -5e-321], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 53000000000.0], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -3.5e7 or 5.3e10 < (/.f64 x y)

   1. Initial program 87.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 70.2

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

   5. Applied rewrites 70.2%

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

   if -3.5e7 < (/.f64 x y) < -4.2999999999999999e-32 or -4.99994e-321 < (/.f64 x y) < 5.3e10

   1. Initial program 89.4%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 73.1

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 42.8%

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

   if -4.2999999999999999e-32 < (/.f64 x y) < -4.99994e-321

   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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 62.1%

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

   5. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. associate-/l/ N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. *-lft-identity N/A

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

      10. associate-*l/ N/A

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

      11. distribute-lft-out N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 99.9

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

   7. Applied rewrites 99.9%

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

   8. Taylor expanded in t around inf

      \[\leadsto -2 \]
   9. Step-by-step derivation

   10. Applied rewrites 47.9%

       \[\leadsto -2 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := t\_1 + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-17}:\\ \;\;\;\;t\_1 - 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t)) (t_2 (+ t_1 (/ x y))))
   (if (<= (/ x y) -2e+17) t_2 (if (<= (/ x y) 4e-17) (- t_1 2.0) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = t_1 + (x / y);
	double tmp;
	if ((x / y) <= -2e+17) {
		tmp = t_2;
	} else if ((x / y) <= 4e-17) {
		tmp = t_1 - 2.0;
	} 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 / z) - (-2.0d0)) / t
    t_2 = t_1 + (x / y)
    if ((x / y) <= (-2d+17)) then
        tmp = t_2
    else if ((x / y) <= 4d-17) then
        tmp = t_1 - 2.0d0
    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 / z) - -2.0) / t;
	double t_2 = t_1 + (x / y);
	double tmp;
	if ((x / y) <= -2e+17) {
		tmp = t_2;
	} else if ((x / y) <= 4e-17) {
		tmp = t_1 - 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / z) - -2.0) / t
	t_2 = t_1 + (x / y)
	tmp = 0
	if (x / y) <= -2e+17:
		tmp = t_2
	elif (x / y) <= 4e-17:
		tmp = t_1 - 2.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / z) - -2.0) / t)
	t_2 = Float64(t_1 + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -2e+17)
		tmp = t_2;
	elseif (Float64(x / y) <= 4e-17)
		tmp = Float64(t_1 - 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((2.0 / z) - -2.0) / t;
	t_2 = t_1 + (x / y);
	tmp = 0.0;
	if ((x / y) <= -2e+17)
		tmp = t_2;
	elseif ((x / y) <= 4e-17)
		tmp = t_1 - 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+17], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 4e-17], N[(t$95$1 - 2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e17 or 4.00000000000000029e-17 < (/.f64 x y)

   1. Initial program 88.3%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l/ N/A

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

   5. Applied rewrites 98.1%

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

   if -2e17 < (/.f64 x y) < 4.00000000000000029e-17

   1. Initial program 84.2%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.1%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+17}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ (fma z 2.0 2.0) (* t z)) (/ x y))))
   (if (<= (/ x y) -2e+17)
     t_1
     (if (<= (/ x y) 4e-17) (- (/ (- (/ 2.0 z) -2.0) t) 2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (fma(z, 2.0, 2.0) / (t * z)) + (x / y);
	double tmp;
	if ((x / y) <= -2e+17) {
		tmp = t_1;
	} else if ((x / y) <= 4e-17) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(fma(z, 2.0, 2.0) / Float64(t * z)) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -2e+17)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-17)
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+17], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-17], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e17 or 4.00000000000000029e-17 < (/.f64 x y)

   1. Initial program 88.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 97.1

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

   5. Applied rewrites 97.1%

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

   if -2e17 < (/.f64 x y) < 4.00000000000000029e-17

   1. Initial program 84.2%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.1%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+17}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{t} - 2\right) + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+41)
   (+ (/ 2.0 t) (/ x y))
   (if (<= (/ x y) 5e-13)
     (- (/ (- (/ 2.0 z) -2.0) t) 2.0)
     (+ (- (/ 2.0 t) 2.0) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+41) {
		tmp = (2.0 / t) + (x / y);
	} else if ((x / y) <= 5e-13) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = ((2.0 / t) - 2.0) + (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) <= (-2d+41)) then
        tmp = (2.0d0 / t) + (x / y)
    else if ((x / y) <= 5d-13) then
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    else
        tmp = ((2.0d0 / t) - 2.0d0) + (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) <= -2e+41) {
		tmp = (2.0 / t) + (x / y);
	} else if ((x / y) <= 5e-13) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = ((2.0 / t) - 2.0) + (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+41:
		tmp = (2.0 / t) + (x / y)
	elif (x / y) <= 5e-13:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	else:
		tmp = ((2.0 / t) - 2.0) + (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+41)
		tmp = Float64(Float64(2.0 / t) + Float64(x / y));
	elseif (Float64(x / y) <= 5e-13)
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	else
		tmp = Float64(Float64(Float64(2.0 / t) - 2.0) + Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+41)
		tmp = (2.0 / t) + (x / y);
	elseif ((x / y) <= 5e-13)
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	else
		tmp = ((2.0 / t) - 2.0) + (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+41], N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-13], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.00000000000000001e41

