Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 89.3% → 94.9%

Time: 14.2s

Alternatives: 17

Speedup: 0.8×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

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

C

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

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 * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

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

C

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

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 * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x}{x + 1}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+157}:\\ \;\;\;\;t_2 + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{z \cdot y}{t_1} - \left(\frac{1}{\frac{t_1}{x}} - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ x (+ x 1.0))))
   (if (<= z -1.6e+157)
     (+ t_2 (/ y (* (+ x 1.0) t)))
     (if (<= z 9e+95)
       (/ (- (/ (* z y) t_1) (- (/ 1.0 (/ t_1 x)) x)) (+ x 1.0))
       (+ t_2 (/ (- (/ y (+ x 1.0)) (/ x (* z (+ x 1.0)))) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = x / (x + 1.0);
	double tmp;
	if (z <= -1.6e+157) {
		tmp = t_2 + (y / ((x + 1.0) * t));
	} else if (z <= 9e+95) {
		tmp = (((z * y) / t_1) - ((1.0 / (t_1 / x)) - x)) / (x + 1.0);
	} else {
		tmp = t_2 + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = x / (x + 1.0d0)
    if (z <= (-1.6d+157)) then
        tmp = t_2 + (y / ((x + 1.0d0) * t))
    else if (z <= 9d+95) then
        tmp = (((z * y) / t_1) - ((1.0d0 / (t_1 / x)) - x)) / (x + 1.0d0)
    else
        tmp = t_2 + (((y / (x + 1.0d0)) - (x / (z * (x + 1.0d0)))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = x / (x + 1.0);
	double tmp;
	if (z <= -1.6e+157) {
		tmp = t_2 + (y / ((x + 1.0) * t));
	} else if (z <= 9e+95) {
		tmp = (((z * y) / t_1) - ((1.0 / (t_1 / x)) - x)) / (x + 1.0);
	} else {
		tmp = t_2 + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = x / (x + 1.0)
	tmp = 0
	if z <= -1.6e+157:
		tmp = t_2 + (y / ((x + 1.0) * t))
	elif z <= 9e+95:
		tmp = (((z * y) / t_1) - ((1.0 / (t_1 / x)) - x)) / (x + 1.0)
	else:
		tmp = t_2 + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -1.6e+157)
		tmp = Float64(t_2 + Float64(y / Float64(Float64(x + 1.0) * t)));
	elseif (z <= 9e+95)
		tmp = Float64(Float64(Float64(Float64(z * y) / t_1) - Float64(Float64(1.0 / Float64(t_1 / x)) - x)) / Float64(x + 1.0));
	else
		tmp = Float64(t_2 + Float64(Float64(Float64(y / Float64(x + 1.0)) - Float64(x / Float64(z * Float64(x + 1.0)))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = x / (x + 1.0);
	tmp = 0.0;
	if (z <= -1.6e+157)
		tmp = t_2 + (y / ((x + 1.0) * t));
	elseif (z <= 9e+95)
		tmp = (((z * y) / t_1) - ((1.0 / (t_1 / x)) - x)) / (x + 1.0);
	else
		tmp = t_2 + (((y / (x + 1.0)) - (x / (z * (x + 1.0)))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+157], N[(t$95$2 + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+95], N[(N[(N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(N[(1.0 / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e157

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in y around inf 70.6%

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

   5. Taylor expanded in t around inf 87.9%

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

      1. +-commutative 87.9%

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

      2. +-commutative 87.9%

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

   7. Simplified 87.9%

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

   if -1.6e157 < z < 9.00000000000000033e95

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

   3. Simplified 98.7%

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

      1. +-commutative 98.7%

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

      2. div-sub 98.7%

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

      3. associate-+l- 98.7%

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

   5. Applied egg-rr 98.7%

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

      1. clear-num 98.7%

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

      2. inv-pow 98.7%

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

   7. Applied egg-rr 98.7%

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

      1. unpow-1 98.7%

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

   9. Simplified 98.7%

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

   if 9.00000000000000033e95 < z

   1. Initial program 68.9%

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

      1. *-commutative 68.9%

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

   3. Simplified 68.9%

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

   4. Taylor expanded in t around -inf 96.1%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{z \cdot y}{z \cdot t - x} - \left(\frac{1}{\frac{z \cdot t - x}{x}} - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \]

Alternative 2: 94.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;\frac{\frac{z \cdot y}{t_1} - \left(\frac{1}{\frac{t_1}{x}} - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (<= z -3.9e+157)
     (+ (/ x (+ x 1.0)) (/ y (* (+ x 1.0) t)))
     (if (<= z 5.4e+149)
       (/ (- (/ (* z y) t_1) (- (/ 1.0 (/ t_1 x)) x)) (+ x 1.0))
       (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (z <= -3.9e+157) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else if (z <= 5.4e+149) {
		tmp = (((z * y) / t_1) - ((1.0 / (t_1 / x)) - x)) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	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) :: tmp
    t_1 = (z * t) - x
    if (z <= (-3.9d+157)) then
        tmp = (x / (x + 1.0d0)) + (y / ((x + 1.0d0) * t))
    else if (z <= 5.4d+149) then
        tmp = (((z * y) / t_1) - ((1.0d0 / (t_1 / x)) - x)) / (x + 1.0d0)
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (z <= -3.9e+157) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else if (z <= 5.4e+149) {
		tmp = (((z * y) / t_1) - ((1.0 / (t_1 / x)) - x)) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if z <= -3.9e+157:
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t))
	elif z <= 5.4e+149:
		tmp = (((z * y) / t_1) - ((1.0 / (t_1 / x)) - x)) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (z <= -3.9e+157)
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(Float64(x + 1.0) * t)));
	elseif (z <= 5.4e+149)
		tmp = Float64(Float64(Float64(Float64(z * y) / t_1) - Float64(Float64(1.0 / Float64(t_1 / x)) - x)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if (z <= -3.9e+157)
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	elseif (z <= 5.4e+149)
		tmp = (((z * y) / t_1) - ((1.0 / (t_1 / x)) - x)) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -3.9e+157], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+149], N[(N[(N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(N[(1.0 / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.89999999999999971e157

