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

Percentage Accurate: 86.1% → 99.4%

Time: 12.2s

Alternatives: 14

Speedup: 0.8×

• 22.9% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 99.9%

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

4. Final simplification 99.8%

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

Alternative 2: 86.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ t_2 := \frac{x}{y} + -2\\ t_3 := \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ t_4 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;t\_3 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq -20000000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -1.9999999999995:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+149}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (fma 2.0 z 2.0) (* z t)))
        (t_2 (+ (/ x y) -2.0))
        (t_3 (/ (+ 2.0 (* (* 2.0 z) (- 1.0 t))) (* z t)))
        (t_4 (+ (/ x y) (/ 2.0 t))))
   (if (<= t_3 -4e+127)
     t_1
     (if (<= t_3 -20000000.0)
       t_4
       (if (<= t_3 -1.9999999999995)
         t_2
         (if (<= t_3 4e+149) t_4 (if (<= t_3 INFINITY) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, z, 2.0) / (z * t);
	double t_2 = (x / y) + -2.0;
	double t_3 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double t_4 = (x / y) + (2.0 / t);
	double tmp;
	if (t_3 <= -4e+127) {
		tmp = t_1;
	} else if (t_3 <= -20000000.0) {
		tmp = t_4;
	} else if (t_3 <= -1.9999999999995) {
		tmp = t_2;
	} else if (t_3 <= 4e+149) {
		tmp = t_4;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, z, 2.0) / Float64(z * t))
	t_2 = Float64(Float64(x / y) + -2.0)
	t_3 = Float64(Float64(2.0 + Float64(Float64(2.0 * z) * Float64(1.0 - t))) / Float64(z * t))
	t_4 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (t_3 <= -4e+127)
		tmp = t_1;
	elseif (t_3 <= -20000000.0)
		tmp = t_4;
	elseif (t_3 <= -1.9999999999995)
		tmp = t_2;
	elseif (t_3 <= 4e+149)
		tmp = t_4;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 + N[(N[(2.0 * z), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -4e+127], t$95$1, If[LessEqual[t$95$3, -20000000.0], t$95$4, If[LessEqual[t$95$3, -1.9999999999995], t$95$2, If[LessEqual[t$95$3, 4e+149], t$95$4, If[LessEqual[t$95$3, Infinity], t$95$1, t$95$2]]]]]]]]]

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)) < -3.99999999999999982e127 or 4.0000000000000002e149 < (/.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 98.6%

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

   3. Taylor expanded in t around 0

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

   5. Simplified 91.3%

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

   if -3.99999999999999982e127 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2e7 or -1.9999999999995 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.0000000000000002e149

   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-/r* N/A

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

      2. remove-double-neg N/A

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

      3. distribute-frac-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-rgt-identity N/A

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

      6. *-inverses N/A

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

      7. associate-/l* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. distribute-neg-frac N/A

