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

Percentage Accurate: 85.8% → 99.8%

Time: 19.2s

Alternatives: 11

Speedup: 0.9×

• 23.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 96.3%

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

      1. associate-/r* 99.7%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-commutative 99.7%

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

      5. div-sub 99.7%

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

      6. sub-neg 99.7%

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

      7. *-inverses 99.7%

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

      8. metadata-eval 99.7%

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

      9. distribute-lft-in 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*r/ 99.7%

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

      12. metadata-eval 99.7%

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

      13. *-commutative 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 99.8%

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

Alternative 2: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 96.6%

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

4. Final simplification 99.5%

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

Alternative 3: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -5 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 32000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (- (/ x y) 2.0)))
   (if (<= t -5e-5)
     t_2
     (if (<= t 8.2e-48)
       t_1
       (if (<= t 4.8e-30) (/ x y) (if (<= t 32000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -5e-5) {
		tmp = t_2;
	} else if (t <= 8.2e-48) {
		tmp = t_1;
	} else if (t <= 4.8e-30) {
		tmp = x / y;
	} else if (t <= 32000.0) {
		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 + (2.0d0 / z)) / t
    t_2 = (x / y) - 2.0d0
    if (t <= (-5d-5)) then
        tmp = t_2
    else if (t <= 8.2d-48) then
        tmp = t_1
    else if (t <= 4.8d-30) then
        tmp = x / y
    else if (t <= 32000.0d0) 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 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -5e-5) {
		tmp = t_2;
	} else if (t <= 8.2e-48) {
		tmp = t_1;
	} else if (t <= 4.8e-30) {
		tmp = x / y;
	} else if (t <= 32000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -5e-5:
		tmp = t_2
	elif t <= 8.2e-48:
		tmp = t_1
	elif t <= 4.8e-30:
		tmp = x / y
	elif t <= 32000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -5e-5)
		tmp = t_2;
	elseif (t <= 8.2e-48)
		tmp = t_1;
	elseif (t <= 4.8e-30)
		tmp = Float64(x / y);
	elseif (t <= 32000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -5e-5)
		tmp = t_2;
	elseif (t <= 8.2e-48)
		tmp = t_1;
	elseif (t <= 4.8e-30)
		tmp = x / y;
	elseif (t <= 32000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -5e-5], t$95$2, If[LessEqual[t, 8.2e-48], t$95$1, If[LessEqual[t, 4.8e-30], N[(x / y), $MachinePrecision], If[LessEqual[t, 32000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.00000000000000024e-5 or 32000 < t

   1. Initial program 79.0%

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

   3. Taylor expanded in t around inf 88.9%

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

   if -5.00000000000000024e-5 < t < 8.20000000000000028e-48 or 4.7999999999999997e-30 < t < 32000

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0 82.7%

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

      1. associate-*r/ 82.7%

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

      2. metadata-eval 82.7%

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

   5. Simplified 82.7%

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

   if 8.20000000000000028e-48 < t < 4.7999999999999997e-30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 32000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 125:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (+ (/ x y) (+ (/ 2.0 t) -2.0))))
   (if (<= t -2e-5)
     t_2
     (if (<= t 1e-87)
       t_1
       (if (<= t 3.6e-27) t_2 (if (<= t 125.0) t_1 (- (/ x y) 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) + ((2.0 / t) + -2.0);
	double tmp;
	if (t <= -2e-5) {
		tmp = t_2;
	} else if (t <= 1e-87) {
		tmp = t_1;
	} else if (t <= 3.6e-27) {
		tmp = t_2;
	} else if (t <= 125.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = (x / y) + ((2.0d0 / t) + (-2.0d0))
    if (t <= (-2d-5)) then
        tmp = t_2
    else if (t <= 1d-87) then
        tmp = t_1
    else if (t <= 3.6d-27) then
        tmp = t_2
    else if (t <= 125.0d0) then
        tmp = t_1
    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 t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) + ((2.0 / t) + -2.0);
	double tmp;
	if (t <= -2e-5) {
		tmp = t_2;
	} else if (t <= 1e-87) {
		tmp = t_1;
	} else if (t <= 3.6e-27) {
		tmp = t_2;
	} else if (t <= 125.0) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) + ((2.0 / t) + -2.0)
	tmp = 0
	if t <= -2e-5:
		tmp = t_2
	elif t <= 1e-87:
		tmp = t_1
	elif t <= 3.6e-27:
		tmp = t_2
	elif t <= 125.0:
		tmp = t_1
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0))
	tmp = 0.0
	if (t <= -2e-5)
		tmp = t_2;
	elseif (t <= 1e-87)
		tmp = t_1;
	elseif (t <= 3.6e-27)
		tmp = t_2;
	elseif (t <= 125.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = (x / y) + ((2.0 / t) + -2.0);
	tmp = 0.0;
	if (t <= -2e-5)
		tmp = t_2;
	elseif (t <= 1e-87)
		tmp = t_1;
	elseif (t <= 3.6e-27)
		tmp = t_2;
	elseif (t <= 125.0)
		tmp = t_1;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-5], t$95$2, If[LessEqual[t, 1e-87], t$95$1, If[LessEqual[t, 3.6e-27], t$95$2, If[LessEqual[t, 125.0], t$95$1, N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.00000000000000016e-5 or 1.00000000000000002e-87 < t < 3.5999999999999999e-27

