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

Percentage Accurate: 89.2% → 96.0%

Time: 13.9s

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: 89.2% 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: 96.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{x + 1}\\ t_2 := \frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1}\\ t_3 := z \cdot t - x\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+187}:\\ \;\;\;\;\frac{z}{t\_3} \cdot t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+211}:\\ \;\;\;\;\frac{x + {\left(\frac{t\_3}{\mathsf{fma}\left(y, z, -x\right)}\right)}^{-1}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{t\_1 - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (+ x 1.0)))
        (t_2 (/ (- x (/ (- (* y z) x) (- x (* z t)))) (+ x 1.0)))
        (t_3 (- (* z t) x)))
   (if (<= t_2 -2e+187)
     (* (/ z t_3) t_1)
     (if (<= t_2 1e+211)
       (/ (+ x (pow (/ t_3 (fma y z (- x))) -1.0)) (+ x 1.0))
       (+ (/ x (+ x 1.0)) (/ (- t_1 (/ x (* z (+ x 1.0)))) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (x + 1.0);
	double t_2 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0);
	double t_3 = (z * t) - x;
	double tmp;
	if (t_2 <= -2e+187) {
		tmp = (z / t_3) * t_1;
	} else if (t_2 <= 1e+211) {
		tmp = (x + pow((t_3 / fma(y, z, -x)), -1.0)) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) + ((t_1 - (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(x + 1.0))
	t_2 = Float64(Float64(x - Float64(Float64(Float64(y * z) - x) / Float64(x - Float64(z * t)))) / Float64(x + 1.0))
	t_3 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (t_2 <= -2e+187)
		tmp = Float64(Float64(z / t_3) * t_1);
	elseif (t_2 <= 1e+211)
		tmp = Float64(Float64(x + (Float64(t_3 / fma(y, z, Float64(-x))) ^ -1.0)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(t_1 - Float64(x / Float64(z * Float64(x + 1.0)))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+187], N[(N[(z / t$95$3), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 1e+211], N[(N[(x + N[Power[N[(t$95$3 / N[(y * z + (-x)), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $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))) < -1.99999999999999981e187

   1. Initial program 38.0%

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

      1. *-commutative 38.0%

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

   3. Simplified 38.0%

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

      1. clear-num 37.7%

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

      2. inv-pow 37.7%

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

      3. fma-neg 37.7%

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

   6. Applied egg-rr 37.7%

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

   7. Taylor expanded in y around inf 37.2%

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

      1. times-frac 78.7%

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

      2. *-commutative 78.7%

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

   9. Simplified 78.7%

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

   if -1.99999999999999981e187 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999996e210

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

   3. Simplified 98.9%

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

      1. clear-num 99.0%

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

      2. inv-pow 99.0%

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

      3. fma-neg 99.0%

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

   6. Applied egg-rr 99.0%

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

   if 9.9999999999999996e210 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 14.1%

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

      1. *-commutative 14.1%

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

   3. Simplified 14.1%

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

   5. Taylor expanded in t around -inf 95.7%

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

      1. +-commutative 95.7%

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

      2. mul-1-neg 95.7%

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

      3. unsub-neg 95.7%

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

      4. +-commutative 95.7%

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

   7. Simplified 95.7%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1} \leq -2 \cdot 10^{+187}:\\ \;\;\;\;\frac{z}{z \cdot t - x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1} \leq 10^{+211}:\\ \;\;\;\;\frac{x + {\left(\frac{z \cdot t - x}{\mathsf{fma}\left(y, z, -x\right)}\right)}^{-1}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1}\\ t_2 := \frac{y}{x + 1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+289}:\\ \;\;\;\;\frac{z}{z \cdot t - x} \cdot t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+211}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{t\_2 - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- (* y z) x) (- x (* z t)))) (+ x 1.0)))
        (t_2 (/ y (+ x 1.0))))
   (if (<= t_1 -5e+289)
     (* (/ z (- (* z t) x)) t_2)
     (if (<= t_1 1e+211)
       t_1
       (+ (/ x (+ x 1.0)) (/ (- t_2 (/ x (* z (+ x 1.0)))) t))))))