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

      11. associate-/r* N/A

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

      12. /-lowering-/.f64 N/A

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

   5. Simplified 96.8%

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

   6. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 83.5

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

   8. Simplified 83.5%

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

   if -2e7 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.9999999999995 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 71.7%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 99.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -4 \cdot 10^{+127}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -20000000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -1.9999999999995:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 4 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+238}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+107}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* 2.0 z) (- 1.0 t))) (* z t)))
        (t_2 (+ (/ x y) -2.0)))
   (if (<= t_1 -4e+238)
     (+ -2.0 (/ 2.0 (* z t)))
     (if (<= t_1 -5e+107)
       (+ -2.0 (/ 2.0 t))
       (if (<= t_1 4e+135)
         t_2
         (if (<= t_1 5e+306)
           (/ 2.0 t)
           (if (<= t_1 INFINITY) (/ (/ 2.0 z) t) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t_1 <= -4e+238) {
		tmp = -2.0 + (2.0 / (z * t));
	} else if (t_1 <= -5e+107) {
		tmp = -2.0 + (2.0 / t);
	} else if (t_1 <= 4e+135) {
		tmp = t_2;
	} else if (t_1 <= 5e+306) {
		tmp = 2.0 / t;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t_1 <= -4e+238) {
		tmp = -2.0 + (2.0 / (z * t));
	} else if (t_1 <= -5e+107) {
		tmp = -2.0 + (2.0 / t);
	} else if (t_1 <= 4e+135) {
		tmp = t_2;
	} else if (t_1 <= 5e+306) {
		tmp = 2.0 / t;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t)
	t_2 = (x / y) + -2.0
	tmp = 0
	if t_1 <= -4e+238:
		tmp = -2.0 + (2.0 / (z * t))
	elif t_1 <= -5e+107:
		tmp = -2.0 + (2.0 / t)
	elif t_1 <= 4e+135:
		tmp = t_2
	elif t_1 <= 5e+306:
		tmp = 2.0 / t
	elif t_1 <= math.inf:
		tmp = (2.0 / z) / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(2.0 * z) * Float64(1.0 - t))) / Float64(z * t))
	t_2 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_1 <= -4e+238)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * t)));
	elseif (t_1 <= -5e+107)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (t_1 <= 4e+135)
		tmp = t_2;
	elseif (t_1 <= 5e+306)
		tmp = Float64(2.0 / t);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(2.0 / z) / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	t_2 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_1 <= -4e+238)
		tmp = -2.0 + (2.0 / (z * t));
	elseif (t_1 <= -5e+107)
		tmp = -2.0 + (2.0 / t);
	elseif (t_1 <= 4e+135)
		tmp = t_2;
	elseif (t_1 <= 5e+306)
		tmp = 2.0 / t;
	elseif (t_1 <= Inf)
		tmp = (2.0 / z) / t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(2.0 * z), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+238], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+107], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+135], t$95$2, If[LessEqual[t$95$1, 5e+306], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(2.0 / z), $MachinePrecision] / t), $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)) < -4.0000000000000002e238

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 89.2%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 78.8%

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

      1. +-lowering-+.f64 N/A

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

      2. *-rgt-identity N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 78.8

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

   10. Applied egg-rr 78.8%

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

   if -4.0000000000000002e238 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -5.0000000000000002e107

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 90.2%

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

   6. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 60.7

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

   8. Simplified 60.7%

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

   if -5.0000000000000002e107 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 3.99999999999999985e135 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 82.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 87.0%

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

   if 3.99999999999999985e135 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.99999999999999993e306

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 86.6%

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

   6. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 54.1

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

   8. Simplified 54.1%

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

   9. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 54.1

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

   11. Simplified 54.1%

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

   if 4.99999999999999993e306 < (/.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 99.9%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 99.9

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

   5. Simplified 99.9%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 100.0

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -4 \cdot 10^{+238}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 4 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ t_2 := \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+238}:\\ \;\;\;\;-2 + t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+107}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+135}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t)))
        (t_2 (/ (+ 2.0 (* (* 2.0 z) (- 1.0 t))) (* z t)))
        (t_3 (+ (/ x y) -2.0)))
   (if (<= t_2 -4e+238)
     (+ -2.0 t_1)
     (if (<= t_2 -5e+107)
       (+ -2.0 (/ 2.0 t))
       (if (<= t_2 4e+135)
         t_3
         (if (<= t_2 5e+306) (/ 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 / (z * t);
	double t_2 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -4e+238) {
		tmp = -2.0 + t_1;
	} else if (t_2 <= -5e+107) {
		tmp = -2.0 + (2.0 / t);
	} else if (t_2 <= 4e+135) {
		tmp = t_3;
	} else if (t_2 <= 5e+306) {
		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 / (z * t);
	double t_2 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -4e+238) {
		tmp = -2.0 + t_1;
	} else if (t_2 <= -5e+107) {
		tmp = -2.0 + (2.0 / t);
	} else if (t_2 <= 4e+135) {
		tmp = t_3;
	} else if (t_2 <= 5e+306) {
		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 / (z * t)
	t_2 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t)
	t_3 = (x / y) + -2.0
	tmp = 0
	if t_2 <= -4e+238:
		tmp = -2.0 + t_1
	elif t_2 <= -5e+107:
		tmp = -2.0 + (2.0 / t)
	elif t_2 <= 4e+135:
		tmp = t_3
	elif t_2 <= 5e+306:
		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(z * t))
	t_2 = Float64(Float64(2.0 + Float64(Float64(2.0 * z) * Float64(1.0 - t))) / Float64(z * t))
	t_3 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_2 <= -4e+238)
		tmp = Float64(-2.0 + t_1);
	elseif (t_2 <= -5e+107)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (t_2 <= 4e+135)
		tmp = t_3;
	elseif (t_2 <= 5e+306)
		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 / (z * t);
	t_2 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	t_3 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_2 <= -4e+238)
		tmp = -2.0 + t_1;
	elseif (t_2 <= -5e+107)
		tmp = -2.0 + (2.0 / t);
	elseif (t_2 <= 4e+135)
		tmp = t_3;
	elseif (t_2 <= 5e+306)
		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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(2.0 * z), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+238], N[(-2.0 + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, -5e+107], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+135], t$95$3, If[LessEqual[t$95$2, 5e+306], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]]]

