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

Percentage Accurate: 89.5% → 99.1%

Time: 12.1s

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: 89.5% 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: 99.1% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))) (t_2 (- x (* z t))))
   (if (<= (/ (- x (/ (- (* y z) x) t_2)) (+ x 1.0)) INFINITY)
     (- (+ t_1 (/ t_1 t_2)) (* y (/ (/ z (+ x 1.0)) t_2)))
     (/ (+ x (/ 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 = x - (z * t);
	double tmp;
	if (((x - (((y * z) - x) / t_2)) / (x + 1.0)) <= ((double) INFINITY)) {
		tmp = (t_1 + (t_1 / t_2)) - (y * ((z / (x + 1.0)) / t_2));
	} 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 = x / (x + 1.0);
	double t_2 = x - (z * t);
	double tmp;
	if (((x - (((y * z) - x) / t_2)) / (x + 1.0)) <= Double.POSITIVE_INFINITY) {
		tmp = (t_1 + (t_1 / t_2)) - (y * ((z / (x + 1.0)) / t_2));
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	t_2 = x - (z * t)
	tmp = 0
	if ((x - (((y * z) - x) / t_2)) / (x + 1.0)) <= math.inf:
		tmp = (t_1 + (t_1 / t_2)) - (y * ((z / (x + 1.0)) / t_2))
	else:
		tmp = (x + (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(x - Float64(z * t))
	tmp = 0.0
	if (Float64(Float64(x - Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0)) <= Inf)
		tmp = Float64(Float64(t_1 + Float64(t_1 / t_2)) - Float64(y * Float64(Float64(z / Float64(x + 1.0)) / t_2)));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	t_2 = x - (z * t);
	tmp = 0.0;
	if (((x - (((y * z) - x) / t_2)) / (x + 1.0)) <= Inf)
		tmp = (t_1 + (t_1 / t_2)) - (y * ((z / (x + 1.0)) / t_2));
	else
		tmp = (x + (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[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x - N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(t$95$1 + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $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 92.0%

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

      1. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around -inf 98.4%

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

   6. Taylor expanded in y around 0 92.0%

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

      1. distribute-lft-out 92.0%

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

      2. +-commutative 92.0%

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

      3. *-commutative 92.0%

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

      4. +-commutative 92.0%

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

      5. associate-/l/ 92.0%

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

      6. associate-/l* 98.6%

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

      7. associate-/r* 99.8%

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

      8. +-commutative 99.8%

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

   8. Simplified 99.8%

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

   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 z around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \left(\frac{z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)} + \frac{1}{y}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+195}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- (* y z) x) (- x (* z t)))) (+ x 1.0))))
   (if (<= t_1 -2e+169)
     (* y (+ (/ z (* (- (* z t) x) (+ x 1.0))) (/ 1.0 y)))
     (if (<= t_1 5e+195) t_1 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e+169) {
		tmp = y * ((z / (((z * t) - x) * (x + 1.0))) + (1.0 / y));
	} else if (t_1 <= 5e+195) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0d0)
    if (t_1 <= (-2d+169)) then
        tmp = y * ((z / (((z * t) - x) * (x + 1.0d0))) + (1.0d0 / y))
    else if (t_1 <= 5d+195) then
        tmp = t_1
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e+169) {
		tmp = y * ((z / (((z * t) - x) * (x + 1.0))) + (1.0 / y));
	} else if (t_1 <= 5e+195) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0)
	tmp = 0
	if t_1 <= -2e+169:
		tmp = y * ((z / (((z * t) - x) * (x + 1.0))) + (1.0 / y))
	elif t_1 <= 5e+195:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(Float64(y * z) - x) / Float64(x - Float64(z * t)))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -2e+169)
		tmp = Float64(y * Float64(Float64(z / Float64(Float64(Float64(z * t) - x) * Float64(x + 1.0))) + Float64(1.0 / y)));
	elseif (t_1 <= 5e+195)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -2e+169)
		tmp = y * ((z / (((z * t) - x) * (x + 1.0))) + (1.0 / y));
	elseif (t_1 <= 5e+195)
		tmp = t_1;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+169], N[(y * N[(N[(z / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+195], t$95$1, 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 #s(literal 1 binary64))) < -1.99999999999999987e169