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 t_2 = y / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+289) {
		tmp = (z / ((z * t) - x)) * t_2;
	} else if (t_1 <= 1e+211) {
		tmp = t_1;
	} else {
		tmp = (x / (x + 1.0)) + ((t_2 - (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0d0)
    t_2 = y / (x + 1.0d0)
    if (t_1 <= (-5d+289)) then
        tmp = (z / ((z * t) - x)) * t_2
    else if (t_1 <= 1d+211) then
        tmp = t_1
    else
        tmp = (x / (x + 1.0d0)) + ((t_2 - (x / (z * (x + 1.0d0)))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0);
	double t_2 = y / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+289) {
		tmp = (z / ((z * t) - x)) * t_2;
	} else if (t_1 <= 1e+211) {
		tmp = t_1;
	} else {
		tmp = (x / (x + 1.0)) + ((t_2 - (x / (z * (x + 1.0)))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (((y * z) - x) / (x - (z * t)))) / (x + 1.0)
	t_2 = y / (x + 1.0)
	tmp = 0
	if t_1 <= -5e+289:
		tmp = (z / ((z * t) - x)) * t_2
	elif t_1 <= 1e+211:
		tmp = t_1
	else:
		tmp = (x / (x + 1.0)) + ((t_2 - (x / (z * (x + 1.0)))) / t)
	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))
	t_2 = Float64(y / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -5e+289)
		tmp = Float64(Float64(z / Float64(Float64(z * t) - x)) * t_2);
	elseif (t_1 <= 1e+211)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(t_2 - Float64(x / Float64(z * Float64(x + 1.0)))) / t));
	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);
	t_2 = y / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -5e+289)
		tmp = (z / ((z * t) - x)) * t_2;
	elseif (t_1 <= 1e+211)
		tmp = t_1;
	else
		tmp = (x / (x + 1.0)) + ((t_2 - (x / (z * (x + 1.0)))) / t);
	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]}, Block[{t$95$2 = N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+289], N[(N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 1e+211], t$95$1, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $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))) < -5.00000000000000031e289

   1. Initial program 13.2%

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

      1. *-commutative 13.2%

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

   3. Simplified 13.2%

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

      1. clear-num 13.2%

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

      2. inv-pow 13.2%

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

      3. fma-neg 13.2%

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

   6. Applied egg-rr 13.2%

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

   7. Taylor expanded in y around inf 12.0%

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

      1. times-frac 70.4%

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

      2. *-commutative 70.4%

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

   9. Simplified 70.4%

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

   if -5.00000000000000031e289 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999996e210

   1. Initial program 99.0%

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

   if 9.9999999999999996e210 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 14.1%

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

      1. *-commutative 14.1%

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

   3. Simplified 14.1%

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

   5. Taylor expanded in t around -inf 95.7%

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

      1. +-commutative 95.7%

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

      2. mul-1-neg 95.7%

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

      3. unsub-neg 95.7%

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

      4. +-commutative 95.7%

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

   7. Simplified 95.7%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1} \leq -5 \cdot 10^{+289}:\\ \;\;\;\;\frac{z}{z \cdot t - x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1} \leq 10^{+211}:\\ \;\;\;\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+289}:\\ \;\;\;\;\frac{z}{z \cdot t - x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 10^{+211}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- (* y z) x) (- x (* z t)))) (+ x 1.0))))
   (if (<= t_1 -5e+289)
     (* (/ z (- (* z t) x)) (/ y (+ x 1.0)))
     (if (<= t_1 1e+211) 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 <= -5e+289) {
		tmp = (z / ((z * t) - x)) * (y / (x + 1.0));
	} else if (t_1 <= 1e+211) {
		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 <= (-5d+289)) then
        tmp = (z / ((z * t) - x)) * (y / (x + 1.0d0))
    else if (t_1 <= 1d+211) 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 <= -5e+289) {
		tmp = (z / ((z * t) - x)) * (y / (x + 1.0));
	} else if (t_1 <= 1e+211) {
		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 <= -5e+289:
		tmp = (z / ((z * t) - x)) * (y / (x + 1.0))
	elif t_1 <= 1e+211:
		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 <= -5e+289)
		tmp = Float64(Float64(z / Float64(Float64(z * t) - x)) * Float64(y / Float64(x + 1.0)));
	elseif (t_1 <= 1e+211)
		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 <= -5e+289)
		tmp = (z / ((z * t) - x)) * (y / (x + 1.0));
	elseif (t_1 <= 1e+211)
		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, -5e+289], N[(N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] * N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+211], 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))) < -5.00000000000000031e289

   1. Initial program 13.2%

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

      1. *-commutative 13.2%

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

   3. Simplified 13.2%

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

      1. clear-num 13.2%

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

      2. inv-pow 13.2%

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

      3. fma-neg 13.2%

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

   6. Applied egg-rr 13.2%

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

   7. Taylor expanded in y around inf 12.0%

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

      1. times-frac 70.4%

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

      2. *-commutative 70.4%

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

   9. Simplified 70.4%

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

   if -5.00000000000000031e289 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999996e210

   1. Initial program 99.0%

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

   if 9.9999999999999996e210 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 14.1%

