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

Percentage Accurate: 86.3% → 99.5%

Time: 10.0s

Alternatives: 12

Speedup: 0.7×

• 23.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 - N[(N[(t - 1.0), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] + 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 99.9%

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

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

      8. metadata-eval N/A

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

      9. distribute-lft-neg-in N/A

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

      10. metadata-eval N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. associate-*r/ N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 94.6

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

   5. Applied rewrites 94.6%

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

4. Final simplification 99.1%

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

Alternative 2: 68.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ t_2 := \frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z}\\ t_3 := \frac{2}{t} - 2\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+287}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 500000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+291}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y)))
        (t_2 (/ (- 2.0 (* (- t 1.0) (* z 2.0))) (* t z)))
        (t_3 (- (/ 2.0 t) 2.0)))
   (if (<= t_2 -1e+287)
     (/ (/ 2.0 z) t)
     (if (<= t_2 -2e+88)
       t_3
       (if (<= t_2 500000.0)
         t_1
         (if (<= t_2 1e+291)
           t_3
           (if (<= t_2 INFINITY) (/ 2.0 (* t z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double t_2 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	double t_3 = (2.0 / t) - 2.0;
	double tmp;
	if (t_2 <= -1e+287) {
		tmp = (2.0 / z) / t;
	} else if (t_2 <= -2e+88) {
		tmp = t_3;
	} else if (t_2 <= 500000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+291) {
		tmp = t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double t_2 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	double t_3 = (2.0 / t) - 2.0;
	double tmp;
	if (t_2 <= -1e+287) {
		tmp = (2.0 / z) / t;
	} else if (t_2 <= -2e+88) {
		tmp = t_3;
	} else if (t_2 <= 500000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+291) {
		tmp = t_3;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	t_2 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z)
	t_3 = (2.0 / t) - 2.0
	tmp = 0
	if t_2 <= -1e+287:
		tmp = (2.0 / z) / t
	elif t_2 <= -2e+88:
		tmp = t_3
	elif t_2 <= 500000.0:
		tmp = t_1
	elif t_2 <= 1e+291:
		tmp = t_3
	elif t_2 <= math.inf:
		tmp = 2.0 / (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	t_2 = Float64(Float64(2.0 - Float64(Float64(t - 1.0) * Float64(z * 2.0))) / Float64(t * z))
	t_3 = Float64(Float64(2.0 / t) - 2.0)
	tmp = 0.0
	if (t_2 <= -1e+287)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif (t_2 <= -2e+88)
		tmp = t_3;
	elseif (t_2 <= 500000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+291)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	t_2 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	t_3 = (2.0 / t) - 2.0;
	tmp = 0.0;
	if (t_2 <= -1e+287)
		tmp = (2.0 / z) / t;
	elseif (t_2 <= -2e+88)
		tmp = t_3;
	elseif (t_2 <= 500000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+291)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = 2.0 / (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 - N[(N[(t - 1.0), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+287], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$2, -2e+88], t$95$3, If[LessEqual[t$95$2, 500000.0], t$95$1, If[LessEqual[t$95$2, 1e+291], t$95$3, If[LessEqual[t$95$2, Infinity], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

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)) < -1.0000000000000001e287

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   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 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 94.9%

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

   if -1.0000000000000001e287 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.99999999999999992e88 or 5e5 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.9999999999999996e290

   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

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 79.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 47.3%

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

   if -1.99999999999999992e88 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5e5 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. Applied rewrites 94.6%

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

   if 9.9999999999999996e290 < (/.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 89.5%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 94.7

