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

Percentage Accurate: 86.5% → 98.9%

Time: 10.6s

Alternatives: 16

Speedup: 0.8×

• 23.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(-2.0 + N[(x / y), $MachinePrecision]), $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)) < +inf.0

   1. Initial program 99.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 100.0%

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

4. Final simplification 99.9%

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

Alternative 2: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ t_2 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+165}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t\_2 \leq 2000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+274}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y)))
        (t_2 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z))))
   (if (<= t_2 -2e+165)
     (/ 2.0 (* t z))
     (if (<= t_2 2000000000000.0)
       t_1
       (if (<= t_2 1e+274)
         (/ 2.0 t)
         (if (<= t_2 INFINITY) (/ (/ 2.0 z) t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double tmp;
	if (t_2 <= -2e+165) {
		tmp = 2.0 / (t * z);
	} else if (t_2 <= 2000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+274) {
		tmp = 2.0 / t;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double tmp;
	if (t_2 <= -2e+165) {
		tmp = 2.0 / (t * z);
	} else if (t_2 <= 2000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+274) {
		tmp = 2.0 / t;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z)
	tmp = 0
	if t_2 <= -2e+165:
		tmp = 2.0 / (t * z)
	elif t_2 <= 2000000000000.0:
		tmp = t_1
	elif t_2 <= 1e+274:
		tmp = 2.0 / t
	elif t_2 <= math.inf:
		tmp = (2.0 / z) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	t_2 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	tmp = 0.0
	if (t_2 <= -2e+165)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t_2 <= 2000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+274)
		tmp = Float64(2.0 / t);
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(2.0 / z) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	tmp = 0.0;
	if (t_2 <= -2e+165)
		tmp = 2.0 / (t * z);
	elseif (t_2 <= 2000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+274)
		tmp = 2.0 / t;
	elseif (t_2 <= Inf)
		tmp = (2.0 / z) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+165], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2000000000000.0], t$95$1, If[LessEqual[t$95$2, 1e+274], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.9999999999999998e165

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 73.2

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

   5. Applied rewrites 73.2%

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

   if -1.9999999999999998e165 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e12 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 88.0%

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

   if 2e12 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.99999999999999921e273

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 48.4%

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

   if 9.99999999999999921e273 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 86.5

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

   5. Applied rewrites 86.5%

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

   7. Applied rewrites 86.5%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -2 \cdot 10^{+165}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 2000000000000:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 10^{+274}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := -2 + \frac{x}{y}\\ t_3 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{+274}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1 - 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (+ -2.0 (/ x y)))
        (t_3 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z))))
   (if (<= t_3 -2e+165)
     t_1
     (if (<= t_3 2000000000000.0)
       t_2
       (if (<= t_3 1e+274)
         (/ 2.0 t)
         (if (<= t_3 INFINITY) (- t_1 2.0) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = -2.0 + (x / y);
	double t_3 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double tmp;
	if (t_3 <= -2e+165) {
		tmp = t_1;
	} else if (t_3 <= 2000000000000.0) {
		tmp = t_2;
	} else if (t_3 <= 1e+274) {
		tmp = 2.0 / t;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1 - 2.0;
	} else {
		tmp = t_2;
	}
	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 + (x / y);
	double t_3 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double tmp;
	if (t_3 <= -2e+165) {
		tmp = t_1;
	} else if (t_3 <= 2000000000000.0) {
		tmp = t_2;
	} else if (t_3 <= 1e+274) {
		tmp = 2.0 / t;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 - 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = -2.0 + (x / y)
	t_3 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z)
	tmp = 0
	if t_3 <= -2e+165:
		tmp = t_1
	elif t_3 <= 2000000000000.0:
		tmp = t_2
	elif t_3 <= 1e+274:
		tmp = 2.0 / t
	elif t_3 <= math.inf:
		tmp = t_1 - 2.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(-2.0 + Float64(x / y))
	t_3 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	tmp = 0.0
	if (t_3 <= -2e+165)
		tmp = t_1;
	elseif (t_3 <= 2000000000000.0)
		tmp = t_2;
	elseif (t_3 <= 1e+274)
		tmp = Float64(2.0 / t);
	elseif (t_3 <= Inf)
		tmp = Float64(t_1 - 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = -2.0 + (x / y);
	t_3 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	tmp = 0.0;
	if (t_3 <= -2e+165)
		tmp = t_1;
	elseif (t_3 <= 2000000000000.0)
		tmp = t_2;
	elseif (t_3 <= 1e+274)
		tmp = 2.0 / t;
	elseif (t_3 <= Inf)
		tmp = t_1 - 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+165], t$95$1, If[LessEqual[t$95$3, 2000000000000.0], t$95$2, If[LessEqual[t$95$3, 1e+274], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(t$95$1 - 2.0), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.9999999999999998e165