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

      1. *-commutative 14.1%

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

   3. Simplified 14.1%

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

   5. Taylor expanded in z around inf 91.7%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1} \leq -5 \cdot 10^{+289}:\\ \;\;\;\;\frac{z}{z \cdot t - x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1} \leq 10^{+211}:\\ \;\;\;\;\frac{x - \frac{y \cdot z - x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \left(y \cdot z\right) \cdot \frac{-1}{x - z \cdot t}}{x + 1}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{y}{t}}{-1 - x}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-154}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(\frac{y}{t} - \frac{\frac{x}{t}}{z}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (* (* y z) (/ -1.0 (- x (* z t))))) (+ x 1.0))))
   (if (<= z -2.5e+73)
     (- (/ x (+ x 1.0)) (/ (/ y t) (- -1.0 x)))
     (if (<= z -9e-117)
       t_1
       (if (<= z 3.2e-154)
         (/ (- (+ x 1.0) (* y (/ z x))) (+ x 1.0))
         (if (<= z 1.62e+115)
           t_1
           (/ (+ x (- (/ y t) (/ (/ x t) z))) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + ((y * z) * (-1.0 / (x - (z * t))))) / (x + 1.0);
	double tmp;
	if (z <= -2.5e+73) {
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	} else if (z <= -9e-117) {
		tmp = t_1;
	} else if (z <= 3.2e-154) {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	} else if (z <= 1.62e+115) {
		tmp = t_1;
	} else {
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) * ((-1.0d0) / (x - (z * t))))) / (x + 1.0d0)
    if (z <= (-2.5d+73)) then
        tmp = (x / (x + 1.0d0)) - ((y / t) / ((-1.0d0) - x))
    else if (z <= (-9d-117)) then
        tmp = t_1
    else if (z <= 3.2d-154) then
        tmp = ((x + 1.0d0) - (y * (z / x))) / (x + 1.0d0)
    else if (z <= 1.62d+115) then
        tmp = t_1
    else
        tmp = (x + ((y / t) - ((x / t) / z))) / (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) * (-1.0 / (x - (z * t))))) / (x + 1.0);
	double tmp;
	if (z <= -2.5e+73) {
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	} else if (z <= -9e-117) {
		tmp = t_1;
	} else if (z <= 3.2e-154) {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	} else if (z <= 1.62e+115) {
		tmp = t_1;
	} else {
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + ((y * z) * (-1.0 / (x - (z * t))))) / (x + 1.0)
	tmp = 0
	if z <= -2.5e+73:
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x))
	elif z <= -9e-117:
		tmp = t_1
	elif z <= 3.2e-154:
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0)
	elif z <= 1.62e+115:
		tmp = t_1
	else:
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) * Float64(-1.0 / Float64(x - Float64(z * t))))) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -2.5e+73)
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(y / t) / Float64(-1.0 - x)));
	elseif (z <= -9e-117)
		tmp = t_1;
	elseif (z <= 3.2e-154)
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y * Float64(z / x))) / Float64(x + 1.0));
	elseif (z <= 1.62e+115)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(Float64(y / t) - Float64(Float64(x / t) / z))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + ((y * z) * (-1.0 / (x - (z * t))))) / (x + 1.0);
	tmp = 0.0;
	if (z <= -2.5e+73)
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	elseif (z <= -9e-117)
		tmp = t_1;
	elseif (z <= 3.2e-154)
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	elseif (z <= 1.62e+115)
		tmp = t_1;
	else
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] * N[(-1.0 / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+73], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(y / t), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-117], t$95$1, If[LessEqual[z, 3.2e-154], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.62e+115], t$95$1, N[(N[(x + N[(N[(y / t), $MachinePrecision] - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.49999999999999988e73

   1. Initial program 62.0%

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

      1. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in t around -inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. unsub-neg 88.1%

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

      3. sub-neg 88.1%

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

      4. mul-1-neg 88.1%

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

      5. remove-double-neg 88.1%

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

      6. +-commutative 88.1%

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

      7. mul-1-neg 88.1%

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

      8. unsub-neg 88.1%

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

   7. Simplified 88.1%

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

      1. div-sub 88.1%

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

   9. Applied egg-rr 88.1%

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

   10. Taylor expanded in z around inf 88.1%

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

       1. mul-1-neg 88.1%

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

       2. associate-/r* 88.1%

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

       3. +-commutative 88.1%

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

       4. distribute-neg-frac2 88.1%

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

       5. neg-sub0 88.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{\color{blue}{0 - \left(x + 1\right)}} \]

       6. +-commutative 88.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{0 - \color{blue}{\left(1 + x\right)}} \]

       7. associate--r+ 88.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{\color{blue}{\left(0 - 1\right) - x}} \]

       8. metadata-eval 88.1%

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

   12. Simplified 88.1%

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

   if -2.49999999999999988e73 < z < -8.99999999999999939e-117 or 3.20000000000000005e-154 < z < 1.62e115

