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

Percentage Accurate: 89.7% → 98.4%

Time: 16.0s

Alternatives: 14

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: 89.7% 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: 98.4% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	t_2 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(x - Float64(y * z)) / t_2) - x) / Float64(-1.0 - x)) <= Inf)
		tmp = Float64(t_1 + Float64(Float64(y * Float64(z / Float64(t_2 * Float64(x + 1.0)))) + Float64(t_1 / Float64(x - Float64(z * t)))));
	else
		tmp = Float64(t_1 + Float64(y / Float64(t * Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	t_2 = (z * t) - x;
	tmp = 0.0;
	if (((((x - (y * z)) / t_2) - x) / (-1.0 - x)) <= Inf)
		tmp = t_1 + ((y * (z / (t_2 * (x + 1.0)))) + (t_1 / (x - (z * t))));
	else
		tmp = t_1 + (y / (t * (x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in y around 0 94.7%

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

      1. associate--l+ 94.7%

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

      2. +-commutative 94.7%

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

      3. associate-/l* 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. +-commutative 99.8%

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

   7. Simplified 99.8%

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

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

   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. Add Preprocessing

   5. Taylor expanded in t around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{\frac{x - y \cdot z}{t\_1} - x}{-1 - x}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+16}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (- (/ (- x (* y z)) t_1) x) (- -1.0 x))))
   (if (<= t_2 -1e+16)
     (* (/ y (+ x 1.0)) (/ z t_1))
     (if (<= t_2 2e+196) t_2 (+ (/ x (+ x 1.0)) (/ 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)) / t_1) - x) / (-1.0 - x);
	double tmp;
	if (t_2 <= -1e+16) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if (t_2 <= 2e+196) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) + (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) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (((x - (y * z)) / t_1) - x) / ((-1.0d0) - x)
    if (t_2 <= (-1d+16)) then
        tmp = (y / (x + 1.0d0)) * (z / t_1)
    else if (t_2 <= 2d+196) then
        tmp = t_2
    else
        tmp = (x / (x + 1.0d0)) + (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 t_2 = (((x - (y * z)) / t_1) - x) / (-1.0 - x);
	double tmp;
	if (t_2 <= -1e+16) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if (t_2 <= 2e+196) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (((x - (y * z)) / t_1) - x) / (-1.0 - x)
	tmp = 0
	if t_2 <= -1e+16:
		tmp = (y / (x + 1.0)) * (z / t_1)
	elif t_2 <= 2e+196:
		tmp = t_2
	else:
		tmp = (x / (x + 1.0)) + (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(Float64(Float64(x - Float64(y * z)) / t_1) - x) / Float64(-1.0 - x))
	tmp = 0.0
	if (t_2 <= -1e+16)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / t_1));
	elseif (t_2 <= 2e+196)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(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)) / t_1) - x) / (-1.0 - x);
	tmp = 0.0;
	if (t_2 <= -1e+16)
		tmp = (y / (x + 1.0)) * (z / t_1);
	elseif (t_2 <= 2e+196)
		tmp = t_2;
	else
		tmp = (x / (x + 1.0)) + (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[(N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+16], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+196], t$95$2, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $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 #s(literal 1 binary64))) < -1e16

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in y around inf 84.9%

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

      1. times-frac 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

   7. Applied egg-rr 99.7%

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

   if -1e16 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.9999999999999999e196

   1. Initial program 99.8%

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

   if 1.9999999999999999e196 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 22.1%