   1. Initial program 87.6%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l/ N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.2%

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

   if -2.00000000000000001e41 < (/.f64 x y) < 4.9999999999999999e-13

   1. Initial program 84.7%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.5%

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

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

   1. Initial program 88.0%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. lower--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 84.4

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

   5. Applied rewrites 84.4%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{t} - 2\right) + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 t) (/ x y))))
   (if (<= (/ x y) -2e+41)
     t_1
     (if (<= (/ x y) 5e-13) (- (/ (- (/ 2.0 z) -2.0) t) 2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + (x / y);
	double tmp;
	if ((x / y) <= -2e+41) {
		tmp = t_1;
	} else if ((x / y) <= 5e-13) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / t) + (x / y)
    if ((x / y) <= (-2d+41)) then
        tmp = t_1
    else if ((x / y) <= 5d-13) then
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + (x / y);
	double tmp;
	if ((x / y) <= -2e+41) {
		tmp = t_1;
	} else if ((x / y) <= 5e-13) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) + (x / y)
	tmp = 0
	if (x / y) <= -2e+41:
		tmp = t_1
	elif (x / y) <= 5e-13:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -2e+41)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-13)
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) + (x / y);
	tmp = 0.0;
	if ((x / y) <= -2e+41)
		tmp = t_1;
	elseif ((x / y) <= 5e-13)
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+41], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-13], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.00000000000000001e41 or 4.9999999999999999e-13 < (/.f64 x y)

   1. Initial program 87.9%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l/ N/A

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 80.3%

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

   if -2.00000000000000001e41 < (/.f64 x y) < 4.9999999999999999e-13

   1. Initial program 84.7%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.1e+38)
   (/ x y)
   (if (<= (/ x y) 4.0) (- (/ 2.0 t) 2.0) (+ -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.1e+38) {
		tmp = x / y;
	} else if ((x / y) <= 4.0) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = -2.0 + (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.1d+38)) then
        tmp = x / y
    else if ((x / y) <= 4.0d0) then
        tmp = (2.0d0 / t) - 2.0d0
    else
        tmp = (-2.0d0) + (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.1e+38) {
		tmp = x / y;
	} else if ((x / y) <= 4.0) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = -2.0 + (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.1e+38:
		tmp = x / y
	elif (x / y) <= 4.0:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = -2.0 + (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.1e+38)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4.0)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.1e+38)
		tmp = x / y;
	elseif ((x / y) <= 4.0)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = -2.0 + (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.1e+38], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.0], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.10000000000000003e38

   1. Initial program 87.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 69.0

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

   5. Applied rewrites 69.0%

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

   if -1.10000000000000003e38 < (/.f64 x y) < 4

   1. Initial program 84.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 69.0%

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

   5. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. associate-/l/ N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. *-lft-identity N/A

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

      10. associate-*l/ N/A

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

      11. distribute-lft-out N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 98.4

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

   7. Applied rewrites 98.4%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 64.1%

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

   if 4 < (/.f64 x y)

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 72.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 53000000000:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.1e+38)
   (/ x y)
   (if (<= (/ x y) 53000000000.0) (- (/ 2.0 t) 2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.1e+38) {
		tmp = x / y;
	} else if ((x / y) <= 53000000000.0) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.1d+38)) then
        tmp = x / y
    else if ((x / y) <= 53000000000.0d0) then
        tmp = (2.0d0 / t) - 2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.1e+38) {
		tmp = x / y;
	} else if ((x / y) <= 53000000000.0) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.1e+38:
		tmp = x / y
	elif (x / y) <= 53000000000.0:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.1e+38)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 53000000000.0)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.1e+38)
		tmp = x / y;
	elseif ((x / y) <= 53000000000.0)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.1e+38], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 53000000000.0], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.10000000000000003e38 or 5.3e10 < (/.f64 x y)

   1. Initial program 87.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 71.1

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

   5. Applied rewrites 71.1%

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

   if -1.10000000000000003e38 < (/.f64 x y) < 5.3e10

   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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 69.6%