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in y around inf 70.6%

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

   5. Taylor expanded in t around inf 87.9%

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

      1. +-commutative 87.9%

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

      2. +-commutative 87.9%

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

   7. Simplified 87.9%

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

   if -3.89999999999999971e157 < z < 5.4000000000000002e149

   1. Initial program 97.8%

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

      1. *-commutative 97.8%

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

   3. Simplified 97.8%

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

      1. +-commutative 97.8%

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

      2. div-sub 97.8%

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

      3. associate-+l- 97.8%

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

   5. Applied egg-rr 97.8%

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

      1. clear-num 97.8%

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

      2. inv-pow 97.8%

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

   7. Applied egg-rr 97.8%

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

      1. unpow-1 97.8%

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

   9. Simplified 97.8%

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

   if 5.4000000000000002e149 < z

   1. Initial program 59.9%

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

      1. *-commutative 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around inf 99.9%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;\frac{\frac{z \cdot y}{z \cdot t - x} - \left(\frac{1}{\frac{z \cdot t - x}{x}} - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 94.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{\frac{z \cdot y}{t_1} - \left(\frac{x}{t_1} - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (<= z -1.65e+157)
     (+ (/ x (+ x 1.0)) (/ y (* (+ x 1.0) t)))
     (if (<= z 2.9e+150)
       (/ (- (/ (* z y) t_1) (- (/ x t_1) x)) (+ x 1.0))
       (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (z <= -1.65e+157) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else if (z <= 2.9e+150) {
		tmp = (((z * y) / t_1) - ((x / t_1) - x)) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	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) :: tmp
    t_1 = (z * t) - x
    if (z <= (-1.65d+157)) then
        tmp = (x / (x + 1.0d0)) + (y / ((x + 1.0d0) * t))
    else if (z <= 2.9d+150) then
        tmp = (((z * y) / t_1) - ((x / t_1) - x)) / (x + 1.0d0)
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (z <= -1.65e+157) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else if (z <= 2.9e+150) {
		tmp = (((z * y) / t_1) - ((x / t_1) - x)) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if z <= -1.65e+157:
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t))
	elif z <= 2.9e+150:
		tmp = (((z * y) / t_1) - ((x / t_1) - x)) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (z <= -1.65e+157)
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(Float64(x + 1.0) * t)));
	elseif (z <= 2.9e+150)
		tmp = Float64(Float64(Float64(Float64(z * y) / t_1) - Float64(Float64(x / t_1) - x)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if (z <= -1.65e+157)
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	elseif (z <= 2.9e+150)
		tmp = (((z * y) / t_1) - ((x / t_1) - x)) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -1.65e+157], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+150], N[(N[(N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(N[(x / t$95$1), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6500000000000001e157

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in y around inf 70.6%

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

   5. Taylor expanded in t around inf 87.9%

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

      1. +-commutative 87.9%

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

      2. +-commutative 87.9%

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

   7. Simplified 87.9%

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

   if -1.6500000000000001e157 < z < 2.90000000000000011e150

   1. Initial program 97.8%

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

      1. *-commutative 97.8%

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

   3. Simplified 97.8%

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

      1. +-commutative 97.8%

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

      2. div-sub 97.8%

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

      3. associate-+l- 97.8%

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

   5. Applied egg-rr 97.8%

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

   if 2.90000000000000011e150 < z

   1. Initial program 59.9%

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

      1. *-commutative 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around inf 99.9%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{\frac{z \cdot y}{z \cdot t - x} - \left(\frac{x}{z \cdot t - x} - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 4: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{z \cdot y}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-232}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* z y) (- (* z t) x))) (+ x 1.0))))
   (if (<= z -1.6e+157)
     (+ (/ x (+ x 1.0)) (/ y (* (+ x 1.0) t)))
     (if (<= z -3.6e-211)
       t_1
       (if (<= z 2.7e-232)
         (- 1.0 (/ y (/ x z)))
         (if (<= z 2.1e+89) t_1 (/ (+ x (/ y t)) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + ((z * y) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (z <= -1.6e+157) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else if (z <= -3.6e-211) {
		tmp = t_1;
	} else if (z <= 2.7e-232) {
		tmp = 1.0 - (y / (x / z));
	} else if (z <= 2.1e+89) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	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) :: tmp
    t_1 = (x + ((z * y) / ((z * t) - x))) / (x + 1.0d0)
    if (z <= (-1.6d+157)) then
        tmp = (x / (x + 1.0d0)) + (y / ((x + 1.0d0) * t))
    else if (z <= (-3.6d-211)) then
        tmp = t_1
    else if (z <= 2.7d-232) then
        tmp = 1.0d0 - (y / (x / z))
    else if (z <= 2.1d+89) then
        tmp = t_1
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + ((z * y) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (z <= -1.6e+157) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else if (z <= -3.6e-211) {
		tmp = t_1;
	} else if (z <= 2.7e-232) {
		tmp = 1.0 - (y / (x / z));
	} else if (z <= 2.1e+89) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + ((z * y) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if z <= -1.6e+157:
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t))
	elif z <= -3.6e-211:
		tmp = t_1
	elif z <= 2.7e-232:
		tmp = 1.0 - (y / (x / z))
	elif z <= 2.1e+89:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(z * y) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -1.6e+157)
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(Float64(x + 1.0) * t)));
	elseif (z <= -3.6e-211)
		tmp = t_1;
	elseif (z <= 2.7e-232)
		tmp = Float64(1.0 - Float64(y / Float64(x / z)));
	elseif (z <= 2.1e+89)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + ((z * y) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (z <= -1.6e+157)
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	elseif (z <= -3.6e-211)
		tmp = t_1;
	elseif (z <= 2.7e-232)
		tmp = 1.0 - (y / (x / z));
	elseif (z <= 2.1e+89)
		tmp = t_1;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(z * y), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+157], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-211], t$95$1, If[LessEqual[z, 2.7e-232], N[(1.0 - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+89], t$95$1, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6e157