   1. Initial program 56.8%

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

      1. *-commutative 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around -inf 92.9%

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

   6. Taylor expanded in x around inf 92.9%

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

   if -1.99999999999999987e169 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999998e195

   1. Initial program 99.8%

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

   if 4.9999999999999998e195 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 46.5%

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

      1. *-commutative 46.5%

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

   3. Simplified 46.5%

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

   5. Taylor expanded in z around inf 97.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1} \leq -2 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \left(\frac{z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)} + \frac{1}{y}\right)\\ \mathbf{elif}\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1} \leq 5 \cdot 10^{+195}:\\ \;\;\;\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \frac{z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+195}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- (* y z) x) (- x (* z t)))) (+ x 1.0))))
   (if (<= t_1 -2e+169)
     (* y (/ z (* (- (* z t) x) (+ x 1.0))))
     (if (<= t_1 5e+195) t_1 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e+169) {
		tmp = y * (z / (((z * t) - x) * (x + 1.0)));
	} else if (t_1 <= 5e+195) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0d0)
    if (t_1 <= (-2d+169)) then
        tmp = y * (z / (((z * t) - x) * (x + 1.0d0)))
    else if (t_1 <= 5d+195) then
        tmp = t_1
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e+169) {
		tmp = y * (z / (((z * t) - x) * (x + 1.0)));
	} else if (t_1 <= 5e+195) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0)
	tmp = 0
	if t_1 <= -2e+169:
		tmp = y * (z / (((z * t) - x) * (x + 1.0)))
	elif t_1 <= 5e+195:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(Float64(y * z) - x) / Float64(x - Float64(z * t)))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -2e+169)
		tmp = Float64(y * Float64(z / Float64(Float64(Float64(z * t) - x) * Float64(x + 1.0))));
	elseif (t_1 <= 5e+195)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -2e+169)
		tmp = y * (z / (((z * t) - x) * (x + 1.0)));
	elseif (t_1 <= 5e+195)
		tmp = t_1;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+169], N[(y * N[(z / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+195], t$95$1, 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 #s(literal 1 binary64))) < -1.99999999999999987e169

   1. Initial program 56.8%

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

      1. *-commutative 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around -inf 92.9%

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

   6. Taylor expanded in y around inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. associate-/l* 86.4%

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

      3. *-commutative 86.4%

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

      4. +-commutative 86.4%

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

      5. distribute-rgt-neg-out 86.4%

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

      6. distribute-neg-frac 86.4%

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

      7. +-commutative 86.4%

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

      8. *-commutative 86.4%

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

      9. +-commutative 86.4%

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

   8. Simplified 86.4%

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

   if -1.99999999999999987e169 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999998e195

   1. Initial program 99.8%

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

   if 4.9999999999999998e195 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 46.5%

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

      1. *-commutative 46.5%

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

   3. Simplified 46.5%

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

   5. Taylor expanded in z around inf 97.2%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1} \leq -2 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \frac{z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1} \leq 5 \cdot 10^{+195}:\\ \;\;\;\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-73} \lor \neg \left(t \leq 1.3 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\frac{z}{x}}{-1 - x} - \frac{-1}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.45e-73) (not (<= t 1.3e-62)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (* y (- (/ (/ z x) (- -1.0 x)) (/ -1.0 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e-73) || !(t <= 1.3e-62)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = y * (((z / x) / (-1.0 - x)) - (-1.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.45d-73)) .or. (.not. (t <= 1.3d-62))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = y * (((z / x) / ((-1.0d0) - x)) - ((-1.0d0) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.45e-73) || !(t <= 1.3e-62)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = y * (((z / x) / (-1.0 - x)) - (-1.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.45e-73) or not (t <= 1.3e-62):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = y * (((z / x) / (-1.0 - x)) - (-1.0 / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.45e-73) || !(t <= 1.3e-62))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(y * Float64(Float64(Float64(z / x) / Float64(-1.0 - x)) - Float64(-1.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.45e-73) || ~((t <= 1.3e-62)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = y * (((z / x) / (-1.0 - x)) - (-1.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.45e-73], N[Not[LessEqual[t, 1.3e-62]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(z / x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45e-73 or 1.3e-62 < t

