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

Percentage Accurate: 86.8% → 98.2%

Time: 12.5s

Alternatives: 15

Speedup: 0.8×

• 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: 86.8% 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: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right), x\right)}{y}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y} + -2, 2 + \frac{2}{z}\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (fma y (fma (/ 2.0 (* z t)) (+ z 1.0) -2.0) x) y)))
   (if (<= t -2.6e+46)
     t_1
     (if (<= t 1.5e+102)
       (/ (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 = fma(y, fma((2.0 / (z * t)), (z + 1.0), -2.0), x) / y;
	double tmp;
	if (t <= -2.6e+46) {
		tmp = t_1;
	} else if (t <= 1.5e+102) {
		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(fma(y, fma(Float64(2.0 / Float64(z * t)), Float64(z + 1.0), -2.0), x) / y)
	tmp = 0.0
	if (t <= -2.6e+46)
		tmp = t_1;
	elseif (t <= 1.5e+102)
		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[(y * N[(N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(z + 1.0), $MachinePrecision] + -2.0), $MachinePrecision] + x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -2.6e+46], t$95$1, If[LessEqual[t, 1.5e+102], 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 t < -2.60000000000000013e46 or 1.4999999999999999e102 < t

   1. Initial program 68.2%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 99.1%

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

   if -2.60000000000000013e46 < t < 1.4999999999999999e102

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

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

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

      14. lower-+.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. lower-/.f64 99.8

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

   5. Applied rewrites 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right), x\right)}{y}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y} + -2, 2 + \frac{2}{z}\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right), x\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ t_2 := \frac{x}{y} + -2\\ t_3 := \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+205}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t)))
        (t_2 (+ (/ x y) -2.0))
        (t_3 (/ (+ 2.0 (* (* 2.0 z) (- 1.0 t))) (* z t))))
   (if (<= t_3 -2e+126)
     t_1
     (if (<= t_3 2e+130)
       t_2
       (if (<= t_3 2e+205) (/ 2.0 t) (if (<= t_3 INFINITY) t_1 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) + -2.0;
	double t_3 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double tmp;
	if (t_3 <= -2e+126) {
		tmp = t_1;
	} else if (t_3 <= 2e+130) {
		tmp = t_2;
	} else if (t_3 <= 2e+205) {
		tmp = 2.0 / t;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (x / y) + -2.0;
	double t_3 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double tmp;
	if (t_3 <= -2e+126) {
		tmp = t_1;
	} else if (t_3 <= 2e+130) {
		tmp = t_2;
	} else if (t_3 <= 2e+205) {
		tmp = 2.0 / t;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (z * t)
	t_2 = (x / y) + -2.0
	t_3 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t)
	tmp = 0
	if t_3 <= -2e+126:
		tmp = t_1
	elif t_3 <= 2e+130:
		tmp = t_2
	elif t_3 <= 2e+205:
		tmp = 2.0 / t
	elif t_3 <= math.inf:
		tmp = t_1
	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) + -2.0)
	t_3 = Float64(Float64(2.0 + Float64(Float64(2.0 * z) * Float64(1.0 - t))) / Float64(z * t))
	tmp = 0.0
	if (t_3 <= -2e+126)
		tmp = t_1;
	elseif (t_3 <= 2e+130)
		tmp = t_2;
	elseif (t_3 <= 2e+205)
		tmp = Float64(2.0 / t);
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (z * t);
	t_2 = (x / y) + -2.0;
	t_3 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	tmp = 0.0;
	if (t_3 <= -2e+126)
		tmp = t_1;
	elseif (t_3 <= 2e+130)
		tmp = t_2;
	elseif (t_3 <= 2e+205)
		tmp = 2.0 / t;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	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[(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]}, If[LessEqual[t$95$3, -2e+126], t$95$1, If[LessEqual[t$95$3, 2e+130], t$95$2, If[LessEqual[t$95$3, 2e+205], N[(2.0 / t), $MachinePrecision], 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)) < -1.99999999999999985e126 or 2.00000000000000003e205 < (/.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. lower-/.f64 N/A

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

      2. lower-*.f64 68.2

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

   5. Applied rewrites 68.2%

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

   if -1.99999999999999985e126 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2.0000000000000001e130 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 78.3%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 79.1%