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

   5. Applied rewrites 94.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq -1 \cdot 10^{+287}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq -2 \cdot 10^{+88}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq 500000:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq 10^{+291}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{2}{t} - 2\\ t_3 := \frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z}\\ t_4 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 500000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 10^{+291}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (- (/ 2.0 t) 2.0))
        (t_3 (/ (- 2.0 (* (- t 1.0) (* z 2.0))) (* t z)))
        (t_4 (+ -2.0 (/ x y))))
   (if (<= t_3 -1e+287)
     t_1
     (if (<= t_3 -2e+88)
       t_2
       (if (<= t_3 500000.0)
         t_4
         (if (<= t_3 1e+291) t_2 (if (<= t_3 INFINITY) t_1 t_4)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 / t) - 2.0;
	double t_3 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	double t_4 = -2.0 + (x / y);
	double tmp;
	if (t_3 <= -1e+287) {
		tmp = t_1;
	} else if (t_3 <= -2e+88) {
		tmp = t_2;
	} else if (t_3 <= 500000.0) {
		tmp = t_4;
	} else if (t_3 <= 1e+291) {
		tmp = t_2;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	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 = (2.0 / t) - 2.0;
	double t_3 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	double t_4 = -2.0 + (x / y);
	double tmp;
	if (t_3 <= -1e+287) {
		tmp = t_1;
	} else if (t_3 <= -2e+88) {
		tmp = t_2;
	} else if (t_3 <= 500000.0) {
		tmp = t_4;
	} else if (t_3 <= 1e+291) {
		tmp = t_2;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (2.0 / t) - 2.0
	t_3 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z)
	t_4 = -2.0 + (x / y)
	tmp = 0
	if t_3 <= -1e+287:
		tmp = t_1
	elif t_3 <= -2e+88:
		tmp = t_2
	elif t_3 <= 500000.0:
		tmp = t_4
	elif t_3 <= 1e+291:
		tmp = t_2
	elif t_3 <= math.inf:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(2.0 / t) - 2.0)
	t_3 = Float64(Float64(2.0 - Float64(Float64(t - 1.0) * Float64(z * 2.0))) / Float64(t * z))
	t_4 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_3 <= -1e+287)
		tmp = t_1;
	elseif (t_3 <= -2e+88)
		tmp = t_2;
	elseif (t_3 <= 500000.0)
		tmp = t_4;
	elseif (t_3 <= 1e+291)
		tmp = t_2;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (2.0 / t) - 2.0;
	t_3 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	t_4 = -2.0 + (x / y);
	tmp = 0.0;
	if (t_3 <= -1e+287)
		tmp = t_1;
	elseif (t_3 <= -2e+88)
		tmp = t_2;
	elseif (t_3 <= 500000.0)
		tmp = t_4;
	elseif (t_3 <= 1e+291)
		tmp = t_2;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_4;
	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[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 - N[(N[(t - 1.0), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+287], t$95$1, If[LessEqual[t$95$3, -2e+88], t$95$2, If[LessEqual[t$95$3, 500000.0], t$95$4, If[LessEqual[t$95$3, 1e+291], t$95$2, If[LessEqual[t$95$3, Infinity], t$95$1, t$95$4]]]]]]]]]

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)) < -1.0000000000000001e287 or 9.9999999999999996e290 < (/.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 92.1%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 94.8

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

   5. Applied rewrites 94.8%

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

   if -1.0000000000000001e287 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.99999999999999992e88 or 5e5 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.9999999999999996e290

   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

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 79.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 47.3%

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

   if -1.99999999999999992e88 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5e5 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. Applied rewrites 94.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq -1 \cdot 10^{+287}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq -2 \cdot 10^{+88}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq 500000:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq 10^{+291}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z}\\ t_3 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 500000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1 - 2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t))
        (t_2 (/ (- 2.0 (* (- t 1.0) (* z 2.0))) (* t z)))
        (t_3 (+ -2.0 (/ x y))))
   (if (<= t_2 -4e+86)
     t_1
     (if (<= t_2 500000.0) t_3 (if (<= t_2 INFINITY) (- t_1 2.0) 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 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -4e+86) {
		tmp = t_1;
	} else if (t_2 <= 500000.0) {
		tmp = t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1 - 2.0;
	} 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 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -4e+86) {
		tmp = t_1;
	} else if (t_2 <= 500000.0) {
		tmp = t_3;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 - 2.0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / z) - -2.0) / t
	t_2 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z)
	t_3 = -2.0 + (x / y)
	tmp = 0
	if t_2 <= -4e+86:
		tmp = t_1
	elif t_2 <= 500000.0:
		tmp = t_3
	elif t_2 <= math.inf:
		tmp = t_1 - 2.0
	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(2.0 - Float64(Float64(t - 1.0) * Float64(z * 2.0))) / Float64(t * z))
	t_3 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_2 <= -4e+86)
		tmp = t_1;
	elseif (t_2 <= 500000.0)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = Float64(t_1 - 2.0);
	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 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	t_3 = -2.0 + (x / y);
	tmp = 0.0;
	if (t_2 <= -4e+86)
		tmp = t_1;
	elseif (t_2 <= 500000.0)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = t_1 - 2.0;
	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[(2.0 - N[(N[(t - 1.0), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+86], t$95$1, If[LessEqual[t$95$2, 500000.0], t$95$3, If[LessEqual[t$95$2, Infinity], N[(t$95$1 - 2.0), $MachinePrecision], 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)) < -4.0000000000000001e86

   1. Initial program 98.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 88.9

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

   5. Applied rewrites 88.9%

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

   if -4.0000000000000001e86 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5e5 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 71.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 95.4%