   1. Initial program 83.5%

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

   3. Taylor expanded in z around inf 88.4%

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

      1. div-sub 88.4%

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

      2. sub-neg 88.4%

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

      3. *-inverses 88.4%

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

      4. metadata-eval 88.4%

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

      5. distribute-lft-in 88.4%

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

      6. metadata-eval 88.4%

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

      7. associate-*r/ 88.4%

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

      8. metadata-eval 88.4%

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

   5. Simplified 88.4%

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

   if -2.00000000000000016e-5 < t < 1.00000000000000002e-87 or 3.5999999999999999e-27 < t < 125

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 83.5%

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

      1. associate-*r/ 83.5%

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

      2. metadata-eval 83.5%

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

   5. Simplified 83.5%

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

   if 125 < t

   1. Initial program 77.6%

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

   3. Taylor expanded in t around inf 90.0%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;t \leq 10^{-87}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;t \leq 125:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.5 \cdot 10^{+60}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6.6e+82)
   (/ x y)
   (if (<= (/ x y) 1.5e+60) (+ -2.0 (/ (/ 2.0 z) t)) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6.6e+82) {
		tmp = x / y;
	} else if ((x / y) <= 1.5e+60) {
		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 ((x / y) <= (-6.6d+82)) then
        tmp = x / y
    else if ((x / y) <= 1.5d+60) 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 ((x / y) <= -6.6e+82) {
		tmp = x / y;
	} else if ((x / y) <= 1.5e+60) {
		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 (x / y) <= -6.6e+82:
		tmp = x / y
	elif (x / y) <= 1.5e+60:
		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 (Float64(x / y) <= -6.6e+82)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.5e+60)
		tmp = Float64(-2.0 + Float64(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 ((x / y) <= -6.6e+82)
		tmp = x / y;
	elseif ((x / y) <= 1.5e+60)
		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[N[(x / y), $MachinePrecision], -6.6e+82], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.5e+60], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -6.5999999999999997e82

   1. Initial program 85.5%

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

   3. Taylor expanded in x around inf 88.0%

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

   if -6.5999999999999997e82 < (/.f64 x y) < 1.4999999999999999e60

   1. Initial program 89.8%

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

   3. Taylor expanded in x around inf 67.7%

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

      1. associate-/r* 71.2%

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

      2. associate-*r/ 71.2%

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

      3. *-commutative 71.2%

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

      4. *-commutative 71.2%

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

      5. div-sub 71.2%

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

      6. sub-neg 71.2%

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

      7. *-inverses 71.2%

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

      8. metadata-eval 71.2%

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

      9. distribute-lft-in 71.2%

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

      10. metadata-eval 71.2%

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

      11. associate-*r/ 71.2%

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

      12. metadata-eval 71.2%

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

      13. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in x around 0 93.5%

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

      1. sub-neg 93.5%

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

      2. *-commutative 93.5%

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

      3. *-commutative 93.5%

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

      4. associate-/r* 93.5%

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

      5. associate-*l/ 93.5%

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

      6. associate-/l* 93.4%

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

      7. distribute-lft-in 93.4%

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

      8. associate-*l/ 93.4%

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

      9. *-lft-identity 93.4%

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

      10. metadata-eval 93.4%

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

   8. Simplified 93.4%

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

   9. Taylor expanded in z around 0 72.7%

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

   if 1.4999999999999999e60 < (/.f64 x y)