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 73.2

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

   5. Applied rewrites 73.2%

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

   if -1.9999999999999998e165 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e12 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 88.0%

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

   if 2e12 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.99999999999999921e273

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 48.4%

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

   if 9.99999999999999921e273 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-rgt-in N/A

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

      5. associate-+r+ N/A

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

      6. remove-double-neg N/A

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

      7. unsub-neg N/A

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

      8. div-sub N/A

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

      9. distribute-frac-neg N/A

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

      10. associate-/l* N/A

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

      11. *-inverses N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 86.5%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -2 \cdot 10^{+165}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 2000000000000:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 10^{+274}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := -2 + \frac{x}{y}\\ t_3 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{+274}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (+ -2.0 (/ x y)))
        (t_3 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z))))
   (if (<= t_3 -2e+165)
     t_1
     (if (<= t_3 2000000000000.0)
       t_2
       (if (<= t_3 1e+274) (/ 2.0 t) (if (<= t_3 INFINITY) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = -2.0 + (x / y);
	double t_3 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double tmp;
	if (t_3 <= -2e+165) {
		tmp = t_1;
	} else if (t_3 <= 2000000000000.0) {
		tmp = t_2;
	} else if (t_3 <= 1e+274) {
		tmp = 2.0 / t;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = -2.0 + (x / y);
	double t_3 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double tmp;
	if (t_3 <= -2e+165) {
		tmp = t_1;
	} else if (t_3 <= 2000000000000.0) {
		tmp = t_2;
	} else if (t_3 <= 1e+274) {
		tmp = 2.0 / t;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = -2.0 + (x / y)
	t_3 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z)
	tmp = 0
	if t_3 <= -2e+165:
		tmp = t_1
	elif t_3 <= 2000000000000.0:
		tmp = t_2
	elif t_3 <= 1e+274:
		tmp = 2.0 / t
	elif t_3 <= math.inf:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(-2.0 + Float64(x / y))
	t_3 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	tmp = 0.0
	if (t_3 <= -2e+165)
		tmp = t_1;
	elseif (t_3 <= 2000000000000.0)
		tmp = t_2;
	elseif (t_3 <= 1e+274)
		tmp = Float64(2.0 / t);
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = -2.0 + (x / y);
	t_3 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	tmp = 0.0;
	if (t_3 <= -2e+165)
		tmp = t_1;
	elseif (t_3 <= 2000000000000.0)
		tmp = t_2;
	elseif (t_3 <= 1e+274)
		tmp = 2.0 / t;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+165], t$95$1, If[LessEqual[t$95$3, 2000000000000.0], t$95$2, If[LessEqual[t$95$3, 1e+274], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.9999999999999998e165 or 9.99999999999999921e273 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 77.5

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

   5. Applied rewrites 77.5%

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

   if -1.9999999999999998e165 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e12 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 88.0%

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

   if 2e12 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.99999999999999921e273

