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

Percentage Accurate: 89.1% → 95.3%

Time: 11.4s

Alternatives: 11

Speedup: 0.3×

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: 89.1% 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: 95.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq 2000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{\frac{t_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 2000000000000.0)
     t_2
     (if (<= t_2 INFINITY)
       (/ (/ y (+ x 1.0)) (/ t_1 z))
       (/ (+ x (/ y t)) (+ x 1.0))))))

C

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= 2000000000000.0)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y / Float64(x + 1.0)) / Float64(t_1 / z));
	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;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= 2000000000000.0)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = (y / (x + 1.0)) / (t_1 / z);
	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]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 2000000000000.0], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 / z), $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 (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 2e12

   1. Initial program 96.2%

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

   if 2e12 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < +inf.0

   1. Initial program 73.3%

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

      1. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in y around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. *-commutative 72.9%

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

      3. times-frac 97.3%

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

      4. +-commutative 97.3%

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

      5. *-commutative 97.3%

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

   6. Simplified 97.3%

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

   7. Taylor expanded in y around 0 72.9%

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

      1. associate-/l* 89.9%

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

      2. +-commutative 89.9%

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

      3. associate-*l/ 97.5%

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

      4. associate-/l/ 97.5%

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

   9. Simplified 97.5%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2000000000000:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{\frac{z \cdot t - x}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2: 70.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+23} \lor \neg \left(x \leq 9.8 \cdot 10^{+54}\right):\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{y}{t} + -1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z (- (* z t) x)))))
   (if (<= x -7.5e-20)
     1.0
     (if (<= x -4.9e-86)
       t_1
       (if (<= x -2.45e-121)
         x
         (if (<= x 1.95e-54)
           t_1
           (if (or (<= x 2.15e+23) (not (<= x 9.8e+54)))
             (- 1.0 (* (/ y x) (/ z x)))
             (+ 1.0 (/ (+ (/ y t) -1.0) x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -7.5e-20) {
		tmp = 1.0;
	} else if (x <= -4.9e-86) {
		tmp = t_1;
	} else if (x <= -2.45e-121) {
		tmp = x;
	} else if (x <= 1.95e-54) {
		tmp = t_1;
	} else if ((x <= 2.15e+23) || !(x <= 9.8e+54)) {
		tmp = 1.0 - ((y / x) * (z / x));
	} else {
		tmp = 1.0 + (((y / t) + -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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / ((z * t) - x))
    if (x <= (-7.5d-20)) then
        tmp = 1.0d0
    else if (x <= (-4.9d-86)) then
        tmp = t_1
    else if (x <= (-2.45d-121)) then
        tmp = x
    else if (x <= 1.95d-54) then
        tmp = t_1
    else if ((x <= 2.15d+23) .or. (.not. (x <= 9.8d+54))) then
        tmp = 1.0d0 - ((y / x) * (z / x))
    else
        tmp = 1.0d0 + (((y / t) + (-1.0d0)) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -7.5e-20) {
		tmp = 1.0;
	} else if (x <= -4.9e-86) {
		tmp = t_1;
	} else if (x <= -2.45e-121) {
		tmp = x;
	} else if (x <= 1.95e-54) {
		tmp = t_1;
	} else if ((x <= 2.15e+23) || !(x <= 9.8e+54)) {
		tmp = 1.0 - ((y / x) * (z / x));
	} else {
		tmp = 1.0 + (((y / t) + -1.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / ((z * t) - x))
	tmp = 0
	if x <= -7.5e-20:
		tmp = 1.0
	elif x <= -4.9e-86:
		tmp = t_1
	elif x <= -2.45e-121:
		tmp = x
	elif x <= 1.95e-54:
		tmp = t_1
	elif (x <= 2.15e+23) or not (x <= 9.8e+54):
		tmp = 1.0 - ((y / x) * (z / x))
	else:
		tmp = 1.0 + (((y / t) + -1.0) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / Float64(Float64(z * t) - x)))
	tmp = 0.0
	if (x <= -7.5e-20)
		tmp = 1.0;
	elseif (x <= -4.9e-86)
		tmp = t_1;
	elseif (x <= -2.45e-121)
		tmp = x;
	elseif (x <= 1.95e-54)
		tmp = t_1;
	elseif ((x <= 2.15e+23) || !(x <= 9.8e+54))
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / x)));
	else
		tmp = Float64(1.0 + Float64(Float64(Float64(y / t) + -1.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / ((z * t) - x));
	tmp = 0.0;
	if (x <= -7.5e-20)
		tmp = 1.0;
	elseif (x <= -4.9e-86)
		tmp = t_1;
	elseif (x <= -2.45e-121)
		tmp = x;
	elseif (x <= 1.95e-54)
		tmp = t_1;
	elseif ((x <= 2.15e+23) || ~((x <= 9.8e+54)))
		tmp = 1.0 - ((y / x) * (z / x));
	else
		tmp = 1.0 + (((y / t) + -1.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e-20], 1.0, If[LessEqual[x, -4.9e-86], t$95$1, If[LessEqual[x, -2.45e-121], x, If[LessEqual[x, 1.95e-54], t$95$1, If[Or[LessEqual[x, 2.15e+23], N[Not[LessEqual[x, 9.8e+54]], $MachinePrecision]], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(N[(y / t), $MachinePrecision] + -1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.49999999999999981e-20

