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

Percentage Accurate: 85.7% → 99.5%

Time: 11.6s

Alternatives: 14

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. associate-*r/ N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. metadata-eval N/A

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

   7. associate-*r/ N/A

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

   8. associate-/r* N/A

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

   9. associate-*r/ N/A

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

   10. metadata-eval N/A

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

   11. associate-*r* N/A

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

   12. associate-*l/ N/A

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

   13. distribute-rgt-out N/A

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

   14. lower-fma.f64 N/A

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

5. Applied rewrites 99.8%

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

Alternative 2: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+119}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_1 \leq 1.2 \cdot 10^{+112} \lor \neg \left(t\_1 \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_1 (- INFINITY))
     (/ 2.0 (* t z))
     (if (<= t_1 -5e+119)
       (- (/ 2.0 t) 2.0)
       (if (or (<= t_1 1.2e+112) (not (<= t_1 INFINITY)))
         (+ (/ x y) -2.0)
         (/ (/ 2.0 z) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = 2.0 / (t * z);
	} else if (t_1 <= -5e+119) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_1 <= 1.2e+112) || !(t_1 <= ((double) INFINITY))) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / z) / t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 / (t * z);
	} else if (t_1 <= -5e+119) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_1 <= 1.2e+112) || !(t_1 <= Double.POSITIVE_INFINITY)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = 2.0 / (t * z)
	elif t_1 <= -5e+119:
		tmp = (2.0 / t) - 2.0
	elif (t_1 <= 1.2e+112) or not (t_1 <= math.inf):
		tmp = (x / y) + -2.0
	else:
		tmp = (2.0 / z) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t_1 <= -5e+119)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif ((t_1 <= 1.2e+112) || !(t_1 <= Inf))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(2.0 / z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = 2.0 / (t * z);
	elseif (t_1 <= -5e+119)
		tmp = (2.0 / t) - 2.0;
	elseif ((t_1 <= 1.2e+112) || ~((t_1 <= Inf)))
		tmp = (x / y) + -2.0;
	else
		tmp = (2.0 / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+119], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[Or[LessEqual[t$95$1, 1.2e+112], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]]]]]

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)) < -inf.0

   1. Initial program 94.4%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 94.4

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

   8. Applied rewrites 94.4%

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

   if -inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -4.9999999999999999e119

   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 z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 66.5

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 46.8%

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

   if -4.9999999999999999e119 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.2e112 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 75.1%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 78.5%

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

   if 1.2e112 < (/.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 99.6%

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

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

      3. *-inverses N/A

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

      4. associate-/l* N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. div-add N/A

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

      8. +-commutative N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. div-sub N/A

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

      12. metadata-eval N/A

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

      13. associate-*r/ N/A

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

      14. associate-*l/ N/A

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

      15. metadata-eval N/A

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

      16. associate-*r/ N/A

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

      17. associate-*l* N/A

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

      18. lft-mult-inverse N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 N/A

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

      21. associate-*r/ N/A

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

      22. metadata-eval N/A

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

      23. lower-/.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 63.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -\infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -5 \cdot 10^{+119}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 1.2 \cdot 10^{+112} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+119}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_2 \leq 1.2 \cdot 10^{+112} \lor \neg \left(t\_2 \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+119)
       (- (/ 2.0 t) 2.0)
       (if (or (<= t_2 1.2e+112) (not (<= t_2 INFINITY)))
         (+ (/ x y) -2.0)
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+119) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_2 <= 1.2e+112) || !(t_2 <= ((double) INFINITY))) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = t_1;
	}
	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 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e+119) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_2 <= 1.2e+112) || !(t_2 <= Double.POSITIVE_INFINITY)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e+119:
		tmp = (2.0 / t) - 2.0
	elif (t_2 <= 1.2e+112) or not (t_2 <= math.inf):
		tmp = (x / y) + -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+119)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif ((t_2 <= 1.2e+112) || !(t_2 <= Inf))
		tmp = Float64(Float64(x / y) + -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);
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e+119)
		tmp = (2.0 / t) - 2.0;
	elseif ((t_2 <= 1.2e+112) || ~((t_2 <= Inf)))
		tmp = (x / y) + -2.0;
	else
		tmp = t_1;
	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 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+119], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[Or[LessEqual[t$95$2, 1.2e+112], N[Not[LessEqual[t$95$2, Infinity]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]]]