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

      1. *-commutative 22.1%

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

   3. Simplified 22.1%

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

   5. Taylor expanded in t around inf 96.6%

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

      1. +-commutative 96.6%

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

      2. +-commutative 96.6%

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

      3. +-commutative 96.6%

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

   7. Simplified 96.6%

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

   8. Taylor expanded in z around inf 96.6%

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

      1. +-commutative 96.6%

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

      2. +-commutative 96.6%

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

      3. +-commutative 96.6%

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

   10. Simplified 96.6%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{x - y \cdot z}{z \cdot t - x} - x}{-1 - x} \leq -1 \cdot 10^{+16}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;\frac{\frac{x - y \cdot z}{z \cdot t - x} - x}{-1 - x} \leq 2 \cdot 10^{+196}:\\ \;\;\;\;\frac{\frac{x - y \cdot z}{z \cdot t - x} - x}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+64}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+64)
   (/ (+ x (/ y t)) (+ x 1.0))
   (if (<= z 6.5e-6)
     (/ (+ x (/ (* y z) (- (* z t) x))) (+ x 1.0))
     (+ (/ x (+ x 1.0)) (/ y (* t (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+64) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 6.5e-6) {
		tmp = (x + ((y * z) / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) + (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 <= (-1.05d+64)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (z <= 6.5d-6) then
        tmp = (x + ((y * z) / ((z * t) - x))) / (x + 1.0d0)
    else
        tmp = (x / (x + 1.0d0)) + (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 <= -1.05e+64) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 6.5e-6) {
		tmp = (x + ((y * z) / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+64:
		tmp = (x + (y / t)) / (x + 1.0)
	elif z <= 6.5e-6:
		tmp = (x + ((y * z) / ((z * t) - x))) / (x + 1.0)
	else:
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+64)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (z <= 6.5e-6)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05e+64)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (z <= 6.5e-6)
		tmp = (x + ((y * z) / ((z * t) - x))) / (x + 1.0);
	else
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+64], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-6], N[(N[(x + N[(N[(y * z), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e64

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 91.7%

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

   if -1.05e64 < z < 6.4999999999999996e-6

   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. Add Preprocessing

   5. Taylor expanded in y around inf 86.1%

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

      1. *-commutative 86.1%

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

   7. Simplified 86.1%

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

   if 6.4999999999999996e-6 < z

   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. Add Preprocessing

   5. Taylor expanded in t around inf 87.6%

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

      1. +-commutative 87.6%

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

      2. +-commutative 87.6%

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

      3. +-commutative 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in z around inf 94.4%

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

      1. +-commutative 94.4%

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

      2. +-commutative 94.4%

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

      3. +-commutative 94.4%

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

   10. Simplified 94.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+64}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-28} \lor \neg \left(z \leq 3.5 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.3e-28) (not (<= z 3.5e-102)))
   (+ (/ x (+ x 1.0)) (/ y (* t (+ x 1.0))))
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e-28) || !(z <= 3.5e-102)) {
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	} else {
		tmp = (x + (x / (x - (z * 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 <= (-1.3d-28)) .or. (.not. (z <= 3.5d-102))) then
        tmp = (x / (x + 1.0d0)) + (y / (t * (x + 1.0d0)))
    else
        tmp = (x + (x / (x - (z * 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 <= -1.3e-28) || !(z <= 3.5e-102)) {
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.3e-28) or not (z <= 3.5e-102):
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)))
	else:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.3e-28) || !(z <= 3.5e-102))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(x + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.3e-28) || ~((z <= 3.5e-102)))
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	else
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.3e-28], N[Not[LessEqual[z, 3.5e-102]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e-28 or 3.49999999999999986e-102 < z

   1. Initial program 83.1%

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

      1. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in t around inf 84.9%

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

      1. +-commutative 84.9%

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

      2. +-commutative 84.9%

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

      3. +-commutative 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in z around inf 90.1%

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

      1. +-commutative 90.1%

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

      2. +-commutative 90.1%

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

      3. +-commutative 90.1%

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

   10. Simplified 90.1%

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

   if -1.3e-28 < z < 3.49999999999999986e-102

   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. Add Preprocessing

   5. Taylor expanded in y around 0 80.0%

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

      1. +-commutative 80.0%

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

   7. Simplified 80.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-28} \lor \neg \left(z \leq 3.5 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-29} \lor \neg \left(z \leq 5.6 \cdot 10^{-161}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.8e-29) (not (<= z 5.6e-161)))
   (+ (/ x (+ x 1.0)) (/ y (* t (+ x 1.0))))
   (/ (- (+ x 1.0) (* y (/ z x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-29) || !(z <= 5.6e-161)) {
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	} else {
		tmp = ((x + 1.0) - (y * (z / x))) / (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 <= (-8.8d-29)) .or. (.not. (z <= 5.6d-161))) then
        tmp = (x / (x + 1.0d0)) + (y / (t * (x + 1.0d0)))
    else
        tmp = ((x + 1.0d0) - (y * (z / x))) / (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 <= -8.8e-29) || !(z <= 5.6e-161)) {
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	} else {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.8e-29) or not (z <= 5.6e-161):
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)))
	else:
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.8e-29) || !(z <= 5.6e-161))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(x + 1.0))));
	else
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y * Float64(z / x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.8e-29) || ~((z <= 5.6e-161)))
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	else
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.8e-29], N[Not[LessEqual[z, 5.6e-161]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999961e-29 or 5.59999999999999984e-161 < z

   1. Initial program 83.7%

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

      1. *-commutative 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in t around inf 83.7%

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

      1. +-commutative 83.7%

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

      2. +-commutative 83.7%

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

      3. +-commutative 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in z around inf 89.3%