   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 t around inf 77.3%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.5 \cdot 10^{+60}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-15} \lor \neg \left(z \leq 1.2 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.16e-15) (not (<= z 1.2e-19)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.16e-15) || !(z <= 1.2e-19)) {
		tmp = (x / y) + ((2.0 / t) + -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 <= (-1.16d-15)) .or. (.not. (z <= 1.2d-19))) then
        tmp = (x / y) + ((2.0d0 / t) + (-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 <= -1.16e-15) || !(z <= 1.2e-19)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.16e-15) or not (z <= 1.2e-19):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.16e-15) || !(z <= 1.2e-19))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -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 <= -1.16e-15) || ~((z <= 1.2e-19)))
		tmp = (x / y) + ((2.0 / t) + -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, -1.16e-15], N[Not[LessEqual[z, 1.2e-19]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $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 < -1.1599999999999999e-15 or 1.20000000000000011e-19 < z

   1. Initial program 79.6%

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

   3. Taylor expanded in z around inf 98.5%

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

      1. div-sub 98.5%

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

      2. sub-neg 98.5%

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

      3. *-inverses 98.5%

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

      4. metadata-eval 98.5%

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

      5. distribute-lft-in 98.5%

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

      6. metadata-eval 98.5%

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

      7. associate-*r/ 98.5%

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

      8. metadata-eval 98.5%

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

   5. Simplified 98.5%

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

   if -1.1599999999999999e-15 < z < 1.20000000000000011e-19

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 91.9%

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

      1. associate-/r* 92.0%

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

   5. Simplified 92.0%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-15} \lor \neg \left(z \leq 1.2 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.95 \lor \neg \left(\frac{x}{y} \leq 560000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3.95) (not (<= (/ x y) 560000000000.0))) (/ x y) -2.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3.95) || !((x / y) <= 560000000000.0)) {
		tmp = x / y;
	} 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 (((x / y) <= (-3.95d0)) .or. (.not. ((x / y) <= 560000000000.0d0))) then
        tmp = x / y
    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 (((x / y) <= -3.95) || !((x / y) <= 560000000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3.95) or not ((x / y) <= 560000000000.0):
		tmp = x / y
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -3.95) || !(Float64(x / y) <= 560000000000.0))
		tmp = Float64(x / y);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -3.95) || ~(((x / y) <= 560000000000.0)))
		tmp = x / y;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -3.95], N[Not[LessEqual[N[(x / y), $MachinePrecision], 560000000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.9500000000000002 or 5.6e11 < (/.f64 x y)

   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 x around inf 73.6%

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

   if -3.9500000000000002 < (/.f64 x y) < 5.6e11

   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 x around inf 63.4%

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

      1. associate-/r* 67.4%

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

      2. associate-*r/ 67.4%

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

      3. *-commutative 67.4%

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

      4. *-commutative 67.4%

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

      5. div-sub 67.4%

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

      6. sub-neg 67.4%

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

      7. *-inverses 67.4%

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

      8. metadata-eval 67.4%

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

      9. distribute-lft-in 67.4%

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

      10. metadata-eval 67.4%

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

      11. associate-*r/ 67.4%

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

      12. metadata-eval 67.4%

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

      13. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in x around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. associate-*r/ 98.6%

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

      3. metadata-eval 98.6%

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

      4. +-commutative 98.6%

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

      5. associate-*r/ 98.6%

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

      6. metadata-eval 98.6%

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

      7. metadata-eval 98.6%

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

   8. Simplified 98.6%

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

   9. Taylor expanded in t around inf 36.0%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.95 \lor \neg \left(\frac{x}{y} \leq 560000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-68} \lor \neg \left(t \leq 1.55 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.2e-68) (not (<= t 1.55e-123))) (- (/ x y) 2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-68) || !(t <= 1.55e-123)) {
		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 <= (-6.2d-68)) .or. (.not. (t <= 1.55d-123))) 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 <= -6.2e-68) || !(t <= 1.55e-123)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.2e-68) or not (t <= 1.55e-123):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.2e-68) || !(t <= 1.55e-123))
		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 <= -6.2e-68) || ~((t <= 1.55e-123)))
		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, -6.2e-68], N[Not[LessEqual[t, 1.55e-123]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.1999999999999999e-68 or 1.54999999999999999e-123 < t

