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

Percentage Accurate: 86.7% → 99.0%

Time: 12.6s

Alternatives: 11

Speedup: 1.1×

• 24.3% 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: 86.7% 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: 99.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x / y) + (((2.0 / t) / z) + ((2.0 / t) - 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 = (x / y) + (((2.0d0 / t) / z) + ((2.0d0 / t) - 2.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

3. Taylor expanded in t around 0 98.7%

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

   1. associate--l+ 98.7%

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

   2. associate-*r/ 98.7%

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

   3. metadata-eval 98.7%

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

   4. associate-/r* 98.8%

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

5. Simplified 98.8%

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

6. Final simplification 98.8%

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

Alternative 2: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (- (/ x y) 2.0)))
   (if (<= t -1.35e-7)
     t_2
     (if (<= t -9.5e-275)
       t_1
       (if (<= t 2.3e-306) (/ 2.0 t) (if (<= t 1.6e+17) 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 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.35e-7) {
		tmp = t_2;
	} else if (t <= -9.5e-275) {
		tmp = t_1;
	} else if (t <= 2.3e-306) {
		tmp = 2.0 / t;
	} else if (t <= 1.6e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 / (t * z)
    t_2 = (x / y) - 2.0d0
    if (t <= (-1.35d-7)) then
        tmp = t_2
    else if (t <= (-9.5d-275)) then
        tmp = t_1
    else if (t <= 2.3d-306) then
        tmp = 2.0d0 / t
    else if (t <= 1.6d+17) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.35e-7) {
		tmp = t_2;
	} else if (t <= -9.5e-275) {
		tmp = t_1;
	} else if (t <= 2.3e-306) {
		tmp = 2.0 / t;
	} else if (t <= 1.6e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -1.35e-7:
		tmp = t_2
	elif t <= -9.5e-275:
		tmp = t_1
	elif t <= 2.3e-306:
		tmp = 2.0 / t
	elif t <= 1.6e+17:
		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(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.35e-7)
		tmp = t_2;
	elseif (t <= -9.5e-275)
		tmp = t_1;
	elseif (t <= 2.3e-306)
		tmp = Float64(2.0 / t);
	elseif (t <= 1.6e+17)
		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 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.35e-7)
		tmp = t_2;
	elseif (t <= -9.5e-275)
		tmp = t_1;
	elseif (t <= 2.3e-306)
		tmp = 2.0 / t;
	elseif (t <= 1.6e+17)
		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[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.35e-7], t$95$2, If[LessEqual[t, -9.5e-275], t$95$1, If[LessEqual[t, 2.3e-306], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 1.6e+17], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000004e-7 or 1.6e17 < t

   1. Initial program 73.7%

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

   3. Taylor expanded in t around inf 89.8%

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

   if -1.35000000000000004e-7 < t < -9.49999999999999961e-275 or 2.29999999999999989e-306 < t < 1.6e17

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0 96.9%

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

      1. associate--l+ 96.9%

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

      2. associate-*r/ 96.9%

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

      3. metadata-eval 96.9%

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

      4. associate-/r* 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in z around 0 59.5%

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

   if -9.49999999999999961e-275 < t < 2.29999999999999989e-306

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 78.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -9.2e-8)
     t_1
     (if (<= t -4.6e-270)
       (/ (/ 2.0 t) z)
       (if (<= t 3.8e-305)
         (/ 2.0 t)
         (if (<= t 1.6e+17) (/ 2.0 (* t z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -9.2e-8) {
		tmp = t_1;
	} else if (t <= -4.6e-270) {
		tmp = (2.0 / t) / z;
	} else if (t <= 3.8e-305) {
		tmp = 2.0 / t;
	} else if (t <= 1.6e+17) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-9.2d-8)) then
        tmp = t_1
    else if (t <= (-4.6d-270)) then
        tmp = (2.0d0 / t) / z
    else if (t <= 3.8d-305) then
        tmp = 2.0d0 / t
    else if (t <= 1.6d+17) then
        tmp = 2.0d0 / (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -9.2e-8) {
		tmp = t_1;
	} else if (t <= -4.6e-270) {
		tmp = (2.0 / t) / z;
	} else if (t <= 3.8e-305) {
		tmp = 2.0 / t;
	} else if (t <= 1.6e+17) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -9.2e-8:
		tmp = t_1
	elif t <= -4.6e-270:
		tmp = (2.0 / t) / z
	elif t <= 3.8e-305:
		tmp = 2.0 / t
	elif t <= 1.6e+17:
		tmp = 2.0 / (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -9.2e-8)
		tmp = t_1;
	elseif (t <= -4.6e-270)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t <= 3.8e-305)
		tmp = Float64(2.0 / t);
	elseif (t <= 1.6e+17)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -9.2e-8)
		tmp = t_1;
	elseif (t <= -4.6e-270)
		tmp = (2.0 / t) / z;
	elseif (t <= 3.8e-305)
		tmp = 2.0 / t;
	elseif (t <= 1.6e+17)
		tmp = 2.0 / (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -9.2e-8], t$95$1, If[LessEqual[t, -4.6e-270], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 3.8e-305], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 1.6e+17], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.2000000000000003e-8 or 1.6e17 < t