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around inf 73.4%

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

      1. clear-num 73.4%

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

      2. inv-pow 73.4%

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

      3. +-commutative 73.4%

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

      4. +-commutative 73.4%

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

   6. Applied egg-rr 73.4%

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

      1. unpow-1 73.4%

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

   8. Simplified 73.4%

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

   9. Taylor expanded in x around inf 94.3%

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

   if -7.49999999999999981e-20 < x < -4.89999999999999972e-86 or -2.45e-121 < x < 1.95e-54

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in y around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

      3. times-frac 59.0%

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

      4. +-commutative 59.0%

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

      5. *-commutative 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in x around 0 59.0%

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

   if -4.89999999999999972e-86 < x < -2.45e-121

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 73.6%

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

      1. +-commutative 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in x around 0 73.6%

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

   if 1.95e-54 < x < 2.1499999999999999e23 or 9.80000000000000002e54 < x

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in t around 0 84.2%

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

      1. +-commutative 84.2%

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

      2. +-commutative 84.2%

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

      3. associate-+l+ 84.2%

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

      4. +-commutative 84.2%

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

      5. mul-1-neg 84.2%

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

      6. unsub-neg 84.2%

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

      7. associate-/l* 91.7%

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

      8. +-commutative 91.7%

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

   6. Simplified 91.7%

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

   7. Taylor expanded in x around inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unpow2 83.4%

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

      3. associate-/l* 87.4%

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

      4. associate-*r/ 91.0%

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

      5. unsub-neg 91.0%

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

      6. associate-*r/ 87.4%

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

      7. associate-/l* 83.4%

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

      8. times-frac 91.0%

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

   9. Simplified 91.0%

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

   if 2.1499999999999999e23 < x < 9.80000000000000002e54

   1. Initial program 79.9%

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

      1. *-commutative 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in z around inf 88.9%

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

   5. Taylor expanded in x around -inf 88.9%

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

      1. +-commutative 88.9%

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

      2. mul-1-neg 88.9%

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

      3. unsub-neg 88.9%

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

      4. mul-1-neg 88.9%

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

      5. sub-neg 88.9%

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

   7. Simplified 88.9%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+23} \lor \neg \left(x \leq 9.8 \cdot 10^{+54}\right):\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{y}{t} + -1}{x}\\ \end{array} \]