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

      1. +-commutative 89.3%

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

      2. +-commutative 89.3%

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

      3. +-commutative 89.3%

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

   10. Simplified 89.3%

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

   if -8.79999999999999961e-29 < z < 5.59999999999999984e-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. Add Preprocessing

   5. Taylor expanded in t around 0 82.8%

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

      1. associate-+r+ 82.8%

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

      2. mul-1-neg 82.8%

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

      3. unsub-neg 82.8%

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

      4. +-commutative 82.8%

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

      5. associate-/l* 82.8%

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

      6. +-commutative 82.8%

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

   7. Simplified 82.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-29} \lor \neg \left(z \leq 5.6 \cdot 10^{-161}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-27}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.3 \cdot 10^{-109}:\\ \;\;\;\;\frac{1}{\frac{t}{y}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.35e-27)
   1.0
   (if (<= x 8.3e-109)
     (/ 1.0 (/ t y))
     (if (<= x 2.5e-9) (* x (- 1.0 x)) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.35e-27) {
		tmp = 1.0;
	} else if (x <= 8.3e-109) {
		tmp = 1.0 / (t / y);
	} else if (x <= 2.5e-9) {
		tmp = x * (1.0 - 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 <= (-2.35d-27)) then
        tmp = 1.0d0
    else if (x <= 8.3d-109) then
        tmp = 1.0d0 / (t / y)
    else if (x <= 2.5d-9) then
        tmp = x * (1.0d0 - 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 <= -2.35e-27) {
		tmp = 1.0;
	} else if (x <= 8.3e-109) {
		tmp = 1.0 / (t / y);
	} else if (x <= 2.5e-9) {
		tmp = x * (1.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.35e-27:
		tmp = 1.0
	elif x <= 8.3e-109:
		tmp = 1.0 / (t / y)
	elif x <= 2.5e-9:
		tmp = x * (1.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.35e-27)
		tmp = 1.0;
	elseif (x <= 8.3e-109)
		tmp = Float64(1.0 / Float64(t / y));
	elseif (x <= 2.5e-9)
		tmp = Float64(x * Float64(1.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.35e-27)
		tmp = 1.0;
	elseif (x <= 8.3e-109)
		tmp = 1.0 / (t / y);
	elseif (x <= 2.5e-9)
		tmp = x * (1.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.35e-27], 1.0, If[LessEqual[x, 8.3e-109], N[(1.0 / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-9], N[(x * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.35000000000000016e-27 or 2.5000000000000001e-9 < x

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around inf 87.0%

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

      1. +-commutative 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in x around inf 87.2%

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

   if -2.35000000000000016e-27 < x < 8.29999999999999963e-109

   1. Initial program 91.9%

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

      1. *-commutative 91.9%

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

   3. Simplified 91.9%

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

      1. clear-num 91.8%

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

      2. inv-pow 91.8%

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

      3. fma-neg 91.8%

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

   6. Applied egg-rr 91.8%

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

      1. unpow-1 91.8%

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

      2. fma-neg 91.8%

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

      3. *-commutative 91.8%

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

      4. *-commutative 91.8%

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

   8. Simplified 91.8%

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

   9. Taylor expanded in x around 0 57.7%

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

   if 8.29999999999999963e-109 < x < 2.5000000000000001e-9

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in t around inf 55.7%

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

      1. +-commutative 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in x around 0 55.7%

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

      1. neg-mul-1 55.7%

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

      2. sub-neg 55.7%

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

   10. Simplified 55.7%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-27}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.3 \cdot 10^{-109}:\\ \;\;\;\;\frac{1}{\frac{t}{y}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7e+14) 1.0 (if (<= x 2.5e-5) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e+14) {
		tmp = 1.0;
	} else if (x <= 2.5e-5) {
		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 (x <= (-7d+14)) then
        tmp = 1.0d0
    else if (x <= 2.5d-5) 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 (x <= -7e+14) {
		tmp = 1.0;
	} else if (x <= 2.5e-5) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7e+14:
		tmp = 1.0
	elif x <= 2.5e-5:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7e+14)
		tmp = 1.0;
	elseif (x <= 2.5e-5)
		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 (x <= -7e+14)
		tmp = 1.0;
	elseif (x <= 2.5e-5)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7e+14], 1.0, If[LessEqual[x, 2.5e-5], 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 x < -7e14 or 2.50000000000000012e-5 < x