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

   if 5e5 < (/.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 97.2%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 80.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq -4 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq 500000:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z}\\ t_3 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 500000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t))
        (t_2 (/ (- 2.0 (* (- t 1.0) (* z 2.0))) (* t z)))
        (t_3 (+ -2.0 (/ x y))))
   (if (<= t_2 -4e+86)
     t_1
     (if (<= t_2 500000.0) 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 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -4e+86) {
		tmp = t_1;
	} else if (t_2 <= 500000.0) {
		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 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -4e+86) {
		tmp = t_1;
	} else if (t_2 <= 500000.0) {
		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 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z)
	t_3 = -2.0 + (x / y)
	tmp = 0
	if t_2 <= -4e+86:
		tmp = t_1
	elif t_2 <= 500000.0:
		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(2.0 - Float64(Float64(t - 1.0) * Float64(z * 2.0))) / Float64(t * z))
	t_3 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_2 <= -4e+86)
		tmp = t_1;
	elseif (t_2 <= 500000.0)
		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 = (2.0 - ((t - 1.0) * (z * 2.0))) / (t * z);
	t_3 = -2.0 + (x / y);
	tmp = 0.0;
	if (t_2 <= -4e+86)
		tmp = t_1;
	elseif (t_2 <= 500000.0)
		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[(2.0 - N[(N[(t - 1.0), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+86], t$95$1, If[LessEqual[t$95$2, 500000.0], 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)) < -4.0000000000000001e86 or 5e5 < (/.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 97.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 84.2

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

   5. Applied rewrites 84.2%

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

   if -4.0000000000000001e86 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5e5 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 71.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 95.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq -4 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq 500000:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{2 - \left(t - 1\right) \cdot \left(z \cdot 2\right)}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -50:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0005:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ (fma 2.0 z 2.0) (* t z)) (/ x y))))
   (if (<= (/ x y) -50.0)
     t_1
     (if (<= (/ x y) 0.0005) (- (/ (- (/ 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(2.0, z, 2.0) / (t * z)) + (x / y);
	double tmp;
	if ((x / y) <= -50.0) {
		tmp = t_1;
	} else if ((x / y) <= 0.0005) {
		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(2.0, z, 2.0) / Float64(t * z)) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -50.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.0005)
		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[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -50.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.0005], 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) < -50 or 5.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 85.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 96.3

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

   5. Applied rewrites 96.3%

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

   if -50 < (/.f64 x y) < 5.0000000000000001e-4

   1. Initial program 85.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 98.7%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0005:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -50:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+24}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 (* t z)) (/ x y))))
   (if (<= (/ x y) -50.0)
     t_1
     (if (<= (/ x y) 1e+24) (- (/ (- (/ 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 * z)) + (x / y);
	double tmp;
	if ((x / y) <= -50.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e+24) {
		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 * z)) + (x / y)
    if ((x / y) <= (-50.0d0)) then
        tmp = t_1
    else if ((x / y) <= 1d+24) 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 * z)) + (x / y);
	double tmp;
	if ((x / y) <= -50.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e+24) {
		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 * z)) + (x / y)
	tmp = 0
	if (x / y) <= -50.0:
		tmp = t_1
	elif (x / y) <= 1e+24:
		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 / Float64(t * z)) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -50.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e+24)
		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 * z)) + (x / y);
	tmp = 0.0;
	if ((x / y) <= -50.0)
		tmp = t_1;
	elseif ((x / y) <= 1e+24)
		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 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -50.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e+24], 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) < -50 or 9.9999999999999998e23 < (/.f64 x y)

   1. Initial program 84.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 87.5%

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

   if -50 < (/.f64 x y) < 9.9999999999999998e23

   1. Initial program 85.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 98.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+24}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -4000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+24}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- -2.0 (/ -2.0 t)) (/ x y))))
   (if (<= (/ x y) -4000000.0)
     t_1
     (if (<= (/ x y) 1e+24) (- (/ (- (/ 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 - (-2.0 / t)) + (x / y);
	double tmp;
	if ((x / y) <= -4000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e+24) {
		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) - ((-2.0d0) / t)) + (x / y)
    if ((x / y) <= (-4000000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 1d+24) 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 - (-2.0 / t)) + (x / y);
	double tmp;
	if ((x / y) <= -4000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e+24) {
		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 - (-2.0 / t)) + (x / y)
	tmp = 0
	if (x / y) <= -4000000.0:
		tmp = t_1
	elif (x / y) <= 1e+24:
		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 - Float64(-2.0 / t)) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -4000000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e+24)
		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 - (-2.0 / t)) + (x / y);
	tmp = 0.0;
	if ((x / y) <= -4000000.0)
		tmp = t_1;
	elseif ((x / y) <= 1e+24)
		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 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -4000000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e+24], 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) < -4e6 or 9.9999999999999998e23 < (/.f64 x y)