Alternative 3: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.52 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z (- (* z t) x)))))
   (if (<= x -1.7e-18)
     1.0
     (if (<= x -2e-86)
       t_1
       (if (<= x -1.52e-121) x (if (<= x 4.3e-109) t_1 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.7e-18) {
		tmp = 1.0;
	} else if (x <= -2e-86) {
		tmp = t_1;
	} else if (x <= -1.52e-121) {
		tmp = x;
	} else if (x <= 4.3e-109) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / ((z * t) - x))
    if (x <= (-1.7d-18)) then
        tmp = 1.0d0
    else if (x <= (-2d-86)) then
        tmp = t_1
    else if (x <= (-1.52d-121)) then
        tmp = x
    else if (x <= 4.3d-109) then
        tmp = t_1
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.7e-18) {
		tmp = 1.0;
	} else if (x <= -2e-86) {
		tmp = t_1;
	} else if (x <= -1.52e-121) {
		tmp = x;
	} else if (x <= 4.3e-109) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / ((z * t) - x))
	tmp = 0
	if x <= -1.7e-18:
		tmp = 1.0
	elif x <= -2e-86:
		tmp = t_1
	elif x <= -1.52e-121:
		tmp = x
	elif x <= 4.3e-109:
		tmp = t_1
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / Float64(Float64(z * t) - x)))
	tmp = 0.0
	if (x <= -1.7e-18)
		tmp = 1.0;
	elseif (x <= -2e-86)
		tmp = t_1;
	elseif (x <= -1.52e-121)
		tmp = x;
	elseif (x <= 4.3e-109)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / ((z * t) - x));
	tmp = 0.0;
	if (x <= -1.7e-18)
		tmp = 1.0;
	elseif (x <= -2e-86)
		tmp = t_1;
	elseif (x <= -1.52e-121)
		tmp = x;
	elseif (x <= 4.3e-109)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e-18], 1.0, If[LessEqual[x, -2e-86], t$95$1, If[LessEqual[x, -1.52e-121], x, If[LessEqual[x, 4.3e-109], t$95$1, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.70000000000000001e-18 or 4.2999999999999997e-109 < x

   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. Taylor expanded in z around inf 70.5%

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

      1. clear-num 70.5%

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

      2. inv-pow 70.5%

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

      3. +-commutative 70.5%

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

      4. +-commutative 70.5%

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

   6. Applied egg-rr 70.5%

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

      1. unpow-1 70.5%

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

   8. Simplified 70.5%

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

   9. Taylor expanded in x around inf 82.6%

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

   if -1.70000000000000001e-18 < x < -2.00000000000000017e-86 or -1.52e-121 < x < 4.2999999999999997e-109

   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 y around inf 56.5%

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

      1. *-commutative 56.5%

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

      2. *-commutative 56.5%

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

      3. times-frac 61.8%

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

      4. +-commutative 61.8%

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

      5. *-commutative 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in x around 0 61.8%