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)) < -inf.0 or 1.2e112 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 70.2

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

   8. Applied rewrites 70.2%

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

   if -inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -4.9999999999999999e119

   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 z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 66.5

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 46.8%

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

   if -4.9999999999999999e119 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.2e112 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 75.1%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 78.5%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -\infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -5 \cdot 10^{+119}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 1.2 \cdot 10^{+112} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+33} \lor \neg \left(t\_1 \leq -1 \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (or (<= t_1 -5e+33) (not (or (<= t_1 -1.0) (not (<= t_1 INFINITY)))))
     (/ (- (/ 2.0 z) -2.0) t)
     (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -5e+33) || !((t_1 <= -1.0) || !(t_1 <= ((double) INFINITY)))) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -5e+33) || !((t_1 <= -1.0) || !(t_1 <= Double.POSITIVE_INFINITY))) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if (t_1 <= -5e+33) or not ((t_1 <= -1.0) or not (t_1 <= math.inf)):
		tmp = ((2.0 / z) - -2.0) / t
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if ((t_1 <= -5e+33) || !((t_1 <= -1.0) || !(t_1 <= Inf)))
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if ((t_1 <= -5e+33) || ~(((t_1 <= -1.0) || ~((t_1 <= Inf)))))
		tmp = ((2.0 / z) - -2.0) / t;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+33], N[Not[Or[LessEqual[t$95$1, -1.0], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]]], $MachinePrecision]], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

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)) < -4.99999999999999973e33 or -1 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. metadata-eval N/A

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

      3. *-inverses N/A

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

      4. associate-/l* N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. div-add N/A

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

      8. +-commutative N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. div-sub N/A

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

      12. metadata-eval N/A

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

      13. associate-*r/ N/A

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

      14. associate-*l/ N/A

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

      15. metadata-eval N/A

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

      16. associate-*r/ N/A

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

      17. associate-*l* N/A

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

      18. lft-mult-inverse N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 N/A

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

      21. associate-*r/ N/A

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

      22. metadata-eval N/A

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

      23. lower-/.f64 77.9

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

   5. Applied rewrites 77.9%

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

   if -4.99999999999999973e33 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1 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 64.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 93.2%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -5 \cdot 10^{+33} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -1 \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-out N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 99.8

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

   5. Applied rewrites 99.8%

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

   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. Add Preprocessing

Alternative 6: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500000000000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -500000000000.0) (not (<= (/ x y) 4e-5)))
   (+ (/ x y) (/ (- (/ 2.0 z) -2.0) t))
   (- -2.0 (/ (- (/ -2.0 z) 2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -500000000000.0) || !((x / y) <= 4e-5)) {
		tmp = (x / y) + (((2.0 / z) - -2.0) / t);
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-500000000000.0d0)) .or. (.not. ((x / y) <= 4d-5))) then
        tmp = (x / y) + (((2.0d0 / z) - (-2.0d0)) / t)
    else
        tmp = (-2.0d0) - ((((-2.0d0) / z) - 2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -500000000000.0) || !((x / y) <= 4e-5)) {
		tmp = (x / y) + (((2.0 / z) - -2.0) / t);
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -500000000000.0) or not ((x / y) <= 4e-5):
		tmp = (x / y) + (((2.0 / z) - -2.0) / t)
	else:
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -500000000000.0) || !(Float64(x / y) <= 4e-5))
		tmp = Float64(Float64(x / y) + Float64(Float64(Float64(2.0 / z) - -2.0) / t));
	else
		tmp = Float64(-2.0 - Float64(Float64(Float64(-2.0 / z) - 2.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -500000000000.0) || ~(((x / y) <= 4e-5)))
		tmp = (x / y) + (((2.0 / z) - -2.0) / t);
	else
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -500000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e-5]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 - N[(N[(N[(-2.0 / z), $MachinePrecision] - 2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e11 or 4.00000000000000033e-5 < (/.f64 x y)