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

   if 2.0000000000000001e130 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2.00000000000000003e205

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0

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

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

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

      14. lower-+.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. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 81.5%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 50.2%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -2 \cdot 10^{+126}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 2 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 2 \cdot 10^{+205}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq \infty:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ t_2 := \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+63}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 -5e+44)
     t_1
     (if (<= t_2 1e+63) 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 <= -5e+44) {
		tmp = t_1;
	} else if (t_2 <= 1e+63) {
		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 <= -5e+44)
		tmp = t_1;
	elseif (t_2 <= 1e+63)
		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, -5e+44], t$95$1, If[LessEqual[t$95$2, 1e+63], 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)) < -4.9999999999999996e44 or 1.00000000000000006e63 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 79.4%

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

   if -4.9999999999999996e44 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.00000000000000006e63 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 72.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 90.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -5 \cdot 10^{+44}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 10^{+63}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.5% 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 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 100.0%

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

4. Final simplification 99.5%

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

Alternative 5: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ t_2 := \frac{\mathsf{fma}\left(y, t\_1, x\right)}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 200000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ 2.0 (* z t)) (+ z 1.0) -2.0)) (t_2 (/ (fma y t_1 x) y)))
   (if (<= (/ x y) -5e+28) t_2 (if (<= (/ x y) 200000000000.0) t_1 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((2.0 / (z * t)), (z + 1.0), -2.0);
	double t_2 = fma(y, t_1, x) / y;
	double tmp;
	if ((x / y) <= -5e+28) {
		tmp = t_2;
	} else if ((x / y) <= 200000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(2.0 / Float64(z * t)), Float64(z + 1.0), -2.0)
	t_2 = Float64(fma(y, t_1, x) / y)
	tmp = 0.0
	if (Float64(x / y) <= -5e+28)
		tmp = t_2;
	elseif (Float64(x / y) <= 200000000000.0)
		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 / N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(z + 1.0), $MachinePrecision] + -2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * t$95$1 + x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+28], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 200000000000.0], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.99999999999999957e28 or 2e11 < (/.f64 x y)

   1. Initial program 86.6%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 98.9%

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

   if -4.99999999999999957e28 < (/.f64 x y) < 2e11

   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

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

   5. Applied rewrites 97.7%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right), x\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 200000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right), x\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -2.9 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.45 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4050000000000:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t))))
   (if (<= (/ x y) -2.9e+27)
     (/ x y)
     (if (<= (/ x y) -1.45e-18)
       t_1
       (if (<= (/ x y) 4050000000000.0) (fma t_1 z -2.0) (+ (/ x y) -2.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double tmp;
	if ((x / y) <= -2.9e+27) {
		tmp = x / y;
	} else if ((x / y) <= -1.45e-18) {
		tmp = t_1;
	} else if ((x / y) <= 4050000000000.0) {
		tmp = fma(t_1, z, -2.0);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(z * t))
	tmp = 0.0
	if (Float64(x / y) <= -2.9e+27)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -1.45e-18)
		tmp = t_1;
	elseif (Float64(x / y) <= 4050000000000.0)
		tmp = fma(t_1, z, -2.0);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2.9e+27], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1.45e-18], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4050000000000.0], N[(t$95$1 * z + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2.9000000000000001e27

   1. Initial program 80.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 85.1

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

   5. Applied rewrites 85.1%

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

   if -2.9000000000000001e27 < (/.f64 x y) < -1.45e-18

   1. Initial program 86.6%

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

   3. Taylor expanded in 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 59.2

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

   5. Applied rewrites 59.2%

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

   if -1.45e-18 < (/.f64 x y) < 4.05e12

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 61.8%

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

   10. Applied rewrites 66.6%

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

   if 4.05e12 < (/.f64 x y)