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in y around inf 70.6%

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

   5. Taylor expanded in t around inf 87.9%

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

      1. +-commutative 87.9%

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

      2. +-commutative 87.9%

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

   7. Simplified 87.9%

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

   if -1.6e157 < z < -3.5999999999999999e-211 or 2.6999999999999999e-232 < z < 2.09999999999999986e89

   1. Initial program 98.4%

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

      1. *-commutative 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 90.1%

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

   if -3.5999999999999999e-211 < z < 2.6999999999999999e-232

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 91.8%

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

   5. Taylor expanded in x around 0 91.9%

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

      1. mul-1-neg 91.9%

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

      2. sub-neg 91.9%

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

   7. Simplified 91.9%

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

   8. Taylor expanded in t around 0 94.6%

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

      1. mul-1-neg 94.6%

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

      2. associate-/l* 94.6%

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

   10. Simplified 94.6%

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

   if 2.09999999999999986e89 < z

   1. Initial program 68.9%

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

      1. *-commutative 68.9%

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

   3. Simplified 68.9%

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

   4. Taylor expanded in z around inf 94.2%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-211}:\\ \;\;\;\;\frac{x + \frac{z \cdot y}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-232}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+89}:\\ \;\;\;\;\frac{x + \frac{z \cdot y}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 5: 94.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+149}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e+157)
   (+ (/ x (+ x 1.0)) (/ y (* (+ x 1.0) t)))
   (if (<= z 5.2e+149)
     (/ (+ x (/ (- (* z y) x) (- (* z t) x))) (+ x 1.0))
     (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e+157) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else if (z <= 5.2e+149) {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	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 (z <= (-2.1d+157)) then
        tmp = (x / (x + 1.0d0)) + (y / ((x + 1.0d0) * t))
    else if (z <= 5.2d+149) then
        tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0d0)
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e+157) {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	} else if (z <= 5.2e+149) {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.1e+157:
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t))
	elif z <= 5.2e+149:
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e+157)
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(Float64(x + 1.0) * t)));
	elseif (z <= 5.2e+149)
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.1e+157)
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	elseif (z <= 5.2e+149)
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e+157], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+149], N[(N[(x + N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e157

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in y around inf 70.6%

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

   5. Taylor expanded in t around inf 87.9%

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

      1. +-commutative 87.9%

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

      2. +-commutative 87.9%

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

   7. Simplified 87.9%

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

   if -2.1e157 < z < 5.19999999999999957e149

   1. Initial program 97.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]

   if 5.19999999999999957e149 < z

   1. Initial program 59.9%

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

      1. *-commutative 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around inf 99.9%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+149}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 6: 79.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -29500000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 56:\\ \;\;\;\;\frac{x + \left(\frac{y}{t} - \frac{\frac{x}{t}}{z}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{z}{x + 1}}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -29500000000.0)
   1.0
   (if (<= x 56.0)
     (/ (+ x (- (/ y t) (/ (/ x t) z))) (+ x 1.0))
     (- 1.0 (/ (/ z (+ x 1.0)) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -29500000000.0) {
		tmp = 1.0;
	} else if (x <= 56.0) {
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-29500000000.0d0)) then
        tmp = 1.0d0
    else if (x <= 56.0d0) then
        tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((z / (x + 1.0d0)) / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -29500000000.0) {
		tmp = 1.0;
	} else if (x <= 56.0) {
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -29500000000.0:
		tmp = 1.0
	elif x <= 56.0:
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0)
	else:
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -29500000000.0)
		tmp = 1.0;
	elseif (x <= 56.0)
		tmp = Float64(Float64(x + Float64(Float64(y / t) - Float64(Float64(x / t) / z))) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(z / Float64(x + 1.0)) / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -29500000000.0)
		tmp = 1.0;
	elseif (x <= 56.0)
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0);
	else
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -29500000000.0], 1.0, If[LessEqual[x, 56.0], N[(N[(x + N[(N[(y / t), $MachinePrecision] - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.95e10

   1. Initial program 88.2%

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

      1. *-commutative 88.2%

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

   3. Simplified 88.2%

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

      1. +-commutative 88.2%

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

      2. div-sub 88.2%

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

      3. associate-+l- 88.2%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in z around 0 95.6%

      \[\leadsto \color{blue}{1} \]

   if -2.95e10 < x < 56

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in t around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. associate-/r* 78.1%

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

   6. Simplified 78.1%

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

   if 56 < x

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around 0 87.4%

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

   5. Taylor expanded in y around inf 92.1%

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

   6. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. distribute-lft-in 85.2%

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

      3. *-rgt-identity 85.2%

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

      4. unpow2 85.2%

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

      5. *-commutative 85.2%

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

      6. associate-*r/ 92.1%

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

      7. sub-neg 92.1%

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

      8. associate-*r/ 85.2%

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

      9. *-commutative 85.2%

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

      10. *-rgt-identity 85.2%

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

      11. unpow2 85.2%

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

      12. distribute-lft-in 85.2%

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

      13. times-frac 92.1%

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

      14. +-commutative 92.1%

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

   8. Simplified 92.1%

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

      1. *-commutative 92.1%

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

      2. clear-num 92.1%

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

      3. un-div-inv 92.1%

         \[\leadsto 1 - \color{blue}{\frac{\frac{z}{x + 1}}{\frac{x}{y}}} \]