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)) < -4.0000000000000002e238

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 89.2%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 78.8%

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

      1. +-lowering-+.f64 N/A

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

      2. *-rgt-identity N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 78.8

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

   10. Applied egg-rr 78.8%

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

   if -4.0000000000000002e238 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -5.0000000000000002e107

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 90.2%

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

   6. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 60.7

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

   8. Simplified 60.7%

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

   if -5.0000000000000002e107 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 3.99999999999999985e135 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 82.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 87.0%

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

   if 3.99999999999999985e135 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.99999999999999993e306

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 86.6%

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

   6. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 54.1

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

   8. Simplified 54.1%

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

   9. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 54.1

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

   11. Simplified 54.1%

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

   if 4.99999999999999993e306 < (/.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 99.9%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 99.9

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

   5. Simplified 99.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -4 \cdot 10^{+238}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 4 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq \infty:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ t_2 := \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+107}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+135}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t)))
        (t_2 (/ (+ 2.0 (* (* 2.0 z) (- 1.0 t))) (* z t)))
        (t_3 (+ (/ x y) -2.0)))
   (if (<= t_2 -4e+238)
     t_1
     (if (<= t_2 -5e+107)
       (+ -2.0 (/ 2.0 t))
       (if (<= t_2 4e+135)
         t_3
         (if (<= t_2 5e+306) (/ 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 / (z * t);
	double t_2 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -4e+238) {
		tmp = t_1;
	} else if (t_2 <= -5e+107) {
		tmp = -2.0 + (2.0 / t);
	} else if (t_2 <= 4e+135) {
		tmp = t_3;
	} else if (t_2 <= 5e+306) {
		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 / (z * t);
	double t_2 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -4e+238) {
		tmp = t_1;
	} else if (t_2 <= -5e+107) {
		tmp = -2.0 + (2.0 / t);
	} else if (t_2 <= 4e+135) {
		tmp = t_3;
	} else if (t_2 <= 5e+306) {
		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 / (z * t)
	t_2 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t)
	t_3 = (x / y) + -2.0
	tmp = 0
	if t_2 <= -4e+238:
		tmp = t_1
	elif t_2 <= -5e+107:
		tmp = -2.0 + (2.0 / t)
	elif t_2 <= 4e+135:
		tmp = t_3
	elif t_2 <= 5e+306:
		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(z * t))
	t_2 = Float64(Float64(2.0 + Float64(Float64(2.0 * z) * Float64(1.0 - t))) / Float64(z * t))
	t_3 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_2 <= -4e+238)
		tmp = t_1;
	elseif (t_2 <= -5e+107)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (t_2 <= 4e+135)
		tmp = t_3;
	elseif (t_2 <= 5e+306)
		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 / (z * t);
	t_2 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	t_3 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_2 <= -4e+238)
		tmp = t_1;
	elseif (t_2 <= -5e+107)
		tmp = -2.0 + (2.0 / t);
	elseif (t_2 <= 4e+135)
		tmp = t_3;
	elseif (t_2 <= 5e+306)
		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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(2.0 * z), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+238], t$95$1, If[LessEqual[t$95$2, -5e+107], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+135], t$95$3, If[LessEqual[t$95$2, 5e+306], 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)) < -4.0000000000000002e238 or 4.99999999999999993e306 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 85.1