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

   5. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. associate-/l/ N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. *-lft-identity N/A

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

      10. associate-*l/ N/A

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

      11. distribute-lft-out N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 97.0

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

   7. Applied rewrites 97.0%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 63.4%

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

Alternative 15: 53.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.2 \cdot 10^{-5}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0) (/ x y) (if (<= (/ x y) 6.2e-5) -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) <= 6.2e-5) {
		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) <= 6.2d-5) 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) <= 6.2e-5) {
		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) <= 6.2e-5:
		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) <= 6.2e-5)
		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) <= 6.2e-5)
		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], 6.2e-5], -2.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2 or 6.20000000000000027e-5 < (/.f64 x y)

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 68.7

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

   5. Applied rewrites 68.7%

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

   if -2 < (/.f64 x y) < 6.20000000000000027e-5

   1. Initial program 84.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. associate-/l/ N/A

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

      7. metadata-eval N/A

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

      8. associate-*r/ N/A

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

      9. *-lft-identity N/A

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

      10. associate-*l/ N/A

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

      11. distribute-lft-out N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 99.0

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

   7. Applied rewrites 99.0%

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

   8. Taylor expanded in t around inf

      \[\leadsto -2 \]
   9. Step-by-step derivation

   10. Applied rewrites 33.0%

       \[\leadsto -2 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{2}{t} - 2\right) + \frac{x}{y}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- (/ 2.0 t) 2.0) (/ x y))))
   (if (<= z -4.5e-19)
     t_1
     (if (<= z 1.35e-16) (+ (/ 2.0 (* t z)) (/ x y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / t) - 2.0) + (x / y);
	double tmp;
	if (z <= -4.5e-19) {
		tmp = t_1;
	} else if (z <= 1.35e-16) {
		tmp = (2.0 / (t * z)) + (x / y);
	} 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) - 2.0d0) + (x / y)
    if (z <= (-4.5d-19)) then
        tmp = t_1
    else if (z <= 1.35d-16) then
        tmp = (2.0d0 / (t * z)) + (x / y)
    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) - 2.0) + (x / y);
	double tmp;
	if (z <= -4.5e-19) {
		tmp = t_1;
	} else if (z <= 1.35e-16) {
		tmp = (2.0 / (t * z)) + (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / t) - 2.0) + (x / y)
	tmp = 0
	if z <= -4.5e-19:
		tmp = t_1
	elif z <= 1.35e-16:
		tmp = (2.0 / (t * z)) + (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / t) - 2.0) + Float64(x / y))
	tmp = 0.0
	if (z <= -4.5e-19)
		tmp = t_1;
	elseif (z <= 1.35e-16)
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((2.0 / t) - 2.0) + (x / y);
	tmp = 0.0;
	if (z <= -4.5e-19)
		tmp = t_1;
	elseif (z <= 1.35e-16)
		tmp = (2.0 / (t * z)) + (x / y);
	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] - 2.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e-19], t$95$1, If[LessEqual[z, 1.35e-16], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000013e-19 or 1.35e-16 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. lower--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 97.2

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

   5. Applied rewrites 97.2%

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

   if -4.50000000000000013e-19 < z < 1.35e-16

   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 z around 0

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

   5. Applied rewrites 90.9%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-19}:\\ \;\;\;\;\left(\frac{2}{t} - 2\right) + \frac{x}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{t} - 2\right) + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 20.3% accurate, 47.0× 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 86.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/r* N/A

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

   4. lower-/.f64 N/A

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

4. Applied rewrites 74.4%

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

5. Taylor expanded in y around inf

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

   1. sub-neg N/A

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

   2. metadata-eval N/A

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

   3. associate-*r/ N/A

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

   4. metadata-eval N/A

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

   5. *-commutative N/A

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

   6. associate-/l/ N/A

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

   7. metadata-eval N/A

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

   8. associate-*r/ N/A

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

   9. *-lft-identity N/A

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

   10. associate-*l/ N/A

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

   11. distribute-lft-out N/A

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

   12. lower-fma.f64 N/A

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

   13. lower-/.f64 N/A

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

   14. +-commutative N/A

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

   15. lower-+.f64 N/A

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

   16. associate-*r/ N/A

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

   17. metadata-eval N/A

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

   18. lower-/.f64 67.9

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

7. Applied rewrites 67.9%

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

8. Taylor expanded in t around inf

   \[\leadsto -2 \]
9. Step-by-step derivation

10. Applied rewrites 18.5%

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

Developer Target 1: 99.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024255 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

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