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 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. +-commutative N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-neg-in N/A

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

      10. metadata-eval N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. associate-*r/ N/A

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

      15. metadata-eval N/A

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

      16. lower-/.f64 80.9

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

   5. Applied rewrites 80.9%

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

   if -4e6 < (/.f64 x y) < 9.9999999999999998e23

   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

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 98.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4000000:\\ \;\;\;\;\left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+24}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -230:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.65 \cdot 10^{+24}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -230.0)
   (+ -2.0 (/ x y))
   (if (<= (/ x y) 1.65e+24) (- (/ 2.0 t) 2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -230.0) {
		tmp = -2.0 + (x / y);
	} else if ((x / y) <= 1.65e+24) {
		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) <= (-230.0d0)) then
        tmp = (-2.0d0) + (x / y)
    else if ((x / y) <= 1.65d+24) 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) <= -230.0) {
		tmp = -2.0 + (x / y);
	} else if ((x / y) <= 1.65e+24) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -230.0:
		tmp = -2.0 + (x / y)
	elif (x / y) <= 1.65e+24:
		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) <= -230.0)
		tmp = Float64(-2.0 + Float64(x / y));
	elseif (Float64(x / y) <= 1.65e+24)
		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) <= -230.0)
		tmp = -2.0 + (x / y);
	elseif ((x / y) <= 1.65e+24)
		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], -230.0], N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.65e+24], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -230

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 64.5%

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

   if -230 < (/.f64 x y) < 1.6499999999999999e24

   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

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 98.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 64.1%

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

   if 1.6499999999999999e24 < (/.f64 x y)

   1. Initial program 84.2%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 24.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 20.7%

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

   9. Taylor expanded in x around inf

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

       1. lower-/.f64 79.4

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

   11. Applied rewrites 79.4%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -230:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.65 \cdot 10^{+24}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -19000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.65 \cdot 10^{+24}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -19000.0)
   (/ x y)
   (if (<= (/ x y) 1.65e+24) (- (/ 2.0 t) 2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -19000.0) {
		tmp = x / y;
	} else if ((x / y) <= 1.65e+24) {
		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) <= (-19000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 1.65d+24) 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) <= -19000.0) {
		tmp = x / y;
	} else if ((x / y) <= 1.65e+24) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -19000.0:
		tmp = x / y
	elif (x / y) <= 1.65e+24:
		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) <= -19000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.65e+24)
		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) <= -19000.0)
		tmp = x / y;
	elseif ((x / y) <= 1.65e+24)
		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], -19000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.65e+24], 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) < -19000 or 1.6499999999999999e24 < (/.f64 x y)

   1. Initial program 84.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 31.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 23.2%

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

   9. Taylor expanded in x around inf

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

       1. lower-/.f64 70.6

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

   11. Applied rewrites 70.6%

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

   if -19000 < (/.f64 x y) < 1.6499999999999999e24

   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

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 98.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 64.1%

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

Alternative 11: 52.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -85:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2700000:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -85.0) (/ x y) (if (<= (/ x y) 2700000.0) -2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -85.0) {
		tmp = x / y;
	} else if ((x / y) <= 2700000.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-85.0d0)) then
        tmp = x / y
    else if ((x / y) <= 2700000.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -85.0) {
		tmp = x / y;
	} else if ((x / y) <= 2700000.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -85.0:
		tmp = x / y
	elif (x / y) <= 2700000.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -85.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2700000.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -85.0)
		tmp = x / y;
	elseif ((x / y) <= 2700000.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -85.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2700000.0], -2.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -85 or 2.7e6 < (/.f64 x y)

   1. Initial program 85.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 34.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 24.3%

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

   9. Taylor expanded in x around inf

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

       1. lower-/.f64 67.9

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

   11. Applied rewrites 67.9%

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

   if -85 < (/.f64 x y) < 2.7e6

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   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. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. metadata-eval N/A

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

      13. sub-neg 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 98.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 38.7%

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

Alternative 12: 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 85.4%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
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. +-commutative N/A

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

   8. associate-+r+ N/A

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

   9. associate-*r/ N/A

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

   10. metadata-eval N/A

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

   11. +-commutative N/A

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

   12. metadata-eval N/A

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

   13. sub-neg 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 67.1%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 21.2%

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

Developer Target 1: 99.2% 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 2024298 
(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))))