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

   if -2.00000000000000017e-86 < x < -1.52e-121

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 73.6%

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

      1. +-commutative 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in x around 0 73.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq -1.52 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 70.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z (- (* z t) x)))))
   (if (<= x -1.3e-19)
     1.0
     (if (<= x -1.7e-86)
       t_1
       (if (<= x -2.45e-121)
         x
         (if (<= x 2.9e-54) t_1 (- 1.0 (* (/ y x) (/ z x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.3e-19) {
		tmp = 1.0;
	} else if (x <= -1.7e-86) {
		tmp = t_1;
	} else if (x <= -2.45e-121) {
		tmp = x;
	} else if (x <= 2.9e-54) {
		tmp = t_1;
	} else {
		tmp = 1.0 - ((y / x) * (z / 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / ((z * t) - x))
    if (x <= (-1.3d-19)) then
        tmp = 1.0d0
    else if (x <= (-1.7d-86)) then
        tmp = t_1
    else if (x <= (-2.45d-121)) then
        tmp = x
    else if (x <= 2.9d-54) then
        tmp = t_1
    else
        tmp = 1.0d0 - ((y / x) * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.3e-19) {
		tmp = 1.0;
	} else if (x <= -1.7e-86) {
		tmp = t_1;
	} else if (x <= -2.45e-121) {
		tmp = x;
	} else if (x <= 2.9e-54) {
		tmp = t_1;
	} else {
		tmp = 1.0 - ((y / x) * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / ((z * t) - x))
	tmp = 0
	if x <= -1.3e-19:
		tmp = 1.0
	elif x <= -1.7e-86:
		tmp = t_1
	elif x <= -2.45e-121:
		tmp = x
	elif x <= 2.9e-54:
		tmp = t_1
	else:
		tmp = 1.0 - ((y / x) * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / Float64(Float64(z * t) - x)))
	tmp = 0.0
	if (x <= -1.3e-19)
		tmp = 1.0;
	elseif (x <= -1.7e-86)
		tmp = t_1;
	elseif (x <= -2.45e-121)
		tmp = x;
	elseif (x <= 2.9e-54)
		tmp = t_1;
	else
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / ((z * t) - x));
	tmp = 0.0;
	if (x <= -1.3e-19)
		tmp = 1.0;
	elseif (x <= -1.7e-86)
		tmp = t_1;
	elseif (x <= -2.45e-121)
		tmp = x;
	elseif (x <= 2.9e-54)
		tmp = t_1;
	else
		tmp = 1.0 - ((y / x) * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e-19], 1.0, If[LessEqual[x, -1.7e-86], t$95$1, If[LessEqual[x, -2.45e-121], x, If[LessEqual[x, 2.9e-54], t$95$1, N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.30000000000000006e-19

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around inf 73.4%

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

      1. clear-num 73.4%

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

      2. inv-pow 73.4%

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

      3. +-commutative 73.4%

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

      4. +-commutative 73.4%

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

   6. Applied egg-rr 73.4%

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

      1. unpow-1 73.4%

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

   8. Simplified 73.4%

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

   9. Taylor expanded in x around inf 94.3%

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

   if -1.30000000000000006e-19 < x < -1.7e-86 or -2.45e-121 < x < 2.90000000000000015e-54

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in y around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

      3. times-frac 59.0%

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

      4. +-commutative 59.0%

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

      5. *-commutative 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in x around 0 59.0%

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

   if -1.7e-86 < x < -2.45e-121

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 73.6%

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

      1. +-commutative 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in x around 0 73.6%

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

   if 2.90000000000000015e-54 < x

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in t around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. +-commutative 76.0%

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

      3. associate-+l+ 76.0%

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

      4. +-commutative 76.0%

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

      5. mul-1-neg 76.0%

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

      6. unsub-neg 76.0%

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

      7. associate-/l* 82.5%

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

      8. +-commutative 82.5%

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

   6. Simplified 82.5%

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

   7. Taylor expanded in x around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. unpow2 75.2%

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

      3. associate-/l* 79.8%

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

      4. associate-*r/ 83.1%

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

      5. unsub-neg 83.1%

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

      6. associate-*r/ 79.8%

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

      7. associate-/l* 75.2%

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

      8. times-frac 83.0%

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

   9. Simplified 83.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \end{array} \]

Alternative 5: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-66} \lor \neg \left(t \leq 3.8 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.7e-66) (not (<= t 3.8e+19)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (- 1.0 (/ y (/ x z)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.7e-66) || !(t <= 3.8e+19)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 - (y / (x / z)))) / (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 ((t <= (-2.7d-66)) .or. (.not. (t <= 3.8d+19))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (1.0d0 - (y / (x / z)))) / (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 ((t <= -2.7e-66) || !(t <= 3.8e+19)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.7e-66) or not (t <= 3.8e+19):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.7e-66) || !(t <= 3.8e+19))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(1.0 - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.7e-66) || ~((t <= 3.8e+19)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.7e-66], N[Not[LessEqual[t, 3.8e+19]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.69999999999999996e-66 or 3.8e19 < t