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 48.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -2 \cdot 10^{+165}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 2000000000000:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 10^{+274}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ t_2 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ t_3 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2000000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (fma z 2.0 2.0) (* t z)))
        (t_2 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z)))
        (t_3 (+ -2.0 (/ x y))))
   (if (<= t_2 -2e+105)
     t_1
     (if (<= t_2 2000000000000.0) t_3 (if (<= t_2 INFINITY) t_1 t_3)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(z, 2.0, 2.0) / (t * z);
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -2e+105) {
		tmp = t_1;
	} else if (t_2 <= 2000000000000.0) {
		tmp = t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(z, 2.0, 2.0) / Float64(t * z))
	t_2 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	t_3 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_2 <= -2e+105)
		tmp = t_1;
	elseif (t_2 <= 2000000000000.0)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+105], t$95$1, If[LessEqual[t$95$2, 2000000000000.0], t$95$3, If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.9999999999999999e105 or 2e12 < (/.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

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

   5. Applied rewrites 80.9%

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

   if -1.9999999999999999e105 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e12 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 76.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 93.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -2 \cdot 10^{+105}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 2000000000000:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(1 + z, \frac{\frac{2}{t}}{z}, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 (* t z)) (/ x y))))
   (if (<= (/ x y) -1e+25)
     t_1
     (if (<= (/ x y) 5e+35) (fma (+ 1.0 z) (/ (/ 2.0 t) z) -2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / (t * z)) + (x / y);
	double tmp;
	if ((x / y) <= -1e+25) {
		tmp = t_1;
	} else if ((x / y) <= 5e+35) {
		tmp = fma((1.0 + z), ((2.0 / t) / z), -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / Float64(t * z)) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -1e+25)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e+35)
		tmp = fma(Float64(1.0 + z), Float64(Float64(2.0 / t) / z), -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+25], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e+35], N[(N[(1.0 + z), $MachinePrecision] * N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000009e25 or 5.00000000000000021e35 < (/.f64 x y)

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 95.0%

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

   if -1.00000000000000009e25 < (/.f64 x y) < 5.00000000000000021e35

   1. Initial program 88.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 95.2%

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

   7. Applied rewrites 95.4%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(1 + z, \frac{\frac{2}{t}}{z}, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := t\_1 + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(1 + z, t\_1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (+ t_1 (/ x y))))
   (if (<= (/ x y) -1e+23)
     t_2
     (if (<= (/ x y) 5e+35) (fma (+ 1.0 z) t_1 -2.0) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = t_1 + (x / y);
	double tmp;
	if ((x / y) <= -1e+23) {
		tmp = t_2;
	} else if ((x / y) <= 5e+35) {
		tmp = fma((1.0 + z), t_1, -2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(t_1 + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -1e+23)
		tmp = t_2;
	elseif (Float64(x / y) <= 5e+35)
		tmp = fma(Float64(1.0 + z), t_1, -2.0);
	else
		tmp = t_2;
	end
	return 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[(t$95$1 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+23], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 5e+35], N[(N[(1.0 + z), $MachinePrecision] * t$95$1 + -2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.9999999999999992e22 or 5.00000000000000021e35 < (/.f64 x y)

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 95.1%

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

   if -9.9999999999999992e22 < (/.f64 x y) < 5.00000000000000021e35

   1. Initial program 88.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 95.2%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(1 + z, \frac{2}{t \cdot z}, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{2}{t} - 2\right) + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.001:\\ \;\;\;\;\mathsf{fma}\left(1 + z, \frac{2}{t \cdot z}, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- (/ 2.0 t) 2.0) (/ x y))))
   (if (<= (/ x y) -1e-12)
     t_1
     (if (<= (/ x y) 0.001) (fma (+ 1.0 z) (/ 2.0 (* t z)) -2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / t) - 2.0) + (x / y);
	double tmp;
	if ((x / y) <= -1e-12) {
		tmp = t_1;
	} else if ((x / y) <= 0.001) {
		tmp = fma((1.0 + z), (2.0 / (t * z)), -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / t) - 2.0) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -1e-12)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.001)
		tmp = fma(Float64(1.0 + z), Float64(2.0 / Float64(t * z)), -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e-12], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.001], N[(N[(1.0 + z), $MachinePrecision] * N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.9999999999999998e-13 or 1e-3 < (/.f64 x y)

   1. Initial program 89.6%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. lower--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 80.3