   1. Initial program 73.7%

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

   3. Taylor expanded in t around inf 89.8%

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

   if -9.2000000000000003e-8 < t < -4.6000000000000003e-270

   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 0 76.0%

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

      1. associate-/r* 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in x around 0 63.4%

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

      1. associate-/r* 63.5%

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

   8. Simplified 63.5%

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

   if -4.6000000000000003e-270 < t < 3.8e-305

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 78.8%

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

   if 3.8e-305 < t < 1.6e17

   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 t around 0 94.5%

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

      1. associate--l+ 94.5%

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

      2. associate-*r/ 94.5%

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

      3. metadata-eval 94.5%

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

      4. associate-/r* 94.5%

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

   5. Simplified 94.5%

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

   6. Taylor expanded in z around 0 56.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 10^{+42}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+20) (not (<= (/ x y) 1e+42)))
   (+ (/ x y) (/ (/ 2.0 t) z))
   (+ (/ 2.0 (* t z)) (+ (/ 2.0 t) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+20) || !((x / y) <= 1e+42)) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = (2.0 / (t * z)) + ((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) <= (-2d+20)) .or. (.not. ((x / y) <= 1d+42))) then
        tmp = (x / y) + ((2.0d0 / t) / z)
    else
        tmp = (2.0d0 / (t * z)) + ((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) <= -2e+20) || !((x / y) <= 1e+42)) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+20) or not ((x / y) <= 1e+42):
		tmp = (x / y) + ((2.0 / t) / z)
	else:
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+20) || !(Float64(x / y) <= 1e+42))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + 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) <= -2e+20) || ~(((x / y) <= 1e+42)))
		tmp = (x / y) + ((2.0 / t) / z);
	else
		tmp = (2.0 / (t * z)) + ((2.0 / t) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+20], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+42]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e20 or 1.00000000000000004e42 < (/.f64 x y)

   1. Initial program 82.7%

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

   3. Taylor expanded in z around 0 93.9%

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

      1. associate-/r* 93.9%

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

   5. Simplified 93.9%

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

   if -2e20 < (/.f64 x y) < 1.00000000000000004e42

   1. Initial program 84.7%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 95.8%

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

      1. sub-neg 95.8%

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

      2. associate-*r/ 95.8%

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

      3. metadata-eval 95.8%

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

      4. +-commutative 95.8%

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

      5. associate-*r/ 95.8%

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

      6. metadata-eval 95.8%

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

      7. metadata-eval 95.8%

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

      8. associate-+r+ 95.8%

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

   8. Simplified 95.8%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 10^{+42}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1300000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0011:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 5.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1300000000000.0)
   (/ x y)
   (if (<= (/ x y) 0.0011) -2.0 (if (<= (/ x y) 5.3e+41) (/ 2.0 t) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1300000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 0.0011) {
		tmp = -2.0;
	} else if ((x / y) <= 5.3e+41) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1300000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 0.0011d0) then
        tmp = -2.0d0
    else if ((x / y) <= 5.3d+41) then
        tmp = 2.0d0 / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1300000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 0.0011) {
		tmp = -2.0;
	} else if ((x / y) <= 5.3e+41) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1300000000000.0:
		tmp = x / y
	elif (x / y) <= 0.0011:
		tmp = -2.0
	elif (x / y) <= 5.3e+41:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1300000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 0.0011)
		tmp = -2.0;
	elseif (Float64(x / y) <= 5.3e+41)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1300000000000.0)
		tmp = x / y;
	elseif ((x / y) <= 0.0011)
		tmp = -2.0;
	elseif ((x / y) <= 5.3e+41)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1300000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0011], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 5.3e+41], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.3e12 or 5.2999999999999997e41 < (/.f64 x y)