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t around inf 91.8%

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

      1. +-commutative 91.8%

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

   7. Simplified 91.8%

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

   8. Taylor expanded in x around inf 92.4%

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

   if -7e14 < x < 2.50000000000000012e-5

   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. Add Preprocessing

   5. Taylor expanded in z around inf 75.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-63} \lor \neg \left(x \leq 6.1 \cdot 10^{-109}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.8e-63) (not (<= x 6.1e-109)))
   (/ x (+ x 1.0))
   (/ y (* t (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e-63) || !(x <= 6.1e-109)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 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 ((x <= (-3.8d-63)) .or. (.not. (x <= 6.1d-109))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = 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 ((x <= -3.8e-63) || !(x <= 6.1e-109)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / (t * (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.8e-63) or not (x <= 6.1e-109):
		tmp = x / (x + 1.0)
	else:
		tmp = y / (t * (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.8e-63) || !(x <= 6.1e-109))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.8e-63) || ~((x <= 6.1e-109)))
		tmp = x / (x + 1.0);
	else
		tmp = y / (t * (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.8e-63], N[Not[LessEqual[x, 6.1e-109]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000017e-63 or 6.0999999999999997e-109 < x

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in t around inf 81.6%

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

      1. +-commutative 81.6%

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

   7. Simplified 81.6%

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

   if -3.80000000000000017e-63 < x < 6.0999999999999997e-109

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

   3. Simplified 91.1%

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

      1. clear-num 91.0%

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

      2. inv-pow 91.0%

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

      3. fma-neg 91.0%

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

   6. Applied egg-rr 91.0%

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

      1. unpow-1 91.0%

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

      2. fma-neg 91.0%

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

      3. *-commutative 91.0%

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

      4. *-commutative 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in z around inf 76.4%

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

       1. +-commutative 76.4%

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

   11. Simplified 76.4%

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

   12. Taylor expanded in y around inf 62.2%

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

       1. +-commutative 62.2%

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

   14. Simplified 62.2%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-63} \lor \neg \left(x \leq 6.1 \cdot 10^{-109}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 / ((x + 1.0) / (x + (y * (z / ((z * t) - 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 = 1.0d0 / ((x + 1.0d0) / (x + (y * (z / ((z * t) - x)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing
5. Step-by-step derivation

   1. clear-num 89.1%

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

   2. inv-pow 89.1%

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

   3. fma-neg 89.1%

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

6. Applied egg-rr 89.1%

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

   1. unpow-1 89.1%

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

   2. fma-neg 89.1%

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

   3. *-commutative 89.1%

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

   4. *-commutative 89.1%

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

8. Simplified 89.1%

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

9. Taylor expanded in y around inf 81.8%

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

    1. associate-/l* 90.6%

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

11. Simplified 90.6%

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

12. Final simplification 90.6%

    \[\leadsto \frac{1}{\frac{x + 1}{x + y \cdot \frac{z}{z \cdot t - x}}} \]
13. Add Preprocessing

Alternative 10: 68.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-62} \lor \neg \left(x \leq 9.2 \cdot 10^{-109}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.1e-62) (not (<= x 9.2e-109)))
   (/ x (+ x 1.0))
   (/ 1.0 (/ t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-62) || !(x <= 9.2e-109)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0 / (t / 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 <= (-3.1d-62)) .or. (.not. (x <= 9.2d-109))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = 1.0d0 / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-62) || !(x <= 9.2e-109)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0 / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.1e-62) or not (x <= 9.2e-109):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0 / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.1e-62) || !(x <= 9.2e-109))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(1.0 / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.1e-62) || ~((x <= 9.2e-109)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0 / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.1e-62], N[Not[LessEqual[x, 9.2e-109]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0999999999999999e-62 or 9.2000000000000006e-109 < x