   1. Initial program 84.4%

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

   3. Taylor expanded in t around inf 75.6%

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

   if -6.1999999999999999e-68 < t < 1.54999999999999999e-123

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 86.9%

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

      1. associate-*r/ 86.9%

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

      2. metadata-eval 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in z around inf 39.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-68} \lor \neg \left(t \leq 1.55 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-204} \lor \neg \left(z \leq 1.35 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e-204) (not (<= z 1.35e-139)))
   (- (/ x y) 2.0)
   (/ 2.0 (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-204) || !(z <= 1.35e-139)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9d-204)) .or. (.not. (z <= 1.35d-139))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 / (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-204) || !(z <= 1.35e-139)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e-204) or not (z <= 1.35e-139):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e-204) || !(z <= 1.35e-139))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9e-204) || ~((z <= 1.35e-139)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e-204], N[Not[LessEqual[z, 1.35e-139]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999948e-204 or 1.3499999999999999e-139 < z

   1. Initial program 86.0%

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

   3. Taylor expanded in t around inf 65.7%

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

   if -8.99999999999999948e-204 < z < 1.3499999999999999e-139

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. associate-/r* 77.3%

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

      2. associate-*r/ 77.3%

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

      3. *-commutative 77.3%

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

      4. *-commutative 77.3%

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

      5. div-sub 77.3%

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

      6. sub-neg 77.3%

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

      7. *-inverses 77.3%

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

      8. metadata-eval 77.3%

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

      9. distribute-lft-in 77.3%

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

      10. metadata-eval 77.3%

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

      11. associate-*r/ 77.3%

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

      12. metadata-eval 77.3%

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

      13. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in z around 0 77.6%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-204} \lor \neg \left(z \leq 1.35 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-10}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-5}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.8e-10) -2.0 (if (<= t 2.75e-5) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.8e-10) {
		tmp = -2.0;
	} else if (t <= 2.75e-5) {
		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 <= (-2.8d-10)) then
        tmp = -2.0d0
    else if (t <= 2.75d-5) 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 <= -2.8e-10) {
		tmp = -2.0;
	} else if (t <= 2.75e-5) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.8e-10:
		tmp = -2.0
	elif t <= 2.75e-5:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.8e-10)
		tmp = -2.0;
	elseif (t <= 2.75e-5)
		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 <= -2.8e-10)
		tmp = -2.0;
	elseif (t <= 2.75e-5)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.8e-10], -2.0, If[LessEqual[t, 2.75e-5], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000015e-10 or 2.7500000000000001e-5 < t

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf 86.9%

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

      1. associate-/r* 90.5%

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

      2. associate-*r/ 90.5%

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

      3. *-commutative 90.5%

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

      4. *-commutative 90.5%

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

      5. div-sub 90.5%

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

      6. sub-neg 90.5%

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

      7. *-inverses 90.5%

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

      8. metadata-eval 90.5%

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

      9. distribute-lft-in 90.5%

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

      10. metadata-eval 90.5%

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

      11. associate-*r/ 90.5%

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

      12. metadata-eval 90.5%

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

      13. *-commutative 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in x around 0 45.9%

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

      1. sub-neg 45.9%

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

      2. associate-*r/ 45.9%

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

      3. metadata-eval 45.9%

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

      4. +-commutative 45.9%

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

      5. associate-*r/ 45.9%

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

      6. metadata-eval 45.9%

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

      7. metadata-eval 45.9%

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

   8. Simplified 45.9%

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

   9. Taylor expanded in t around inf 31.4%

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

   if -2.80000000000000015e-10 < t < 2.7500000000000001e-5

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0 79.1%

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

      1. associate-*r/ 79.1%

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

      2. metadata-eval 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in z around inf 33.6%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-10}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-5}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 20.4% 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 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 x around inf 80.9%

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

   1. associate-/r* 82.9%

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

   2. associate-*r/ 82.9%

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

   3. *-commutative 82.9%

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

   4. *-commutative 82.9%

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

   5. div-sub 82.9%

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

   6. sub-neg 82.9%

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

   7. *-inverses 82.9%

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

   8. metadata-eval 82.9%

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

   9. distribute-lft-in 82.9%

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

   10. metadata-eval 82.9%

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

   11. associate-*r/ 82.9%

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

   12. metadata-eval 82.9%

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

   13. *-commutative 82.9%

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

5. Simplified 82.9%

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

6. Taylor expanded in x around 0 61.6%

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

   1. sub-neg 61.6%

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

   2. associate-*r/ 61.6%

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

   3. metadata-eval 61.6%

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

   4. +-commutative 61.6%

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

   5. associate-*r/ 61.6%

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

   6. metadata-eval 61.6%

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

   7. metadata-eval 61.6%

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

8. Simplified 61.6%

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

9. Taylor expanded in t around inf 17.8%

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

10. Final simplification 17.8%

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

Developer target: 99.2% 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 2024076 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

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