   10. Applied egg-rr 92.1%

       \[\leadsto 1 - \color{blue}{\frac{\frac{z}{x + 1}}{\frac{x}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -29500000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 56:\\ \;\;\;\;\frac{x + \left(\frac{y}{t} - \frac{\frac{x}{t}}{z}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{z}{x + 1}}{\frac{x}{y}}\\ \end{array} \]

Alternative 7: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-128}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-38}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -2.5e-62)
     t_1
     (if (<= x -2.5e-128)
       (/ y t)
       (if (<= x -3.5e-162)
         (- x (/ x (* z t)))
         (if (<= x 1.5e-104)
           (/ y t)
           (if (<= x 6.2e-38) (- 1.0 (* y (/ z x))) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -2.5e-62) {
		tmp = t_1;
	} else if (x <= -2.5e-128) {
		tmp = y / t;
	} else if (x <= -3.5e-162) {
		tmp = x - (x / (z * t));
	} else if (x <= 1.5e-104) {
		tmp = y / t;
	} else if (x <= 6.2e-38) {
		tmp = 1.0 - (y * (z / x));
	} 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 / (x + 1.0d0)
    if (x <= (-2.5d-62)) then
        tmp = t_1
    else if (x <= (-2.5d-128)) then
        tmp = y / t
    else if (x <= (-3.5d-162)) then
        tmp = x - (x / (z * t))
    else if (x <= 1.5d-104) then
        tmp = y / t
    else if (x <= 6.2d-38) then
        tmp = 1.0d0 - (y * (z / x))
    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 / (x + 1.0);
	double tmp;
	if (x <= -2.5e-62) {
		tmp = t_1;
	} else if (x <= -2.5e-128) {
		tmp = y / t;
	} else if (x <= -3.5e-162) {
		tmp = x - (x / (z * t));
	} else if (x <= 1.5e-104) {
		tmp = y / t;
	} else if (x <= 6.2e-38) {
		tmp = 1.0 - (y * (z / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -2.5e-62:
		tmp = t_1
	elif x <= -2.5e-128:
		tmp = y / t
	elif x <= -3.5e-162:
		tmp = x - (x / (z * t))
	elif x <= 1.5e-104:
		tmp = y / t
	elif x <= 6.2e-38:
		tmp = 1.0 - (y * (z / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -2.5e-62)
		tmp = t_1;
	elseif (x <= -2.5e-128)
		tmp = Float64(y / t);
	elseif (x <= -3.5e-162)
		tmp = Float64(x - Float64(x / Float64(z * t)));
	elseif (x <= 1.5e-104)
		tmp = Float64(y / t);
	elseif (x <= 6.2e-38)
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -2.5e-62)
		tmp = t_1;
	elseif (x <= -2.5e-128)
		tmp = y / t;
	elseif (x <= -3.5e-162)
		tmp = x - (x / (z * t));
	elseif (x <= 1.5e-104)
		tmp = y / t;
	elseif (x <= 6.2e-38)
		tmp = 1.0 - (y * (z / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e-62], t$95$1, If[LessEqual[x, -2.5e-128], N[(y / t), $MachinePrecision], If[LessEqual[x, -3.5e-162], N[(x - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-104], N[(y / t), $MachinePrecision], If[LessEqual[x, 6.2e-38], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.5000000000000001e-62 or 6.19999999999999966e-38 < x

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 86.0%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   5. Step-by-step derivation

      1. +-commutative 86.0%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   6. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   if -2.5000000000000001e-62 < x < -2.5000000000000001e-128 or -3.4999999999999999e-162 < x < 1.5000000000000001e-104

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

      1. +-commutative 88.0%

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

      2. div-sub 88.1%

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

      3. associate-+l- 88.1%

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

   5. Applied egg-rr 88.1%

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

      1. clear-num 88.1%

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

      2. inv-pow 88.1%

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

   7. Applied egg-rr 88.1%

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

      1. unpow-1 88.1%

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

   9. Simplified 88.1%

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

   10. Taylor expanded in x around 0 67.0%

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

   if -2.5000000000000001e-128 < x < -3.4999999999999999e-162

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 87.8%

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

   5. Taylor expanded in t around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. unsub-neg 76.0%

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

      3. *-commutative 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in x around 0 75.8%

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

      1. distribute-rgt-out-- 75.8%

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

      2. *-lft-identity 75.8%

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

      3. *-commutative 75.8%

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

      4. associate-*l/ 76.0%

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

      5. *-lft-identity 76.0%

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

      6. *-commutative 76.0%

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

   10. Simplified 76.0%

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

   if 1.5000000000000001e-104 < x < 6.19999999999999966e-38

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 51.6%

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

   5. Taylor expanded in y around inf 52.6%

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

   6. Taylor expanded in z around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. distribute-lft-in 58.5%

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

      3. *-rgt-identity 58.5%

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

      4. unpow2 58.5%

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

      5. *-commutative 58.5%

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

      6. associate-*r/ 52.6%

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

      7. sub-neg 52.6%

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

      8. associate-*r/ 58.5%

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

      9. *-commutative 58.5%

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

      10. *-rgt-identity 58.5%

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

      11. unpow2 58.5%

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

      12. distribute-lft-in 58.5%

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

      13. times-frac 52.6%

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

      14. +-commutative 52.6%

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

   8. Simplified 52.6%

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

   9. Taylor expanded in x around 0 58.5%

      \[\leadsto 1 - \color{blue}{\frac{y \cdot z}{x}} \]
   10. Step-by-step derivation