   1. Initial program 82.8%

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

   3. Taylor expanded in x around inf 77.4%

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

   if -1.3e12 < (/.f64 x y) < 0.00110000000000000007

   1. Initial program 86.1%

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

   3. Taylor expanded in t around inf 44.2%

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

   4. Taylor expanded in x around 0 42.7%

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

   if 0.00110000000000000007 < (/.f64 x y) < 5.2999999999999997e41

   1. Initial program 72.9%

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

   3. Taylor expanded in t around 0 74.2%

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

      1. associate-*r/ 74.2%

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

      2. metadata-eval 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in z around inf 55.0%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1300000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0011:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 5.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-36} \lor \neg \left(z \leq 2.5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{2}{t} + \left(\frac{x}{y} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.75e-36) (not (<= z 2.5e-13)))
   (+ (/ 2.0 t) (+ (/ x y) -2.0))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.75e-36) || !(z <= 2.5e-13)) {
		tmp = (2.0 / t) + ((x / y) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	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 <= (-1.75d-36)) .or. (.not. (z <= 2.5d-13))) then
        tmp = (2.0d0 / t) + ((x / y) + (-2.0d0))
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.75e-36) || !(z <= 2.5e-13)) {
		tmp = (2.0 / t) + ((x / y) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.75e-36) or not (z <= 2.5e-13):
		tmp = (2.0 / t) + ((x / y) + -2.0)
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.75e-36) || !(z <= 2.5e-13))
		tmp = Float64(Float64(2.0 / t) + Float64(Float64(x / y) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.75e-36) || ~((z <= 2.5e-13)))
		tmp = (2.0 / t) + ((x / y) + -2.0);
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.75e-36], N[Not[LessEqual[z, 2.5e-13]], $MachinePrecision]], N[(N[(2.0 / t), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e-36 or 2.49999999999999995e-13 < z

   1. Initial program 71.7%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/r* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 98.7%

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

      1. associate--l+ 98.7%

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

      2. associate-*r/ 98.7%

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

      3. metadata-eval 98.7%

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

      4. sub-neg 98.7%

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

      5. metadata-eval 98.7%

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

   8. Simplified 98.7%

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

   if -1.75e-36 < z < 2.49999999999999995e-13

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 87.5%

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

      1. associate-/r* 87.6%

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

   5. Simplified 87.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-36} \lor \neg \left(z \leq 2.5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{2}{t} + \left(\frac{x}{y} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -220000000 \lor \neg \left(t \leq 5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -220000000.0) (not (<= t 5e+19)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -220000000.0) || !(t <= 5e+19)) {
		tmp = (x / y) - 2.0;
	} 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 ((t <= (-220000000.0d0)) .or. (.not. (t <= 5d+19))) then
        tmp = (x / y) - 2.0d0
    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 ((t <= -220000000.0) || !(t <= 5e+19)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -220000000.0) or not (t <= 5e+19):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -220000000.0) || !(t <= 5e+19))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -220000000.0) || ~((t <= 5e+19)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -220000000.0], N[Not[LessEqual[t, 5e+19]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2e8 or 5e19 < t