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

   5. Simplified 85.1%

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

   if -4.0000000000000002e238 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -5.0000000000000002e107

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 90.2%

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

   6. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 60.7

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

   8. Simplified 60.7%

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

   if -5.0000000000000002e107 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 3.99999999999999985e135 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 82.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 87.0%

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

   if 3.99999999999999985e135 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.99999999999999993e306

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 86.6%

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

   6. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 54.1

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

   8. Simplified 54.1%

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

   9. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 54.1

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

   11. Simplified 54.1%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -4 \cdot 10^{+238}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -5 \cdot 10^{+107}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 4 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq \infty:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ t_2 := \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+135}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (fma 2.0 z 2.0) (* z t)))
        (t_2 (/ (+ 2.0 (* (* 2.0 z) (- 1.0 t))) (* z t)))
        (t_3 (+ (/ x y) -2.0)))
   (if (<= t_2 -2e+100)
     t_1
     (if (<= t_2 4e+135) 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(2.0, z, 2.0) / (z * t);
	double t_2 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -2e+100) {
		tmp = t_1;
	} else if (t_2 <= 4e+135) {
		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(2.0, z, 2.0) / Float64(z * t))
	t_2 = Float64(Float64(2.0 + Float64(Float64(2.0 * z) * Float64(1.0 - t))) / Float64(z * t))
	t_3 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_2 <= -2e+100)
		tmp = t_1;
	elseif (t_2 <= 4e+135)
		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[(2.0 * z + 2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(2.0 * z), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+100], t$95$1, If[LessEqual[t$95$2, 4e+135], 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)) < -2.00000000000000003e100 or 3.99999999999999985e135 < (/.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 98.7%

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

   3. Taylor expanded in t around 0

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

   5. Simplified 89.3%

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

   if -2.00000000000000003e100 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 3.99999999999999985e135 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 82.1%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 87.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -2 \cdot 10^{+100}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 4 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.2:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y} + -2, 2 + \frac{2}{z}\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (fma 2.0 z 2.0) (* z t)))))
   (if (<= (/ x y) -2e+19)
     t_1
     (if (<= (/ x y) 0.2)
       (/ (fma t (+ (/ x y) -2.0) (+ 2.0 (/ 2.0 z))) t)
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (fma(2.0, z, 2.0) / (z * t));
	double tmp;
	if ((x / y) <= -2e+19) {
		tmp = t_1;
	} else if ((x / y) <= 0.2) {
		tmp = fma(t, ((x / y) + -2.0), (2.0 + (2.0 / z))) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(fma(2.0, z, 2.0) / Float64(z * t)))
	tmp = 0.0
	if (Float64(x / y) <= -2e+19)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.2)
		tmp = Float64(fma(t, Float64(Float64(x / y) + -2.0), Float64(2.0 + Float64(2.0 / z))) / t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+19], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.2], N[(N[(t * N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision] + N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e19 or 0.20000000000000001 < (/.f64 x y)

   1. Initial program 90.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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-/r* N/A

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

      2. remove-double-neg N/A

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

      3. distribute-frac-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-rgt-identity N/A

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

      6. *-inverses N/A

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

      7. associate-/l* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. distribute-neg-frac N/A