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

      5. div-add N/A

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

      6. *-inverses N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. distribute-lft1-in N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

      12. lower-/.f64 N/A

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

   5. Applied rewrites 98.9%

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

   if -5e11 < (/.f64 x y) < 4.00000000000000033e-5

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 98.3%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500000000000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{\frac{2}{z}}{t} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -500000000000.0) (not (<= (/ x y) 5e+35)))
   (+ (/ (/ 2.0 z) t) (/ x y))
   (- -2.0 (/ (- (/ -2.0 z) 2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -500000000000.0) || !((x / y) <= 5e+35)) {
		tmp = ((2.0 / z) / t) + (x / y);
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-500000000000.0d0)) .or. (.not. ((x / y) <= 5d+35))) then
        tmp = ((2.0d0 / z) / t) + (x / y)
    else
        tmp = (-2.0d0) - ((((-2.0d0) / z) - 2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -500000000000.0) || !((x / y) <= 5e+35)) {
		tmp = ((2.0 / z) / t) + (x / y);
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -500000000000.0) or not ((x / y) <= 5e+35):
		tmp = ((2.0 / z) / t) + (x / y)
	else:
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -500000000000.0) || !(Float64(x / y) <= 5e+35))
		tmp = Float64(Float64(Float64(2.0 / z) / t) + Float64(x / y));
	else
		tmp = Float64(-2.0 - Float64(Float64(Float64(-2.0 / z) - 2.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -500000000000.0) || ~(((x / y) <= 5e+35)))
		tmp = ((2.0 / z) / t) + (x / y);
	else
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -500000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+35]], $MachinePrecision]], N[(N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 - N[(N[(N[(-2.0 / z), $MachinePrecision] - 2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e11 or 5.00000000000000021e35 < (/.f64 x y)

   1. Initial program 88.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 94.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 94.4

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 94.5

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

   7. Applied rewrites 94.5%

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

   if -5e11 < (/.f64 x y) < 5.00000000000000021e35

   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

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 97.7%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{\frac{2}{z}}{t} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -265000000000 \lor \neg \left(\frac{x}{y} \leq 2.8 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -265000000000.0) (not (<= (/ x y) 2.8e+35)))
   (+ (/ x y) (/ 2.0 (* t z)))
   (- -2.0 (/ (- (/ -2.0 z) 2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -265000000000.0) || !((x / y) <= 2.8e+35)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-265000000000.0d0)) .or. (.not. ((x / y) <= 2.8d+35))) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = (-2.0d0) - ((((-2.0d0) / z) - 2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -265000000000.0) || !((x / y) <= 2.8e+35)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -265000000000.0) or not ((x / y) <= 2.8e+35):
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -265000000000.0) || !(Float64(x / y) <= 2.8e+35))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(-2.0 - Float64(Float64(Float64(-2.0 / z) - 2.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -265000000000.0) || ~(((x / y) <= 2.8e+35)))
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -265000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2.8e+35]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 - N[(N[(N[(-2.0 / z), $MachinePrecision] - 2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.65e11 or 2.79999999999999999e35 < (/.f64 x y)