       1. associate-*r/ 58.5%

          \[\leadsto 1 - \color{blue}{y \cdot \frac{z}{x}} \]

   11. Simplified 58.5%

       \[\leadsto 1 - \color{blue}{y \cdot \frac{z}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-128}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-162}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-38}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 8: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-130}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-161}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.75e-62)
   (/ x (+ x 1.0))
   (if (<= x -2.1e-130)
     (/ y t)
     (if (<= x -1.3e-161)
       (- x (/ x (* z t)))
       (if (<= x 1.4e-104)
         (/ y t)
         (if (<= x 1.35e-16)
           (- 1.0 (* y (/ z x)))
           (/ 1.0 (/ (+ x 1.0) x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.75e-62) {
		tmp = x / (x + 1.0);
	} else if (x <= -2.1e-130) {
		tmp = y / t;
	} else if (x <= -1.3e-161) {
		tmp = x - (x / (z * t));
	} else if (x <= 1.4e-104) {
		tmp = y / t;
	} else if (x <= 1.35e-16) {
		tmp = 1.0 - (y * (z / x));
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	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 <= (-1.75d-62)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-2.1d-130)) then
        tmp = y / t
    else if (x <= (-1.3d-161)) then
        tmp = x - (x / (z * t))
    else if (x <= 1.4d-104) then
        tmp = y / t
    else if (x <= 1.35d-16) then
        tmp = 1.0d0 - (y * (z / x))
    else
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.75e-62) {
		tmp = x / (x + 1.0);
	} else if (x <= -2.1e-130) {
		tmp = y / t;
	} else if (x <= -1.3e-161) {
		tmp = x - (x / (z * t));
	} else if (x <= 1.4e-104) {
		tmp = y / t;
	} else if (x <= 1.35e-16) {
		tmp = 1.0 - (y * (z / x));
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.75e-62:
		tmp = x / (x + 1.0)
	elif x <= -2.1e-130:
		tmp = y / t
	elif x <= -1.3e-161:
		tmp = x - (x / (z * t))
	elif x <= 1.4e-104:
		tmp = y / t
	elif x <= 1.35e-16:
		tmp = 1.0 - (y * (z / x))
	else:
		tmp = 1.0 / ((x + 1.0) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.75e-62)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -2.1e-130)
		tmp = Float64(y / t);
	elseif (x <= -1.3e-161)
		tmp = Float64(x - Float64(x / Float64(z * t)));
	elseif (x <= 1.4e-104)
		tmp = Float64(y / t);
	elseif (x <= 1.35e-16)
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	else
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.75e-62)
		tmp = x / (x + 1.0);
	elseif (x <= -2.1e-130)
		tmp = y / t;
	elseif (x <= -1.3e-161)
		tmp = x - (x / (z * t));
	elseif (x <= 1.4e-104)
		tmp = y / t;
	elseif (x <= 1.35e-16)
		tmp = 1.0 - (y * (z / x));
	else
		tmp = 1.0 / ((x + 1.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.75e-62], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-130], N[(y / t), $MachinePrecision], If[LessEqual[x, -1.3e-161], N[(x - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e-104], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.35e-16], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.7500000000000001e-62

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around inf 84.1%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   5. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   6. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   if -1.7500000000000001e-62 < x < -2.10000000000000002e-130 or -1.29999999999999998e-161 < x < 1.4e-104

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

      1. +-commutative 88.0%

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

      2. div-sub 88.1%

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

      3. associate-+l- 88.1%

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

   5. Applied egg-rr 88.1%

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

      1. clear-num 88.1%

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

      2. inv-pow 88.1%

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

   7. Applied egg-rr 88.1%

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

      1. unpow-1 88.1%

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

   9. Simplified 88.1%

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

   10. Taylor expanded in x around 0 67.0%

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

   if -2.10000000000000002e-130 < x < -1.29999999999999998e-161

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 87.8%

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

   5. Taylor expanded in t around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. unsub-neg 76.0%

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

      3. *-commutative 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in x around 0 75.8%

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

      1. distribute-rgt-out-- 75.8%

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

      2. *-lft-identity 75.8%

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

      3. *-commutative 75.8%

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

      4. associate-*l/ 76.0%

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

      5. *-lft-identity 76.0%

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

      6. *-commutative 76.0%

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

   10. Simplified 76.0%

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

   if 1.4e-104 < x < 1.35e-16

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 51.6%

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

   5. Taylor expanded in y around inf 52.6%

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

   6. Taylor expanded in z around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. distribute-lft-in 58.5%

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

      3. *-rgt-identity 58.5%

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

      4. unpow2 58.5%

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

      5. *-commutative 58.5%

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

      6. associate-*r/ 52.6%

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

      7. sub-neg 52.6%

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

      8. associate-*r/ 58.5%

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

      9. *-commutative 58.5%

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

      10. *-rgt-identity 58.5%

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

      11. unpow2 58.5%

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

      12. distribute-lft-in 58.5%

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

      13. times-frac 52.6%

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

      14. +-commutative 52.6%

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

   8. Simplified 52.6%

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

   9. Taylor expanded in x around 0 58.5%

      \[\leadsto 1 - \color{blue}{\frac{y \cdot z}{x}} \]
   10. Step-by-step derivation

       1. associate-*r/ 58.5%

          \[\leadsto 1 - \color{blue}{y \cdot \frac{z}{x}} \]

   11. Simplified 58.5%

       \[\leadsto 1 - \color{blue}{y \cdot \frac{z}{x}} \]

   if 1.35e-16 < x

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in t around inf 88.5%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   5. Step-by-step derivation