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

      11. associate-/r* N/A

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

      12. /-lowering-/.f64 N/A

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

   5. Simplified 99.2%

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

   if -2e19 < (/.f64 x y) < 0.20000000000000001

   1. Initial program 86.0%

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

   3. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. *-lft-identity N/A

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

      9. associate-*l/ N/A

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

      10. +-lowering-+.f64 N/A

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

      11. associate-*l/ N/A

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

      12. *-lft-identity N/A

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

      13. /-lowering-/.f64 N/A

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

      14. +-lowering-+.f64 N/A

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

      15. associate-*r/ N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 99.9

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

   5. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.2:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y} + -2, 2 + \frac{2}{z}\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -10:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (fma 2.0 z 2.0) (* z t)))))
   (if (<= (/ x y) -10.0)
     t_1
     (if (<= (/ x y) 0.2) (fma (/ 2.0 (* z t)) (+ z 1.0) -2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (fma(2.0, z, 2.0) / (z * t));
	double tmp;
	if ((x / y) <= -10.0) {
		tmp = t_1;
	} else if ((x / y) <= 0.2) {
		tmp = fma((2.0 / (z * t)), (z + 1.0), -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(fma(2.0, z, 2.0) / Float64(z * t)))
	tmp = 0.0
	if (Float64(x / y) <= -10.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.2)
		tmp = fma(Float64(2.0 / Float64(z * t)), Float64(z + 1.0), -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -10.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.2], N[(N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(z + 1.0), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -10 or 0.20000000000000001 < (/.f64 x y)

   1. Initial program 90.1%

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

   3. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. remove-double-neg N/A

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

      3. distribute-frac-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-rgt-identity N/A

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

      6. *-inverses N/A

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

      7. associate-/l* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. distribute-neg-frac N/A

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

      11. associate-/r* N/A

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

      12. /-lowering-/.f64 N/A

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

   5. Simplified 98.7%

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

   if -10 < (/.f64 x y) < 0.20000000000000001

   1. Initial program 86.5%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 99.1%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10:\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ t_2 := \frac{x}{y} + t\_1\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t))) (t_2 (+ (/ x y) t_1)))
   (if (<= (/ x y) -1e+37)
     t_2
     (if (<= (/ x y) 1e+28) (fma t_1 (+ z 1.0) -2.0) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double t_2 = (x / y) + t_1;
	double tmp;
	if ((x / y) <= -1e+37) {
		tmp = t_2;
	} else if ((x / y) <= 1e+28) {
		tmp = fma(t_1, (z + 1.0), -2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(z * t))
	t_2 = Float64(Float64(x / y) + t_1)
	tmp = 0.0
	if (Float64(x / y) <= -1e+37)
		tmp = t_2;
	elseif (Float64(x / y) <= 1e+28)
		tmp = fma(t_1, Float64(z + 1.0), -2.0);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+37], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 1e+28], N[(t$95$1 * N[(z + 1.0), $MachinePrecision] + -2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999954e36 or 9.99999999999999958e27 < (/.f64 x y)

   1. Initial program 90.0%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 89.3

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

   5. Simplified 89.3%

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

   if -9.99999999999999954e36 < (/.f64 x y) < 9.99999999999999958e27

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 98.5%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.95 \cdot 10^{-17}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+28}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0)
   (/ x y)
   (if (<= (/ x y) 1.95e-17) -2.0 (if (<= (/ x y) 5e+28) (/ 2.0 t) (/ 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) <= 1.95e-17) {
		tmp = -2.0;
	} else if ((x / y) <= 5e+28) {
		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) <= (-2.0d0)) then
        tmp = x / y
    else if ((x / y) <= 1.95d-17) then
        tmp = -2.0d0
    else if ((x / y) <= 5d+28) 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) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 1.95e-17) {
		tmp = -2.0;
	} else if ((x / y) <= 5e+28) {
		tmp = 2.0 / t;
	} 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) <= 1.95e-17:
		tmp = -2.0
	elif (x / y) <= 5e+28:
		tmp = 2.0 / t
	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) <= 1.95e-17)
		tmp = -2.0;
	elseif (Float64(x / y) <= 5e+28)
		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) <= -2.0)
		tmp = x / y;
	elseif ((x / y) <= 1.95e-17)
		tmp = -2.0;
	elseif ((x / y) <= 5e+28)
		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], -2.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.95e-17], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 5e+28], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2 or 4.99999999999999957e28 < (/.f64 x y)