   1. Initial program 92.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 78.2%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.9 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.45 \cdot 10^{-18}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 4050000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ t_2 := \frac{x}{y} + t\_1\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t))) (t_2 (+ (/ x y) t_1)))
   (if (<= (/ x y) -5e+28)
     t_2
     (if (<= (/ x y) 4e+66) (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) <= -5e+28) {
		tmp = t_2;
	} else if ((x / y) <= 4e+66) {
		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) <= -5e+28)
		tmp = t_2;
	elseif (Float64(x / y) <= 4e+66)
		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], -5e+28], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 4e+66], 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) < -4.99999999999999957e28 or 3.99999999999999978e66 < (/.f64 x y)

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 95.2%

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

   if -4.99999999999999957e28 < (/.f64 x y) < 3.99999999999999978e66

   1. Initial program 86.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 97.1%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-322}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.15 \cdot 10^{+66}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0)
   (/ x y)
   (if (<= (/ x y) 2e-322) -2.0 (if (<= (/ x y) 2.15e+66) (/ 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) <= 2e-322) {
		tmp = -2.0;
	} else if ((x / y) <= 2.15e+66) {
		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) <= 2d-322) then
        tmp = -2.0d0
    else if ((x / y) <= 2.15d+66) 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) <= 2e-322) {
		tmp = -2.0;
	} else if ((x / y) <= 2.15e+66) {
		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) <= 2e-322:
		tmp = -2.0
	elif (x / y) <= 2.15e+66:
		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) <= 2e-322)
		tmp = -2.0;
	elseif (Float64(x / y) <= 2.15e+66)
		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) <= 2e-322)
		tmp = -2.0;
	elseif ((x / y) <= 2.15e+66)
		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], 2e-322], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 2.15e+66], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2 or 2.15000000000000013e66 < (/.f64 x y)

   1. Initial program 86.4%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 77.2

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

   5. Applied rewrites 77.2%

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

   if -2 < (/.f64 x y) < 1.97626e-322

   1. Initial program 82.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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. Applied rewrites 98.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 44.5%

      \[\leadsto -2 \]

   if 1.97626e-322 < (/.f64 x y) < 2.15000000000000013e66

   1. Initial program 92.2%

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

   3. Taylor expanded in t around 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. lower-/.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. lower-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. lower-+.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. lower-/.f64 N/A

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

      14. lower-+.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. lower-/.f64 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 82.5%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 36.4%

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

Alternative 9: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.9 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.8 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.9e+27)
   (+ (/ x y) (/ 2.0 t))
   (if (<= (/ x y) 1.8e+133) (fma (/ 2.0 (* z t)) (+ z 1.0) -2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.9e+27) {
		tmp = (x / y) + (2.0 / t);
	} else if ((x / y) <= 1.8e+133) {
		tmp = fma((2.0 / (z * t)), (z + 1.0), -2.0);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.9e+27)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (Float64(x / y) <= 1.8e+133)
		tmp = fma(Float64(2.0 / Float64(z * t)), Float64(z + 1.0), -2.0);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.9e+27], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.8e+133], N[(N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(z + 1.0), $MachinePrecision] + -2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.9000000000000001e27

   1. Initial program 80.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]
   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. lower-+.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 90.8

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

   5. Applied rewrites 90.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 90.8%

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

   if -2.9000000000000001e27 < (/.f64 x y) < 1.79999999999999989e133

   1. Initial program 86.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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. Applied rewrites 93.4%

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

   if 1.79999999999999989e133 < (/.f64 x y)

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.9 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.8 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.8 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4e+27)
   (/ x y)
   (if (<= (/ x y) 1.8e+133) (fma (/ 2.0 (* z t)) (+ z 1.0) -2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e+27) {
		tmp = x / y;
	} else if ((x / y) <= 1.8e+133) {
		tmp = fma((2.0 / (z * t)), (z + 1.0), -2.0);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4e+27)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.8e+133)
		tmp = fma(Float64(2.0 / Float64(z * t)), Float64(z + 1.0), -2.0);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4e+27], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.8e+133], N[(N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(z + 1.0), $MachinePrecision] + -2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.0000000000000001e27 or 1.79999999999999989e133 < (/.f64 x y)