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

   5. Applied rewrites 80.3%

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

   if -9.9999999999999998e-13 < (/.f64 x y) < 1e-3

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 99.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-12}:\\ \;\;\;\;\left(\frac{2}{t} - 2\right) + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.001:\\ \;\;\;\;\mathsf{fma}\left(1 + z, \frac{2}{t \cdot z}, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{t} - 2\right) + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{y}, t, \frac{2}{z} - -2\right)}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) 2e+61)
   (- (/ (fma (/ x y) t (- (/ 2.0 z) -2.0)) t) 2.0)
   (+ (/ 2.0 (* t z)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 2e+61) {
		tmp = (fma((x / y), t, ((2.0 / z) - -2.0)) / t) - 2.0;
	} else {
		tmp = (2.0 / (t * z)) + (x / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 2e+61)
		tmp = Float64(Float64(fma(Float64(x / y), t, Float64(Float64(2.0 / z) - -2.0)) / t) - 2.0);
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(x / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 2e+61], N[(N[(N[(N[(x / y), $MachinePrecision] * t + N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 1.9999999999999999e61

   1. Initial program 88.0%

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

   3. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-rgt-in N/A

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

      5. associate-+r+ N/A

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

      6. remove-double-neg N/A

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

      7. unsub-neg N/A

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

      8. div-sub N/A

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

      9. distribute-frac-neg N/A

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

      10. associate-/l* N/A

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

      11. *-inverses N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.2%

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

   if 1.9999999999999999e61 < (/.f64 x y)

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 99.2%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{y}, t, \frac{2}{z} - -2\right)}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(1 + z, \frac{2}{t \cdot z}, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 t) (/ x y))))
   (if (<= (/ x y) -1e+25)
     t_1
     (if (<= (/ x y) 0.02) (fma (+ 1.0 z) (/ 2.0 (* t z)) -2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + (x / y);
	double tmp;
	if ((x / y) <= -1e+25) {
		tmp = t_1;
	} else if ((x / y) <= 0.02) {
		tmp = fma((1.0 + z), (2.0 / (t * z)), -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -1e+25)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.02)
		tmp = fma(Float64(1.0 + z), Float64(2.0 / Float64(t * z)), -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+25], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.02], N[(N[(1.0 + z), $MachinePrecision] * N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000009e25 or 0.0200000000000000004 < (/.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. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. lower--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 79.7

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

   5. Applied rewrites 79.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 79.4%

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

   if -1.00000000000000009e25 < (/.f64 x y) < 0.0200000000000000004

   1. Initial program 88.3%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 97.1%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(1 + z, \frac{2}{t \cdot z}, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(1 + z, \frac{2}{t \cdot z}, -2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+25)
   (/ x y)
   (if (<= (/ x y) 4e+63)
     (fma (+ 1.0 z) (/ 2.0 (* t z)) -2.0)
     (+ -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+25) {
		tmp = x / y;
	} else if ((x / y) <= 4e+63) {
		tmp = fma((1.0 + z), (2.0 / (t * z)), -2.0);
	} else {
		tmp = -2.0 + (x / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+25)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4e+63)
		tmp = fma(Float64(1.0 + z), Float64(2.0 / Float64(t * z)), -2.0);
	else
		tmp = Float64(-2.0 + Float64(x / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e+25], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4e+63], N[(N[(1.0 + z), $MachinePrecision] * N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision], N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.00000000000000009e25

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 74.3

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

   5. Applied rewrites 74.3%

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

   if -1.00000000000000009e25 < (/.f64 x y) < 4.00000000000000023e63

   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. Taylor expanded in y around inf

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

   5. Applied rewrites 93.6%

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

   if 4.00000000000000023e63 < (/.f64 x y)