   1. Initial program 83.3%

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

      1. *-commutative 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in z around inf 88.1%

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

   if -1.45e-73 < t < 1.3e-62

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around 0 81.2%

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

      1. associate-+r+ 81.2%

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

      2. mul-1-neg 81.2%

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

      3. unsub-neg 81.2%

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

      4. +-commutative 81.2%

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

      5. associate-/l* 84.0%

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

      6. +-commutative 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in y around -inf 83.8%

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

      1. associate-*r* 83.8%

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

      2. neg-mul-1 83.8%

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

      3. sub-neg 83.8%

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

      4. associate-/r* 84.7%

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

      5. +-commutative 84.7%

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

      6. distribute-neg-frac 84.7%

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

      7. metadata-eval 84.7%

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

   10. Simplified 84.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-73} \lor \neg \left(t \leq 1.3 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\frac{z}{x}}{-1 - x} - \frac{-1}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-79} \lor \neg \left(t \leq 1.82 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e-79) (not (<= t 1.82e-62)))
   (/ (+ x (/ 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 ((t <= -3.2e-79) || !(t <= 1.82e-62)) {
		tmp = (x + (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 ((t <= (-3.2d-79)) .or. (.not. (t <= 1.82d-62))) then
        tmp = (x + (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 ((t <= -3.2e-79) || !(t <= 1.82e-62)) {
		tmp = (x + (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 (t <= -3.2e-79) or not (t <= 1.82e-62):
		tmp = (x + (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 ((t <= -3.2e-79) || !(t <= 1.82e-62))
		tmp = Float64(Float64(x + Float64(y / 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 ((t <= -3.2e-79) || ~((t <= 1.82e-62)))
		tmp = (x + (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[t, -3.2e-79], N[Not[LessEqual[t, 1.82e-62]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $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 t < -3.19999999999999988e-79 or 1.81999999999999999e-62 < t

   1. Initial program 83.3%

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

      1. *-commutative 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in z around inf 88.1%

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

   if -3.19999999999999988e-79 < t < 1.81999999999999999e-62

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around 0 81.2%

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

      1. associate-+r+ 81.2%

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

      2. mul-1-neg 81.2%

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

      3. unsub-neg 81.2%

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

      4. +-commutative 81.2%

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

      5. associate-/l* 84.0%

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

      6. +-commutative 84.0%

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

   7. Simplified 84.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-79} \lor \neg \left(t \leq 1.82 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-28}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-114}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 3900000:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7e-28)
   1.0
   (if (<= x 1.4e-114)
     (/ y t)
     (if (<= x 3900000.0) (- 1.0 (/ (* y z) x)) (+ 1.0 (/ -1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e-28) {
		tmp = 1.0;
	} else if (x <= 1.4e-114) {
		tmp = y / t;
	} else if (x <= 3900000.0) {
		tmp = 1.0 - ((y * z) / x);
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-7d-28)) then
        tmp = 1.0d0
    else if (x <= 1.4d-114) then
        tmp = y / t
    else if (x <= 3900000.0d0) then
        tmp = 1.0d0 - ((y * z) / x)
    else
        tmp = 1.0d0 + ((-1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e-28) {
		tmp = 1.0;
	} else if (x <= 1.4e-114) {
		tmp = y / t;
	} else if (x <= 3900000.0) {
		tmp = 1.0 - ((y * z) / x);
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7e-28:
		tmp = 1.0
	elif x <= 1.4e-114:
		tmp = y / t
	elif x <= 3900000.0:
		tmp = 1.0 - ((y * z) / x)
	else:
		tmp = 1.0 + (-1.0 / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7e-28)
		tmp = 1.0;
	elseif (x <= 1.4e-114)
		tmp = Float64(y / t);
	elseif (x <= 3900000.0)
		tmp = Float64(1.0 - Float64(Float64(y * z) / x));
	else
		tmp = Float64(1.0 + Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7e-28)
		tmp = 1.0;
	elseif (x <= 1.4e-114)
		tmp = y / t;
	elseif (x <= 3900000.0)
		tmp = 1.0 - ((y * z) / x);
	else
		tmp = 1.0 + (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7e-28], 1.0, If[LessEqual[x, 1.4e-114], N[(y / t), $MachinePrecision], If[LessEqual[x, 3900000.0], N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.9999999999999999e-28