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 73.2

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

   5. Simplified 73.2%

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

   if -2 < (/.f64 x y) < 1.94999999999999995e-17

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 44.8%

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

   if 1.94999999999999995e-17 < (/.f64 x y) < 4.99999999999999957e28

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 92.6%

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

   6. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 49.0

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

   8. Simplified 49.0%

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

   9. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 47.1

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

   11. Simplified 47.1%

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

Alternative 11: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+83}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= (/ x y) -2e+26)
     t_1
     (if (<= (/ x y) 5e+83) (fma (/ 2.0 (* z t)) (+ z 1.0) -2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -2e+26) {
		tmp = t_1;
	} else if ((x / y) <= 5e+83) {
		tmp = fma((2.0 / (z * t)), (z + 1.0), -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (Float64(x / y) <= -2e+26)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e+83)
		tmp = fma(Float64(2.0 / Float64(z * t)), Float64(z + 1.0), -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+26], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e+83], N[(N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(z + 1.0), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.0000000000000001e26 or 5.00000000000000029e83 < (/.f64 x y)

   1. Initial program 90.7%

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

   3. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. remove-double-neg N/A

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

      3. distribute-frac-neg N/A

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

      4. mul-1-neg N/A

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

      5. *-rgt-identity N/A

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

      6. *-inverses N/A

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

      7. associate-/l* N/A

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

      8. associate-*l/ N/A

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

      9. associate-*r/ N/A

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

      10. distribute-neg-frac N/A

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

      11. associate-/r* N/A

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

      12. /-lowering-/.f64 N/A

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

   5. Simplified 99.1%

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

   6. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 89.3

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

   8. Simplified 89.3%

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

   if -2.0000000000000001e26 < (/.f64 x y) < 5.00000000000000029e83

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 94.3%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+83}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+28}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+37)
   (/ x y)
   (if (<= (/ x y) 1e+28) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+37) {
		tmp = x / y;
	} else if ((x / y) <= 1e+28) {
		tmp = -2.0 + (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) <= (-1d+37)) then
        tmp = x / y
    else if ((x / y) <= 1d+28) then
        tmp = (-2.0d0) + (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) <= -1e+37) {
		tmp = x / y;
	} else if ((x / y) <= 1e+28) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e+37:
		tmp = x / y
	elif (x / y) <= 1e+28:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+37)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1e+28)
		tmp = Float64(-2.0 + 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) <= -1e+37)
		tmp = x / y;
	elseif ((x / y) <= 1e+28)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e+37], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e+28], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999954e36 or 9.99999999999999958e27 < (/.f64 x y)

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 75.7

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

   5. Simplified 75.7%

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

   if -9.99999999999999954e36 < (/.f64 x y) < 9.99999999999999958e27

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 98.5%

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

   6. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 65.8

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

   8. Simplified 65.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+28}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2050000:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.225:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2050000.0) -2.0 (if (<= t 0.225) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2050000.0) {
		tmp = -2.0;
	} else if (t <= 0.225) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2050000.0d0)) then
        tmp = -2.0d0
    else if (t <= 0.225d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2050000.0) {
		tmp = -2.0;
	} else if (t <= 0.225) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2050000.0:
		tmp = -2.0
	elif t <= 0.225:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2050000.0)
		tmp = -2.0;
	elseif (t <= 0.225)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2050000.0)
		tmp = -2.0;
	elseif (t <= 0.225)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2050000.0], -2.0, If[LessEqual[t, 0.225], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -2.05e6 or 0.225000000000000006 < t

   1. Initial program 79.1%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 51.6%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 37.2%

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

   if -2.05e6 < t < 0.225000000000000006

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 72.6%

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

   6. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 39.1

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

   8. Simplified 39.1%

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

   9. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 38.4

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

   11. Simplified 38.4%

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

Alternative 14: 19.7% 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 88.5%

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

3. Taylor expanded in x around 0

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

5. Simplified 61.6%

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

6. Taylor expanded in t around inf

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

8. Simplified 20.8%

   \[\leadsto \color{blue}{-2} \]
9. Add Preprocessing

Developer Target 1: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024196 
(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))))