   1. Initial program 73.2%

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

   3. Taylor expanded in t around inf 90.9%

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

   if -2.2e8 < t < 5e19

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 85.5%

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

      1. associate-*r/ 85.5%

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

      2. metadata-eval 85.5%

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

   5. Simplified 85.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -220000000 \lor \neg \left(t \leq 5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{-7}:\\ \;\;\;\;\frac{2}{t} + \left(\frac{x}{y} + -2\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.18e-7)
   (+ (/ 2.0 t) (+ (/ x y) -2.0))
   (if (<= t 5e+19) (/ (+ 2.0 (/ 2.0 z)) t) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.18e-7) {
		tmp = (2.0 / t) + ((x / y) + -2.0);
	} else if (t <= 5e+19) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x / y) - 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 <= (-1.18d-7)) then
        tmp = (2.0d0 / t) + ((x / y) + (-2.0d0))
    else if (t <= 5d+19) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else
        tmp = (x / y) - 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 <= -1.18e-7) {
		tmp = (2.0 / t) + ((x / y) + -2.0);
	} else if (t <= 5e+19) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.18e-7:
		tmp = (2.0 / t) + ((x / y) + -2.0)
	elif t <= 5e+19:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.18e-7)
		tmp = Float64(Float64(2.0 / t) + Float64(Float64(x / y) + -2.0));
	elseif (t <= 5e+19)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.18e-7)
		tmp = (2.0 / t) + ((x / y) + -2.0);
	elseif (t <= 5e+19)
		tmp = (2.0 + (2.0 / z)) / t;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.18e-7], N[(N[(2.0 / t), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+19], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.18e-7

   1. Initial program 74.6%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/r* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 90.7%

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

      1. associate--l+ 90.7%

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

      2. associate-*r/ 90.7%

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

      3. metadata-eval 90.7%

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

      4. sub-neg 90.7%

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

      5. metadata-eval 90.7%

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

   8. Simplified 90.7%

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

   if -1.18e-7 < t < 5e19

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 85.8%

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

      1. associate-*r/ 85.8%

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

      2. metadata-eval 85.8%

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

   5. Simplified 85.8%

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

   if 5e19 < t

   1. Initial program 72.2%

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

   3. Taylor expanded in t around inf 91.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{-7}:\\ \;\;\;\;\frac{2}{t} + \left(\frac{x}{y} + -2\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-6} \lor \neg \left(t \leq 1.65 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.7e-6) (not (<= t 1.65e-51))) (- (/ x y) 2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.7e-6) || !(t <= 1.65e-51)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 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 ((t <= (-1.7d-6)) .or. (.not. (t <= 1.65d-51))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 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 ((t <= -1.7e-6) || !(t <= 1.65e-51)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.7e-6) or not (t <= 1.65e-51):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.7e-6) || !(t <= 1.65e-51))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.7e-6) || ~((t <= 1.65e-51)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.7e-6], N[Not[LessEqual[t, 1.65e-51]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.70000000000000003e-6 or 1.64999999999999986e-51 < t

   1. Initial program 75.4%

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

   3. Taylor expanded in t around inf 86.0%

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

   if -1.70000000000000003e-6 < t < 1.64999999999999986e-51

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0 87.9%

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

      1. associate-*r/ 87.9%

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

      2. metadata-eval 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in z around inf 34.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-6} \lor \neg \left(t \leq 1.65 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+20}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.7e+20) -2.0 (if (<= t 1.6e+17) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.7e+20) {
		tmp = -2.0;
	} else if (t <= 1.6e+17) {
		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 <= (-5.7d+20)) then
        tmp = -2.0d0
    else if (t <= 1.6d+17) 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 <= -5.7e+20) {
		tmp = -2.0;
	} else if (t <= 1.6e+17) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.7e+20:
		tmp = -2.0
	elif t <= 1.6e+17:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.7e+20)
		tmp = -2.0;
	elseif (t <= 1.6e+17)
		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 <= -5.7e+20)
		tmp = -2.0;
	elseif (t <= 1.6e+17)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.7e+20], -2.0, If[LessEqual[t, 1.6e+17], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -5.7e20 or 1.6e17 < t

   1. Initial program 73.4%

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

   3. Taylor expanded in t around inf 90.2%

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

   4. Taylor expanded in x around 0 37.5%

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

   if -5.7e20 < t < 1.6e17

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 85.4%

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

      1. associate-*r/ 85.4%

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

      2. metadata-eval 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around inf 32.0%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+20}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 20.2% accurate, 17.0× 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 83.8%

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

3. Taylor expanded in t around inf 58.4%

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

4. Taylor expanded in x around 0 22.1%

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

5. Final simplification 22.1%

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

Developer target: 99.0% accurate, 1.3× 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 2024096 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))