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around inf 85.6%

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

      1. +-commutative 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in x around inf 87.7%

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

   if -6.9999999999999999e-28 < x < 1.4000000000000001e-114

   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 t around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. cancel-sign-sub-inv 80.0%

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

      4. metadata-eval 80.0%

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

      5. *-lft-identity 80.0%

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

      6. +-commutative 80.0%

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

      7. mul-1-neg 80.0%

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

      8. unsub-neg 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in x around 0 56.7%

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

   if 1.4000000000000001e-114 < x < 3.9e6

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around 0 59.3%

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

      1. associate-+r+ 59.3%

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

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. +-commutative 59.3%

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

      5. associate-/l* 59.5%

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

      6. +-commutative 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in y around 0 59.3%

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

      1. associate-*r/ 59.3%

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

      2. mul-1-neg 59.3%

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

      3. distribute-rgt-neg-out 59.3%

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

      4. +-commutative 59.3%

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

   10. Simplified 59.3%

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

   11. Taylor expanded in x around 0 56.2%

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

   if 3.9e6 < x

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around inf 81.5%

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

      1. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in x around inf 81.5%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-28}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-114}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 3900000:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-73} \lor \neg \left(t \leq 1.35 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot z}{x \cdot \left(-1 - x\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.2e-73) (not (<= t 1.35e-62)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (/ (* y z) (* x (- -1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.2e-73) || !(t <= 1.35e-62)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y * z) / (x * (-1.0 - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.2d-73)) .or. (.not. (t <= 1.35d-62))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((y * z) / (x * ((-1.0d0) - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.2e-73) || !(t <= 1.35e-62)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y * z) / (x * (-1.0 - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.2e-73) or not (t <= 1.35e-62):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + ((y * z) / (x * (-1.0 - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.2e-73) || !(t <= 1.35e-62))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(Float64(y * z) / Float64(x * Float64(-1.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.2e-73) || ~((t <= 1.35e-62)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + ((y * z) / (x * (-1.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.2e-73], N[Not[LessEqual[t, 1.35e-62]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * z), $MachinePrecision] / N[(x * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.20000000000000003e-73 or 1.3500000000000001e-62 < t

   1. Initial program 83.3%

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

      1. *-commutative 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in z around inf 88.1%

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

   if -1.20000000000000003e-73 < t < 1.3500000000000001e-62

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around 0 81.2%

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

      1. associate-+r+ 81.2%

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

      2. mul-1-neg 81.2%

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

      3. unsub-neg 81.2%

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

      4. +-commutative 81.2%

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

      5. associate-/l* 84.0%

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

      6. +-commutative 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in y around 0 81.1%