   1. Initial program 90.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 78.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(1 + z, \frac{2}{t \cdot z}, -2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4.5e+23)
   (/ x y)
   (if (<= (/ x y) 8.5e-12) (- (/ 2.0 t) 2.0) (+ -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.5e+23) {
		tmp = x / y;
	} else if ((x / y) <= 8.5e-12) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = -2.0 + (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-4.5d+23)) then
        tmp = x / y
    else if ((x / y) <= 8.5d-12) then
        tmp = (2.0d0 / t) - 2.0d0
    else
        tmp = (-2.0d0) + (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.5e+23) {
		tmp = x / y;
	} else if ((x / y) <= 8.5e-12) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = -2.0 + (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4.5e+23:
		tmp = x / y
	elif (x / y) <= 8.5e-12:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = -2.0 + (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4.5e+23)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 8.5e-12)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4.5e+23)
		tmp = x / y;
	elseif ((x / y) <= 8.5e-12)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = -2.0 + (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4.5e+23], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 8.5e-12], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.49999999999999979e23

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 74.3

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

   5. Applied rewrites 74.3%

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

   if -4.49999999999999979e23 < (/.f64 x y) < 8.4999999999999997e-12

   1. Initial program 88.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 67.0%

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

   if 8.4999999999999997e-12 < (/.f64 x y)

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 69.2%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.6 \cdot 10^{+35}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4.5e+23)
   (/ x y)
   (if (<= (/ x y) 2.6e+35) (- (/ 2.0 t) 2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.5e+23) {
		tmp = x / y;
	} else if ((x / y) <= 2.6e+35) {
		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) <= (-4.5d+23)) then
        tmp = x / y
    else if ((x / y) <= 2.6d+35) 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) <= -4.5e+23) {
		tmp = x / y;
	} else if ((x / y) <= 2.6e+35) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4.5e+23:
		tmp = x / y
	elif (x / y) <= 2.6e+35:
		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) <= -4.5e+23)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.6e+35)
		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) <= -4.5e+23)
		tmp = x / y;
	elseif ((x / y) <= 2.6e+35)
		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], -4.5e+23], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.6e+35], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.49999999999999979e23 or 2.60000000000000007e35 < (/.f64 x y)

   1. Initial program 89.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 73.7

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

   5. Applied rewrites 73.7%

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

   if -4.49999999999999979e23 < (/.f64 x y) < 2.60000000000000007e35

   1. Initial program 88.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 95.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 65.4%

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

Alternative 14: 53.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -8.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -8.5e-6) (/ x y) (if (<= (/ x y) 2.0) -2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -8.5e-6) {
		tmp = x / y;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-8.5d-6)) then
        tmp = x / y
    else if ((x / y) <= 2.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -8.5e-6) {
		tmp = x / y;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -8.5e-6:
		tmp = x / y
	elif (x / y) <= 2.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -8.5e-6)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -8.5e-6)
		tmp = x / y;
	elseif ((x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -8.5e-6], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.0], -2.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -8.4999999999999999e-6 or 2 < (/.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 68.2

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

   5. Applied rewrites 68.2%

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

   if -8.4999999999999999e-6 < (/.f64 x y) < 2

   1. Initial program 87.8%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 98.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 43.2%

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

Alternative 15: 36.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6800000000:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6800000000.0) -2.0 (if (<= t 1.25e+14) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6800000000.0) {
		tmp = -2.0;
	} else if (t <= 1.25e+14) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-6800000000.0d0)) then
        tmp = -2.0d0
    else if (t <= 1.25d+14) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6800000000.0) {
		tmp = -2.0;
	} else if (t <= 1.25e+14) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6800000000.0:
		tmp = -2.0
	elif t <= 1.25e+14:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6800000000.0)
		tmp = -2.0;
	elseif (t <= 1.25e+14)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6800000000.0)
		tmp = -2.0;
	elseif (t <= 1.25e+14)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6800000000.0], -2.0, If[LessEqual[t, 1.25e+14], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -6.8e9 or 1.25e14 < t

   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 y around inf

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

   5. Applied rewrites 61.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 49.3%

      \[\leadsto -2 \]

   if -6.8e9 < t < 1.25e14

   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

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 33.0%

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

Alternative 16: 20.5% accurate, 47.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.5%

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

3. Taylor expanded in y around inf

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

5. Applied rewrites 68.3%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 23.7%

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

Developer Target 1: 99.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024235 
(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))))