   1. Initial program 88.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 94.4%

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

   if -2.65e11 < (/.f64 x y) < 2.79999999999999999e35

   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

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 97.7%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -265000000000 \lor \neg \left(\frac{x}{y} \leq 2.8 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.8 \cdot 10^{+75} \lor \neg \left(\frac{x}{y} \leq 1.3 \cdot 10^{+44}\right):\\ \;\;\;\;\left(\frac{x}{y} - 2\right) - \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.8e+75) (not (<= (/ x y) 1.3e+44)))
   (- (- (/ x y) 2.0) (/ -2.0 t))
   (- -2.0 (/ (- (/ -2.0 z) 2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.8e+75) || !((x / y) <= 1.3e+44)) {
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2.8d+75)) .or. (.not. ((x / y) <= 1.3d+44))) then
        tmp = ((x / y) - 2.0d0) - ((-2.0d0) / t)
    else
        tmp = (-2.0d0) - ((((-2.0d0) / z) - 2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.8e+75) || !((x / y) <= 1.3e+44)) {
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.8e+75) or not ((x / y) <= 1.3e+44):
		tmp = ((x / y) - 2.0) - (-2.0 / t)
	else:
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.8e+75) || !(Float64(x / y) <= 1.3e+44))
		tmp = Float64(Float64(Float64(x / y) - 2.0) - Float64(-2.0 / t));
	else
		tmp = Float64(-2.0 - Float64(Float64(Float64(-2.0 / z) - 2.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.8e+75) || ~(((x / y) <= 1.3e+44)))
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	else
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.8e+75], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.3e+44]], $MachinePrecision]], N[(N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 - N[(N[(N[(-2.0 / z), $MachinePrecision] - 2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.80000000000000012e75 or 1.3e44 < (/.f64 x y)

   1. Initial program 88.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 84.7

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

   5. Applied rewrites 84.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 84.7%

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

   if -2.80000000000000012e75 < (/.f64 x y) < 1.3e44

   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

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 95.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.8 \cdot 10^{+75} \lor \neg \left(\frac{x}{y} \leq 1.3 \cdot 10^{+44}\right):\\ \;\;\;\;\left(\frac{x}{y} - 2\right) - \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+75} \lor \neg \left(\frac{x}{y} \leq 1.3 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+75) (not (<= (/ x y) 1.3e+44)))
   (/ x y)
   (- -2.0 (/ (/ -2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+75) || !((x / y) <= 1.3e+44)) {
		tmp = x / y;
	} else {
		tmp = -2.0 - ((-2.0 / z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d+75)) .or. (.not. ((x / y) <= 1.3d+44))) then
        tmp = x / y
    else
        tmp = (-2.0d0) - (((-2.0d0) / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+75) || !((x / y) <= 1.3e+44)) {
		tmp = x / y;
	} else {
		tmp = -2.0 - ((-2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+75) or not ((x / y) <= 1.3e+44):
		tmp = x / y
	else:
		tmp = -2.0 - ((-2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+75) || !(Float64(x / y) <= 1.3e+44))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 - Float64(Float64(-2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+75) || ~(((x / y) <= 1.3e+44)))
		tmp = x / y;
	else
		tmp = -2.0 - ((-2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+75], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.3e+44]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 - N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999985e75 or 1.3e44 < (/.f64 x y)

   1. Initial program 88.1%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. frac-add N/A

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

      9. lower-/.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. lower-*.f64 66.0

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

   4. Applied rewrites 66.0%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 82.0

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

   7. Applied rewrites 82.0%

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

   if -1.99999999999999985e75 < (/.f64 x y) < 1.3e44

   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

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 95.1%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 68.0%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+75} \lor \neg \left(\frac{x}{y} \leq 1.3 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -265000000000 \lor \neg \left(\frac{x}{y} \leq 1.1 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -265000000000.0) (not (<= (/ x y) 1.1e+41)))
   (/ x y)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -265000000000.0) || !((x / y) <= 1.1e+41)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-265000000000.0d0)) .or. (.not. ((x / y) <= 1.1d+41))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -265000000000.0) || !((x / y) <= 1.1e+41)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -265000000000.0) or not ((x / y) <= 1.1e+41):
		tmp = x / y
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -265000000000.0) || !(Float64(x / y) <= 1.1e+41))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -265000000000.0) || ~(((x / y) <= 1.1e+41)))
		tmp = x / y;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -265000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.1e+41]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.65e11 or 1.09999999999999995e41 < (/.f64 x y)

   1. Initial program 88.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. frac-add N/A

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

      9. lower-/.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. lower-*.f64 67.1