      1. +-commutative 88.5%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   6. Simplified 88.5%

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

      1. clear-num 88.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 1}{x}}} \]

      2. inv-pow 88.5%

         \[\leadsto \color{blue}{{\left(\frac{x + 1}{x}\right)}^{-1}} \]

   8. Applied egg-rr 88.5%

      \[\leadsto \color{blue}{{\left(\frac{x + 1}{x}\right)}^{-1}} \]
   9. Step-by-step derivation

      1. unpow-1 88.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 1}{x}}} \]

   10. Simplified 88.5%

       \[\leadsto \color{blue}{\frac{1}{\frac{x + 1}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-130}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-161}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \]

Alternative 9: 81.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-103}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-63}:\\ \;\;\;\;1 - \frac{\frac{z}{x + 1}}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.8e-103)
   (/ (+ x (/ y t)) (+ x 1.0))
   (if (<= t 4.3e-63)
     (- 1.0 (/ (/ z (+ x 1.0)) (/ x y)))
     (+ (/ x (+ x 1.0)) (/ y (* (+ x 1.0) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.8e-103) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (t <= 4.3e-63) {
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	} else {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * 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 <= (-6.8d-103)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (t <= 4.3d-63) then
        tmp = 1.0d0 - ((z / (x + 1.0d0)) / (x / y))
    else
        tmp = (x / (x + 1.0d0)) + (y / ((x + 1.0d0) * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.8e-103) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (t <= 4.3e-63) {
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	} else {
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.8e-103:
		tmp = (x + (y / t)) / (x + 1.0)
	elif t <= 4.3e-63:
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y))
	else:
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.8e-103)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (t <= 4.3e-63)
		tmp = Float64(1.0 - Float64(Float64(z / Float64(x + 1.0)) / Float64(x / y)));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(Float64(x + 1.0) * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.8e-103)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (t <= 4.3e-63)
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	else
		tmp = (x / (x + 1.0)) + (y / ((x + 1.0) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.8e-103], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-63], N[(1.0 - N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.80000000000000006e-103

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in z around inf 85.5%

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

   if -6.80000000000000006e-103 < t < 4.2999999999999999e-63

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 79.7%

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

   5. Taylor expanded in y around inf 79.7%

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

   6. Taylor expanded in z around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-lft-in 75.0%

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

      3. *-rgt-identity 75.0%

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

      4. unpow2 75.0%

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

      5. *-commutative 75.0%

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

      6. associate-*r/ 79.7%

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

      7. sub-neg 79.7%

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

      8. associate-*r/ 75.0%

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

      9. *-commutative 75.0%

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

      10. *-rgt-identity 75.0%

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

      11. unpow2 75.0%

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

      12. distribute-lft-in 75.0%

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

      13. times-frac 80.8%

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

      14. +-commutative 80.8%

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

   8. Simplified 80.8%

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

      1. *-commutative 80.8%

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

      2. clear-num 80.7%

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

      3. un-div-inv 80.8%

         \[\leadsto 1 - \color{blue}{\frac{\frac{z}{x + 1}}{\frac{x}{y}}} \]

   10. Applied egg-rr 80.8%

       \[\leadsto 1 - \color{blue}{\frac{\frac{z}{x + 1}}{\frac{x}{y}}} \]

   if 4.2999999999999999e-63 < t

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in y around inf 78.4%

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

   5. Taylor expanded in t around inf 85.3%

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

      1. +-commutative 85.3%

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

      2. +-commutative 85.3%

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

   7. Simplified 85.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-103}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-63}:\\ \;\;\;\;1 - \frac{\frac{z}{x + 1}}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{\left(x + 1\right) \cdot t}\\ \end{array} \]

Alternative 10: 81.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-103} \lor \neg \left(t \leq 4 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z}{x + 1} \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.2e-103) (not (<= t 4e-64)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* (/ z (+ x 1.0)) (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-103) || !(t <= 4e-64)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / (x + 1.0)) * (y / x));
	}
	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-103)) .or. (.not. (t <= 4d-64))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((z / (x + 1.0d0)) * (y / x))
    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-103) || !(t <= 4e-64)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / (x + 1.0)) * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.2e-103) or not (t <= 4e-64):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((z / (x + 1.0)) * (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.2e-103) || !(t <= 4e-64))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(z / Float64(x + 1.0)) * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.2e-103) || ~((t <= 4e-64)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((z / (x + 1.0)) * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.2e-103], N[Not[LessEqual[t, 4e-64]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2000000000000003e-103 or 3.99999999999999986e-64 < t

   1. Initial program 87.4%

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

      1. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -6.2000000000000003e-103 < t < 3.99999999999999986e-64

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 79.7%

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

   5. Taylor expanded in y around inf 79.7%

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

   6. Taylor expanded in z around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-lft-in 75.0%

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

      3. *-rgt-identity 75.0%

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

      4. unpow2 75.0%

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

      5. *-commutative 75.0%

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

      6. associate-*r/ 79.7%

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

      7. sub-neg 79.7%

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

      8. associate-*r/ 75.0%

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

      9. *-commutative 75.0%

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

      10. *-rgt-identity 75.0%

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

      11. unpow2 75.0%

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

      12. distribute-lft-in 75.0%

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

      13. times-frac 80.8%

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

      14. +-commutative 80.8%

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

   8. Simplified 80.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-103} \lor \neg \left(t \leq 4 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z}{x + 1} \cdot \frac{y}{x}\\ \end{array} \]