   1. Initial program 86.1%

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

      1. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in z around inf 87.7%

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

   if -2.69999999999999996e-66 < t < 3.8e19

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in t around 0 75.1%

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

      1. +-commutative 75.1%

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

      2. +-commutative 75.1%

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

      3. associate-+l+ 75.1%

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

      4. +-commutative 75.1%

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

      5. mul-1-neg 75.1%

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

      6. unsub-neg 75.1%

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

      7. associate-/l* 79.3%

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

      8. +-commutative 79.3%

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

   6. Simplified 79.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-66} \lor \neg \left(t \leq 3.8 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \]

Alternative 6: 81.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{-67} \lor \neg \left(t \leq 1.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.8e-67) (not (<= t 1.5e+19)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* (/ y x) (/ z (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.8e-67) || !(t <= 1.5e+19)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / x) * (z / (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 ((t <= (-9.8d-67)) .or. (.not. (t <= 1.5d+19))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y / x) * (z / (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 ((t <= -9.8e-67) || !(t <= 1.5e+19)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.8e-67) or not (t <= 1.5e+19):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.8e-67) || !(t <= 1.5e+19))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.8e-67) || ~((t <= 1.5e+19)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.8e-67], N[Not[LessEqual[t, 1.5e+19]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.79999999999999987e-67 or 1.5e19 < t

   1. Initial program 86.1%

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

      1. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in z around inf 87.7%

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

   if -9.79999999999999987e-67 < t < 1.5e19

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in t around 0 75.1%

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

      1. +-commutative 75.1%

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

      2. +-commutative 75.1%

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

      3. associate-+l+ 75.1%

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

      4. +-commutative 75.1%

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

      5. mul-1-neg 75.1%

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

      6. unsub-neg 75.1%

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

      7. associate-/l* 79.3%

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

      8. +-commutative 79.3%

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

   6. Simplified 79.3%

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

   7. Taylor expanded in y around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

      3. +-commutative 75.0%

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

      4. *-commutative 75.0%

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

      5. times-frac 75.0%

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

      6. +-commutative 75.0%

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

   9. Simplified 75.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{-67} \lor \neg \left(t \leq 1.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \end{array} \]

Alternative 7: 77.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-112} \lor \neg \left(z \leq 1.8 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5e-112) (not (<= z 1.8e-72))) (/ (+ x (/ y t)) (+ x 1.0)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e-112) || !(z <= 1.8e-72)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} 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 ((z <= (-5d-112)) .or. (.not. (z <= 1.8d-72))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    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 ((z <= -5e-112) || !(z <= 1.8e-72)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5e-112) or not (z <= 1.8e-72):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5e-112) || !(z <= 1.8e-72))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5e-112) || ~((z <= 1.8e-72)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5e-112], N[Not[LessEqual[z, 1.8e-72]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000044e-112 or 1.8e-72 < z

   1. Initial program 81.1%

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

      1. *-commutative 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in z around inf 83.6%

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

   if -5.00000000000000044e-112 < z < 1.8e-72

   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 inf 49.5%

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

      1. clear-num 49.5%

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

      2. inv-pow 49.5%

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

      3. +-commutative 49.5%

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

      4. +-commutative 49.5%

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

   6. Applied egg-rr 49.5%

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

      1. unpow-1 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in x around inf 71.9%