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

   4. Applied rewrites 67.1%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 74.3

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

   7. Applied rewrites 74.3%

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

   if -2.65e11 < (/.f64 x y) < 1.09999999999999995e41

   1. Initial program 85.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 56.3

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 54.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -265000000000 \lor \neg \left(\frac{x}{y} \leq 1.1 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -210000000000:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -210000000000.0)
   (+ (/ x y) -2.0)
   (if (<= (/ x y) 1.1e+41) (- (/ 2.0 t) 2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -210000000000.0) {
		tmp = (x / y) + -2.0;
	} else if ((x / y) <= 1.1e+41) {
		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) <= (-210000000000.0d0)) then
        tmp = (x / y) + (-2.0d0)
    else if ((x / y) <= 1.1d+41) 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) <= -210000000000.0) {
		tmp = (x / y) + -2.0;
	} else if ((x / y) <= 1.1e+41) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -210000000000.0:
		tmp = (x / y) + -2.0
	elif (x / y) <= 1.1e+41:
		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) <= -210000000000.0)
		tmp = Float64(Float64(x / y) + -2.0);
	elseif (Float64(x / y) <= 1.1e+41)
		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) <= -210000000000.0)
		tmp = (x / y) + -2.0;
	elseif ((x / y) <= 1.1e+41)
		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], -210000000000.0], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.1e+41], 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) < -2.1e11

   1. Initial program 91.9%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 63.2%

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

   if -2.1e11 < (/.f64 x y) < 1.09999999999999995e41

   1. Initial program 85.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 56.3

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 54.1%

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

   if 1.09999999999999995e41 < (/.f64 x y)

   1. Initial program 85.9%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. frac-add N/A

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

      9. lower-/.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*r* N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. lower-*.f64 65.3

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

   4. Applied rewrites 65.3%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 84.3

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

   7. Applied rewrites 84.3%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -210000000000:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 85.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-14} \lor \neg \left(z \leq 0.00125\right):\\ \;\;\;\;\left(\frac{x}{y} - 2\right) - \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.2e-14) (not (<= z 0.00125)))
   (- (- (/ x y) 2.0) (/ -2.0 t))
   (- -2.0 (/ (/ -2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e-14) || !(z <= 0.00125)) {
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	} else {
		tmp = -2.0 - ((-2.0 / z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9.2d-14)) .or. (.not. (z <= 0.00125d0))) then
        tmp = ((x / y) - 2.0d0) - ((-2.0d0) / t)
    else
        tmp = (-2.0d0) - (((-2.0d0) / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e-14) || !(z <= 0.00125)) {
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	} else {
		tmp = -2.0 - ((-2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.2e-14) or not (z <= 0.00125):
		tmp = ((x / y) - 2.0) - (-2.0 / t)
	else:
		tmp = -2.0 - ((-2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.2e-14) || !(z <= 0.00125))
		tmp = Float64(Float64(Float64(x / y) - 2.0) - Float64(-2.0 / t));
	else
		tmp = Float64(-2.0 - Float64(Float64(-2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.2e-14) || ~((z <= 0.00125)))
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	else
		tmp = -2.0 - ((-2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.2e-14], N[Not[LessEqual[z, 0.00125]], $MachinePrecision]], N[(N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 - N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999993e-14 or 0.00125000000000000003 < z

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 98.4

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

   5. Applied rewrites 98.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 98.4%

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

   if -9.19999999999999993e-14 < z < 0.00125000000000000003

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 76.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 75.4%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-14} \lor \neg \left(z \leq 0.00125\right):\\ \;\;\;\;\left(\frac{x}{y} - 2\right) - \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.6% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t) {
	return 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 = x / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]

Derivation

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. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. +-commutative N/A

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

   4. div-add N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. associate-/r* N/A

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

   8. frac-add N/A

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

   9. lower-/.f64 N/A

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

   10. lower-fma.f64 N/A

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

   11. lower-/.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. *-commutative N/A

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

   14. lift-*.f64 N/A

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

   15. associate-*r* N/A

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

   16. lower-*.f64 N/A

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

   17. lower-*.f64 N/A

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

   18. lower-*.f64 N/A

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

   19. lower-*.f64 69.5

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

4. Applied rewrites 69.5%

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

5. Taylor expanded in x around inf

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

   1. lower-/.f64 33.2

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

7. Applied rewrites 33.2%

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

8. Final simplification 33.2%

   \[\leadsto \frac{x}{y} \]
9. Add Preprocessing

Developer Target 1: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024339 
(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))))