Alternative 11: 81.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-103} \lor \neg \left(t \leq 7.4 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{z}{x + 1}}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.5e-103) (not (<= t 7.4e-62)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ (/ z (+ x 1.0)) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-103) || !(t <= 7.4e-62)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.5d-103)) .or. (.not. (t <= 7.4d-62))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((z / (x + 1.0d0)) / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-103) || !(t <= 7.4e-62)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.5e-103) or not (t <= 7.4e-62):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.5e-103) || !(t <= 7.4e-62))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(z / Float64(x + 1.0)) / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.5e-103) || ~((t <= 7.4e-62)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((z / (x + 1.0)) / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.5e-103], N[Not[LessEqual[t, 7.4e-62]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.50000000000000016e-103 or 7.3999999999999996e-62 < t

   1. Initial program 87.4%

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

      1. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -3.50000000000000016e-103 < t < 7.3999999999999996e-62

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 79.7%

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

   5. Taylor expanded in y around inf 79.7%

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

   6. Taylor expanded in z around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-lft-in 75.0%

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

      3. *-rgt-identity 75.0%

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

      4. unpow2 75.0%

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

      5. *-commutative 75.0%

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

      6. associate-*r/ 79.7%

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

      7. sub-neg 79.7%

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

      8. associate-*r/ 75.0%

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

      9. *-commutative 75.0%

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

      10. *-rgt-identity 75.0%

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

      11. unpow2 75.0%

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

      12. distribute-lft-in 75.0%

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

      13. times-frac 80.8%

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

      14. +-commutative 80.8%

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

   8. Simplified 80.8%

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

      1. *-commutative 80.8%

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

      2. clear-num 80.7%

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

      3. un-div-inv 80.8%

         \[\leadsto 1 - \color{blue}{\frac{\frac{z}{x + 1}}{\frac{x}{y}}} \]

   10. Applied egg-rr 80.8%

       \[\leadsto 1 - \color{blue}{\frac{\frac{z}{x + 1}}{\frac{x}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-103} \lor \neg \left(t \leq 7.4 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{z}{x + 1}}{\frac{x}{y}}\\ \end{array} \]

Alternative 12: 68.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-15}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -2.9e-62)
     t_1
     (if (<= x 1.4e-104)
       (/ y t)
       (if (<= x 3.9e-15) (- 1.0 (* y (/ z x))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -2.9e-62) {
		tmp = t_1;
	} else if (x <= 1.4e-104) {
		tmp = y / t;
	} else if (x <= 3.9e-15) {
		tmp = 1.0 - (y * (z / x));
	} 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 / (x + 1.0d0)
    if (x <= (-2.9d-62)) then
        tmp = t_1
    else if (x <= 1.4d-104) then
        tmp = y / t
    else if (x <= 3.9d-15) then
        tmp = 1.0d0 - (y * (z / x))
    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 / (x + 1.0);
	double tmp;
	if (x <= -2.9e-62) {
		tmp = t_1;
	} else if (x <= 1.4e-104) {
		tmp = y / t;
	} else if (x <= 3.9e-15) {
		tmp = 1.0 - (y * (z / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -2.9e-62:
		tmp = t_1
	elif x <= 1.4e-104:
		tmp = y / t
	elif x <= 3.9e-15:
		tmp = 1.0 - (y * (z / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -2.9e-62)
		tmp = t_1;
	elseif (x <= 1.4e-104)
		tmp = Float64(y / t);
	elseif (x <= 3.9e-15)
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -2.9e-62)
		tmp = t_1;
	elseif (x <= 1.4e-104)
		tmp = y / t;
	elseif (x <= 3.9e-15)
		tmp = 1.0 - (y * (z / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e-62], t$95$1, If[LessEqual[x, 1.4e-104], N[(y / t), $MachinePrecision], If[LessEqual[x, 3.9e-15], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.89999999999999986e-62 or 3.90000000000000026e-15 < x

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 86.0%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   5. Step-by-step derivation

      1. +-commutative 86.0%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   6. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   if -2.89999999999999986e-62 < x < 1.4e-104

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

      1. +-commutative 89.1%

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

      2. div-sub 89.1%

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

      3. associate-+l- 89.1%

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

   5. Applied egg-rr 89.1%

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

      1. clear-num 89.2%

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

      2. inv-pow 89.2%

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

   7. Applied egg-rr 89.2%

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

      1. unpow-1 89.2%

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

   9. Simplified 89.2%

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

   10. Taylor expanded in x around 0 61.6%

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

   if 1.4e-104 < x < 3.90000000000000026e-15

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 51.6%

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

   5. Taylor expanded in y around inf 52.6%

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

   6. Taylor expanded in z around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. distribute-lft-in 58.5%

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

      3. *-rgt-identity 58.5%

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

      4. unpow2 58.5%

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

      5. *-commutative 58.5%

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

      6. associate-*r/ 52.6%

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

      7. sub-neg 52.6%

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

      8. associate-*r/ 58.5%

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

      9. *-commutative 58.5%

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

      10. *-rgt-identity 58.5%

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

      11. unpow2 58.5%

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

      12. distribute-lft-in 58.5%

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

      13. times-frac 52.6%

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

      14. +-commutative 52.6%

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

   8. Simplified 52.6%

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

   9. Taylor expanded in x around 0 58.5%

      \[\leadsto 1 - \color{blue}{\frac{y \cdot z}{x}} \]
   10. Step-by-step derivation

       1. associate-*r/ 58.5%

          \[\leadsto 1 - \color{blue}{y \cdot \frac{z}{x}} \]