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 90.9

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

   5. Applied rewrites 90.9%

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

   if -4.0000000000000001e27 < (/.f64 x y) < 1.79999999999999989e133

   1. Initial program 86.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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. Applied rewrites 93.4%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.8 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;\frac{x}{y} \leq -1.6 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4050000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= (/ x y) -1.6e-17)
     t_1
     (if (<= (/ x y) 4050000000000.0) (+ -2.0 (/ 2.0 t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if ((x / y) <= -1.6e-17) {
		tmp = t_1;
	} else if ((x / y) <= 4050000000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if ((x / y) <= (-1.6d-17)) then
        tmp = t_1
    else if ((x / y) <= 4050000000000.0d0) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if ((x / y) <= -1.6e-17) {
		tmp = t_1;
	} else if ((x / y) <= 4050000000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if (x / y) <= -1.6e-17:
		tmp = t_1
	elif (x / y) <= 4050000000000.0:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (Float64(x / y) <= -1.6e-17)
		tmp = t_1;
	elseif (Float64(x / y) <= 4050000000000.0)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if ((x / y) <= -1.6e-17)
		tmp = t_1;
	elseif ((x / y) <= 4050000000000.0)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1.6e-17], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4050000000000.0], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.6000000000000001e-17 or 4.05e12 < (/.f64 x y)

   1. Initial program 86.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 75.0%

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

   if -1.6000000000000001e-17 < (/.f64 x y) < 4.05e12

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 61.8%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.6 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq 4050000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4050000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5.2e+26)
   (/ x y)
   (if (<= (/ x y) 4050000000000.0) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5.2e+26) {
		tmp = x / y;
	} else if ((x / y) <= 4050000000000.0) {
		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) <= (-5.2d+26)) then
        tmp = x / y
    else if ((x / y) <= 4050000000000.0d0) 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) <= -5.2e+26) {
		tmp = x / y;
	} else if ((x / y) <= 4050000000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5.2e+26:
		tmp = x / y
	elif (x / y) <= 4050000000000.0:
		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) <= -5.2e+26)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4050000000000.0)
		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) <= -5.2e+26)
		tmp = x / y;
	elseif ((x / y) <= 4050000000000.0)
		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], -5.2e+26], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4050000000000.0], 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) < -5.20000000000000004e26 or 4.05e12 < (/.f64 x y)

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 81.6

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

   5. Applied rewrites 81.6%

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

   if -5.20000000000000004e26 < (/.f64 x y) < 4.05e12

   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

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 58.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4050000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 140000000:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0) (/ x y) (if (<= (/ x y) 140000000.0) -2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 140000000.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2.0d0)) then
        tmp = x / y
    else if ((x / y) <= 140000000.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 140000000.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.0:
		tmp = x / y
	elif (x / y) <= 140000000.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 140000000.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2.0)
		tmp = x / y;
	elseif ((x / y) <= 140000000.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 140000000.0], -2.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2 or 1.4e8 < (/.f64 x y)

   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 inf

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

      1. lower-/.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if -2 < (/.f64 x y) < 1.4e8

   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

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 35.6%

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

Alternative 14: 79.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -8 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 480000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= t -8e-49) t_1 (if (<= t 480000000.0) (/ (+ 2.0 (/ 2.0 z)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -8e-49) {
		tmp = t_1;
	} else if (t <= 480000000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (t <= (-8d-49)) then
        tmp = t_1
    else if (t <= 480000000.0d0) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -8e-49) {
		tmp = t_1;
	} else if (t <= 480000000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if t <= -8e-49:
		tmp = t_1
	elif t <= 480000000.0:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -8e-49)
		tmp = t_1;
	elseif (t <= 480000000.0)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -8e-49)
		tmp = t_1;
	elseif (t <= 480000000.0)
		tmp = (2.0 + (2.0 / z)) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -8e-49], t$95$1, If[LessEqual[t, 480000000.0], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.99999999999999949e-49 or 4.8e8 < t

   1. Initial program 77.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 82.5%

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

   if -7.99999999999999949e-49 < t < 4.8e8

   1. Initial program 98.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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. lower-/.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. lower-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. lower-+.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. lower-/.f64 N/A

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

      14. lower-+.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. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 84.3%

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

Alternative 15: 19.9% accurate, 47.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := -2.0

Derivation

1. Initial program 86.2%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 66.3%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 20.7%

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

Developer Target 1: 99.3% 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 2024221 
(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))))