      \[\leadsto \frac{1}{\color{blue}{1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-112} \lor \neg \left(z \leq 1.8 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 68.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-110}:\\ \;\;\;\;\frac{y - x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e-52) 1.0 (if (<= x 3e-110) (/ (- y (* x y)) t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-52) {
		tmp = 1.0;
	} else if (x <= 3e-110) {
		tmp = (y - (x * 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 <= (-2.6d-52)) then
        tmp = 1.0d0
    else if (x <= 3d-110) then
        tmp = (y - (x * 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 <= -2.6e-52) {
		tmp = 1.0;
	} else if (x <= 3e-110) {
		tmp = (y - (x * y)) / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.6e-52:
		tmp = 1.0
	elif x <= 3e-110:
		tmp = (y - (x * y)) / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e-52)
		tmp = 1.0;
	elseif (x <= 3e-110)
		tmp = Float64(Float64(y - Float64(x * y)) / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.6e-52)
		tmp = 1.0;
	elseif (x <= 3e-110)
		tmp = (y - (x * y)) / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e-52], 1.0, If[LessEqual[x, 3e-110], N[(N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e-52 or 2.99999999999999986e-110 < x

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in z around inf 67.8%

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

      1. clear-num 67.8%

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

      2. inv-pow 67.8%

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

      3. +-commutative 67.8%

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

      4. +-commutative 67.8%

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

   6. Applied egg-rr 67.8%

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

      1. unpow-1 67.8%

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

   8. Simplified 67.8%

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

   9. Taylor expanded in x around inf 78.2%

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

   if -2.5999999999999999e-52 < x < 2.99999999999999986e-110

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around inf 71.7%

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

   5. Taylor expanded in y around inf 58.3%

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

      1. associate-/r* 58.3%

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

      2. +-commutative 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in x around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

   10. Simplified 58.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-110}:\\ \;\;\;\;\frac{y - x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 68.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-109}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.1e-52) 1.0 (if (<= x 4.3e-109) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.1e-52) {
		tmp = 1.0;
	} else if (x <= 4.3e-109) {
		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 <= (-2.1d-52)) then
        tmp = 1.0d0
    else if (x <= 4.3d-109) 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 <= -2.1e-52) {
		tmp = 1.0;
	} else if (x <= 4.3e-109) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.1e-52:
		tmp = 1.0
	elif x <= 4.3e-109:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.1e-52)
		tmp = 1.0;
	elseif (x <= 4.3e-109)
		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 <= -2.1e-52)
		tmp = 1.0;
	elseif (x <= 4.3e-109)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.1e-52], 1.0, If[LessEqual[x, 4.3e-109], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0999999999999999e-52 or 4.2999999999999997e-109 < x

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in z around inf 67.8%

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

      1. clear-num 67.8%

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

      2. inv-pow 67.8%

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

      3. +-commutative 67.8%

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

      4. +-commutative 67.8%

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

   6. Applied egg-rr 67.8%

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

      1. unpow-1 67.8%

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

   8. Simplified 67.8%

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

   9. Taylor expanded in x around inf 78.2%

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

   if -2.0999999999999999e-52 < x < 4.2999999999999997e-109

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

      1. clear-num 87.5%

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

      2. inv-pow 87.5%

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

   5. Applied egg-rr 87.5%

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

      1. unpow-1 87.5%

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

      2. *-commutative 87.5%

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

      3. *-commutative 87.5%

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

   7. Simplified 87.5%

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

   8. Taylor expanded in x around 0 58.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-109}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 12.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

   1. *-commutative 89.0%

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

3. Simplified 89.0%

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

4. Taylor expanded in t around inf 49.4%

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

   1. +-commutative 49.4%

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

6. Simplified 49.4%

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

7. Taylor expanded in x around 0 11.0%

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

8. Final simplification 11.0%

   \[\leadsto x \]

Alternative 11: 54.0% 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 89.0%

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

   1. *-commutative 89.0%

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

3. Simplified 89.0%

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

4. Taylor expanded in z around inf 69.3%

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

   1. clear-num 69.3%

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

   2. inv-pow 69.3%

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

   3. +-commutative 69.3%

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

   4. +-commutative 69.3%

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

6. Applied egg-rr 69.3%

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

   1. unpow-1 69.3%

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

8. Simplified 69.3%

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

9. Taylor expanded in x around inf 53.3%

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

10. Final simplification 53.3%

    \[\leadsto 1 \]

Developer target: 99.5% 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 2023240 
(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)))