   11. Simplified 58.5%

       \[\leadsto 1 - \color{blue}{y \cdot \frac{z}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-15}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 13: 78.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-172} \lor \neg \left(z \leq 2.1 \cdot 10^{-155}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.7e-172) (not (<= z 2.1e-155)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.7e-172) || !(z <= 2.1e-155)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y / (x / 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 <= (-3.7d-172)) .or. (.not. (z <= 2.1d-155))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - (y / (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.7e-172) || !(z <= 2.1e-155)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y / (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.7e-172) or not (z <= 2.1e-155):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - (y / (x / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.7e-172) || !(z <= 2.1e-155))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(y / Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.7e-172) || ~((z <= 2.1e-155)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - (y / (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.7e-172], N[Not[LessEqual[z, 2.1e-155]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000001e-172 or 2.1000000000000002e-155 < z

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in z around inf 80.2%

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

   if -3.70000000000000001e-172 < z < 2.1000000000000002e-155

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 82.4%

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

   5. Taylor expanded in x around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. sub-neg 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in t around 0 86.1%

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

      1. mul-1-neg 86.1%

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

      2. associate-/l* 86.1%

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

   10. Simplified 86.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-172} \lor \neg \left(z \leq 2.1 \cdot 10^{-155}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \end{array} \]

Alternative 14: 67.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-62} \lor \neg \left(x \leq 8 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.6e-62) (not (<= x 8e-41))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.6e-62) || !(x <= 8e-41)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.6d-62)) .or. (.not. (x <= 8d-41))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.6e-62) || !(x <= 8e-41)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.6e-62) or not (x <= 8e-41):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.6e-62) || !(x <= 8e-41))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.6e-62) || ~((x <= 8e-41)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.6e-62], N[Not[LessEqual[x, 8e-41]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e-62 or 8.00000000000000005e-41 < x

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 85.4%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   5. Step-by-step derivation

      1. +-commutative 85.4%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   6. Simplified 85.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   if -2.5999999999999999e-62 < x < 8.00000000000000005e-41

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

   3. Simplified 89.7%

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

      1. +-commutative 89.7%

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

      2. div-sub 89.7%

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

      3. associate-+l- 89.7%

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

   5. Applied egg-rr 89.7%

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

      1. clear-num 89.8%

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

      2. inv-pow 89.8%

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

   7. Applied egg-rr 89.8%

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

      1. unpow-1 89.8%

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

   9. Simplified 89.8%

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

   10. Taylor expanded in x around 0 56.3%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-62} \lor \neg \left(x \leq 8 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]

Alternative 15: 67.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.1:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.1) 1.0 (if (<= x 1.5e-104) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.1) {
		tmp = 1.0;
	} else if (x <= 1.5e-104) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	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 <= (-0.1d0)) then
        tmp = 1.0d0
    else if (x <= 1.5d-104) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.1) {
		tmp = 1.0;
	} else if (x <= 1.5e-104) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.1:
		tmp = 1.0
	elif x <= 1.5e-104:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.1)
		tmp = 1.0;
	elseif (x <= 1.5e-104)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -0.1)
		tmp = 1.0;
	elseif (x <= 1.5e-104)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.1], 1.0, If[LessEqual[x, 1.5e-104], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.10000000000000001 or 1.5000000000000001e-104 < x

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

   3. Simplified 89.5%

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

      1. +-commutative 89.5%

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

      2. div-sub 89.5%

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

      3. associate-+l- 89.5%

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

   5. Applied egg-rr 89.5%

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

   6. Taylor expanded in z around 0 83.6%

      \[\leadsto \color{blue}{1} \]

   if -0.10000000000000001 < x < 1.5000000000000001e-104

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

   3. Simplified 88.9%

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

      1. +-commutative 88.9%

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

      2. div-sub 88.9%

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

      3. associate-+l- 88.9%

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

   5. Applied egg-rr 88.9%

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

      1. clear-num 89.0%

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

      2. inv-pow 89.0%

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

   7. Applied egg-rr 89.0%

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

      1. unpow-1 89.0%

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

   9. Simplified 89.0%

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

   10. Taylor expanded in x around 0 54.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.1:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-104}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16: 55.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.092:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.092) 1.0 (if (<= x 8.5e-80) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.092) {
		tmp = 1.0;
	} else if (x <= 8.5e-80) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	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 <= (-0.092d0)) then
        tmp = 1.0d0
    else if (x <= 8.5d-80) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.092) {
		tmp = 1.0;
	} else if (x <= 8.5e-80) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.092:
		tmp = 1.0
	elif x <= 8.5e-80:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.092)
		tmp = 1.0;
	elseif (x <= 8.5e-80)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -0.092)
		tmp = 1.0;
	elseif (x <= 8.5e-80)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.092], 1.0, If[LessEqual[x, 8.5e-80], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.091999999999999998 or 8.49999999999999939e-80 < x

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

   3. Simplified 89.4%

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

      1. +-commutative 89.4%

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

      2. div-sub 89.4%

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

      3. associate-+l- 89.4%

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

   5. Applied egg-rr 89.4%

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

   6. Taylor expanded in z around 0 84.6%

      \[\leadsto \color{blue}{1} \]

   if -0.091999999999999998 < x < 8.49999999999999939e-80

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in t around inf 24.8%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   5. Step-by-step derivation

      1. +-commutative 24.8%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   6. Simplified 24.8%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   7. Taylor expanded in x around 0 23.6%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.092:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17: 53.1% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

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 = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 89.3%

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

   1. *-commutative 89.3%

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

3. Simplified 89.3%

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

   1. +-commutative 89.3%

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

   2. div-sub 89.3%

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

   3. associate-+l- 89.3%

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

5. Applied egg-rr 89.3%

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

6. Taylor expanded in z around 0 53.6%

   \[\leadsto \color{blue}{1} \]

7. Final simplification 53.6%

   \[\leadsto 1 \]

Developer target: 99.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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 / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023334 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

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