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

      1. associate-*r/ 81.1%

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

      2. mul-1-neg 81.1%

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

      3. distribute-rgt-neg-out 81.1%

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

      4. +-commutative 81.1%

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

   10. Simplified 81.1%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-73} \lor \neg \left(t \leq 1.35 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot z}{x \cdot \left(-1 - x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-86} \lor \neg \left(t \leq 8.8 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5e-86) (not (<= t 8.8e-63)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ (* y z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e-86) || !(t <= 8.8e-63)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * 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) :: tmp
    if ((t <= (-5d-86)) .or. (.not. (t <= 8.8d-63))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y * z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e-86) || !(t <= 8.8e-63)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * z) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5e-86) or not (t <= 8.8e-63):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y * z) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5e-86) || !(t <= 8.8e-63))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y * z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5e-86) || ~((t <= 8.8e-63)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y * z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5e-86], N[Not[LessEqual[t, 8.8e-63]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.9999999999999999e-86 or 8.7999999999999998e-63 < t

   1. Initial program 83.3%

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

      1. *-commutative 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in z around inf 88.1%

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

   if -4.9999999999999999e-86 < t < 8.7999999999999998e-63

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around 0 81.2%

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

      1. associate-+r+ 81.2%

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

      2. mul-1-neg 81.2%

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

      3. unsub-neg 81.2%

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

      4. +-commutative 81.2%

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

      5. associate-/l* 84.0%

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

      6. +-commutative 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in y around 0 81.1%

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

      1. associate-*r/ 81.1%

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

      2. mul-1-neg 81.1%

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

      3. distribute-rgt-neg-out 81.1%

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

      4. +-commutative 81.1%

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

   10. Simplified 81.1%

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

   11. Taylor expanded in x around 0 74.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-86} \lor \neg \left(t \leq 8.8 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-29}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-30}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.8e-29) 1.0 (if (<= x 3.7e-30) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.8e-29) {
		tmp = 1.0;
	} else if (x <= 3.7e-30) {
		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 <= (-2.8d-29)) then
        tmp = 1.0d0
    else if (x <= 3.7d-30) 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 <= -2.8e-29) {
		tmp = 1.0;
	} else if (x <= 3.7e-30) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.8e-29:
		tmp = 1.0
	elif x <= 3.7e-30:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.8e-29)
		tmp = 1.0;
	elseif (x <= 3.7e-30)
		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 <= -2.8e-29)
		tmp = 1.0;
	elseif (x <= 3.7e-30)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.8e-29], 1.0, If[LessEqual[x, 3.7e-30], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000002e-29 or 3.7000000000000003e-30 < x

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in t around inf 78.9%

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

      1. +-commutative 78.9%

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

   7. Simplified 78.9%

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

   8. Taylor expanded in x around inf 82.1%

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

   if -2.8000000000000002e-29 < x < 3.7000000000000003e-30

   1. Initial program 87.8%

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

      1. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t around -inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. unsub-neg 74.9%

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

      3. cancel-sign-sub-inv 74.9%

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

      4. metadata-eval 74.9%

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

      5. *-lft-identity 74.9%

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

      6. +-commutative 74.9%

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

      7. mul-1-neg 74.9%

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

      8. unsub-neg 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in x around 0 52.2%

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

Alternative 10: 54.1% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 50.1%

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

   1. +-commutative 50.1%

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

7. Simplified 50.1%

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

8. Taylor expanded in x around inf 50.2%

   \[\leadsto \color{blue}{1} \]
9. Add Preprocessing

Alternative 11: 2.6% 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 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 y around -inf 96.6%

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

6. Taylor expanded in x around inf 50.1%

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

   1. add-sqr-sqrt 0.0%

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

   2. sqrt-unprod 2.6%

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

   3. sqr-neg 2.6%

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

   4. mul-1-neg 2.6%

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

   5. mul-1-neg 2.6%

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

   6. sqrt-unprod 2.6%

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

   7. add-sqr-sqrt 2.6%

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

   8. associate-*r* 2.6%

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

   9. frac-2neg 2.6%

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

   10. metadata-eval 2.6%

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

   11. un-div-inv 2.6%

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

   12. neg-mul-1 2.6%

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

8. Applied egg-rr 2.6%

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

9. Taylor expanded in y around 0 2.6%

   \[\leadsto \color{blue}{-1} \]
10. Add Preprocessing

Developer Target 1: 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 2024135 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1)))

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