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in t around inf 81.6%

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

      1. +-commutative 81.6%

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

   7. Simplified 81.6%

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

   if -3.0999999999999999e-62 < x < 9.2000000000000006e-109

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

   3. Simplified 91.1%

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

      1. clear-num 91.0%

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

      2. inv-pow 91.0%

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

      3. fma-neg 91.0%

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

   6. Applied egg-rr 91.0%

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

      1. unpow-1 91.0%

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

      2. fma-neg 91.0%

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

      3. *-commutative 91.0%

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

      4. *-commutative 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in x around 0 62.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-62} \lor \neg \left(x \leq 9.2 \cdot 10^{-109}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-41}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4e-41) 1.0 (if (<= x 1.8e-10) (* x (- 1.0 x)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e-41) {
		tmp = 1.0;
	} else if (x <= 1.8e-10) {
		tmp = x * (1.0 - 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 <= (-4d-41)) then
        tmp = 1.0d0
    else if (x <= 1.8d-10) then
        tmp = x * (1.0d0 - 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 <= -4e-41) {
		tmp = 1.0;
	} else if (x <= 1.8e-10) {
		tmp = x * (1.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4e-41:
		tmp = 1.0
	elif x <= 1.8e-10:
		tmp = x * (1.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4e-41)
		tmp = 1.0;
	elseif (x <= 1.8e-10)
		tmp = Float64(x * Float64(1.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4e-41)
		tmp = 1.0;
	elseif (x <= 1.8e-10)
		tmp = x * (1.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4e-41], 1.0, If[LessEqual[x, 1.8e-10], N[(x * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000002e-41 or 1.8e-10 < 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. Add Preprocessing

   5. Taylor expanded in t around inf 85.8%

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

      1. +-commutative 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in x around inf 86.0%

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

   if -4.00000000000000002e-41 < x < 1.8e-10

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t around inf 26.5%

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

      1. +-commutative 26.5%

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

   7. Simplified 26.5%

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

   8. Taylor expanded in x around 0 26.5%

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

      1. neg-mul-1 26.5%

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

      2. sub-neg 26.5%

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

   10. Simplified 26.5%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-41}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;1 - \frac{1}{x}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.9) (- 1.0 (/ 1.0 x)) (if (<= x 6e-11) (* x (- 1.0 x)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.9) {
		tmp = 1.0 - (1.0 / x);
	} else if (x <= 6e-11) {
		tmp = x * (1.0 - 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 <= (-0.9d0)) then
        tmp = 1.0d0 - (1.0d0 / x)
    else if (x <= 6d-11) then
        tmp = x * (1.0d0 - 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 <= -0.9) {
		tmp = 1.0 - (1.0 / x);
	} else if (x <= 6e-11) {
		tmp = x * (1.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.9:
		tmp = 1.0 - (1.0 / x)
	elif x <= 6e-11:
		tmp = x * (1.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.9)
		tmp = Float64(1.0 - Float64(1.0 / x));
	elseif (x <= 6e-11)
		tmp = Float64(x * Float64(1.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -0.9)
		tmp = 1.0 - (1.0 / x);
	elseif (x <= 6e-11)
		tmp = x * (1.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.9], N[(1.0 - N[(1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-11], N[(x * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -0.900000000000000022

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in t around inf 87.6%

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

      1. +-commutative 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in x around inf 87.5%

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

   if -0.900000000000000022 < x < 6e-11

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t around inf 26.2%

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

      1. +-commutative 26.2%

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

   7. Simplified 26.2%

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

   8. Taylor expanded in x around 0 26.0%

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

      1. neg-mul-1 26.0%

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

      2. sub-neg 26.0%

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

   10. Simplified 26.0%

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

   if 6e-11 < x

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around inf 92.4%

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

      1. +-commutative 92.4%

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

   7. Simplified 92.4%

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

   8. Taylor expanded in x around inf 93.7%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;1 - \frac{1}{x}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-40}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.2e-40) 1.0 (if (<= x 3.6e-11) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.2e-40) {
		tmp = 1.0;
	} else if (x <= 3.6e-11) {
		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 <= (-3.2d-40)) then
        tmp = 1.0d0
    else if (x <= 3.6d-11) 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 <= -3.2e-40) {
		tmp = 1.0;
	} else if (x <= 3.6e-11) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.2e-40:
		tmp = 1.0
	elif x <= 3.6e-11:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.2e-40)
		tmp = 1.0;
	elseif (x <= 3.6e-11)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.2e-40)
		tmp = 1.0;
	elseif (x <= 3.6e-11)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.2e-40], 1.0, If[LessEqual[x, 3.6e-11], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.20000000000000002e-40 or 3.59999999999999985e-11 < 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. Add Preprocessing

   5. Taylor expanded in t around inf 85.8%

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

      1. +-commutative 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in x around inf 86.0%

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

   if -3.20000000000000002e-40 < x < 3.59999999999999985e-11

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t around inf 26.5%

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

      1. +-commutative 26.5%

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

   7. Simplified 26.5%

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

   8. Taylor expanded in x around 0 26.3%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-40}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.8% 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 89.1%

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

5. Taylor expanded in t around inf 58.7%

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

   1. +-commutative 58.7%

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

7. Simplified 58.7%

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

8. Taylor expanded in x around inf 52.1%

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

9. Final simplification 52.1%

   \[\leadsto 1 \]
10. Add Preprocessing

Developer target: 99.6% 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 2024059 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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