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

   3. Simplified 97.9%

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

      1. div-inv 97.8%

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

      2. fma-neg 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in y around inf 89.2%

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

      1. *-commutative 89.2%

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

   9. Simplified 89.2%

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

   if -8.99999999999999939e-117 < z < 3.20000000000000005e-154

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 92.2%

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

      1. associate-+r+ 92.2%

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

      2. mul-1-neg 92.2%

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

      3. unsub-neg 92.2%

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

      4. +-commutative 92.2%

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

      5. associate-/l* 92.2%

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

      6. +-commutative 92.2%

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

   7. Simplified 92.2%

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

   if 1.62e115 < z

   1. Initial program 71.5%

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

      1. *-commutative 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in t around inf 92.0%

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

      1. associate--l+ 92.0%

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

      2. associate-/r* 92.0%

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

   7. Simplified 92.0%

      \[\leadsto \frac{\color{blue}{x + \left(\frac{y}{t} - \frac{\frac{x}{t}}{z}\right)}}{x + 1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{y}{t}}{-1 - x}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-117}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{-1}{x - z \cdot t}}{x + 1}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-154}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+115}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{-1}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(\frac{y}{t} - \frac{\frac{x}{t}}{z}\right)}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{y}{t}}{-1 - x}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e-50)
   (- (/ x (+ x 1.0)) (/ (/ y t) (- -1.0 x)))
   (if (<= z 3.1e-97)
     (/ (- (+ x 1.0) (* y (/ z x))) (+ x 1.0))
     (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e-50) {
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	} else if (z <= 3.1e-97) {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.5d-50)) then
        tmp = (x / (x + 1.0d0)) - ((y / t) / ((-1.0d0) - x))
    else if (z <= 3.1d-97) then
        tmp = ((x + 1.0d0) - (y * (z / x))) / (x + 1.0d0)
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e-50) {
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	} else if (z <= 3.1e-97) {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5e-50:
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x))
	elif z <= 3.1e-97:
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e-50)
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(y / t) / Float64(-1.0 - x)));
	elseif (z <= 3.1e-97)
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y * Float64(z / x))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.5e-50)
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	elseif (z <= 3.1e-97)
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e-50], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(y / t), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-97], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999962e-50

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in t around -inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

      3. sub-neg 80.5%

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

      4. mul-1-neg 80.5%

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

      5. remove-double-neg 80.5%

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

      6. +-commutative 80.5%

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

      7. mul-1-neg 80.5%

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

      8. unsub-neg 80.5%

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

   7. Simplified 80.5%

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

      1. div-sub 80.5%

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

   9. Applied egg-rr 80.5%

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

   10. Taylor expanded in z around inf 86.0%

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

       1. mul-1-neg 86.0%

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

       2. associate-/r* 86.0%

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

       3. +-commutative 86.0%

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

       4. distribute-neg-frac2 86.0%

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

       5. neg-sub0 86.0%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{\color{blue}{0 - \left(x + 1\right)}} \]

       6. +-commutative 86.0%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{0 - \color{blue}{\left(1 + x\right)}} \]

       7. associate--r+ 86.0%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{\color{blue}{\left(0 - 1\right) - x}} \]

       8. metadata-eval 86.0%

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

   12. Simplified 86.0%

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

   if -4.49999999999999962e-50 < z < 3.10000000000000002e-97

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 88.8%

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

      1. associate-+r+ 88.8%

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

      2. mul-1-neg 88.8%

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

      3. unsub-neg 88.8%

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

      4. +-commutative 88.8%

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

      5. associate-/l* 88.7%

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

      6. +-commutative 88.7%

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

   7. Simplified 88.7%

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

   if 3.10000000000000002e-97 < z

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 82.1%

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

Alternative 6: 80.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{y}{t}}{-1 - x}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-76}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.26e-51)
   (- (/ x (+ x 1.0)) (/ (/ y t) (- -1.0 x)))
   (if (<= z 8e-76)
     (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))
     (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.26e-51) {
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	} else if (z <= 8e-76) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.26d-51)) then
        tmp = (x / (x + 1.0d0)) - ((y / t) / ((-1.0d0) - x))
    else if (z <= 8d-76) then
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.26e-51) {
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	} else if (z <= 8e-76) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.26e-51:
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x))
	elif z <= 8e-76:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.26e-51)
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(y / t) / Float64(-1.0 - x)));
	elseif (z <= 8e-76)
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.26e-51)
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	elseif (z <= 8e-76)
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.26e-51], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(y / t), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-76], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2600000000000001e-51

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in t around -inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. unsub-neg 79.7%

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

      3. sub-neg 79.7%

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

      4. mul-1-neg 79.7%

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

      5. remove-double-neg 79.7%

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

      6. +-commutative 79.7%

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

      7. mul-1-neg 79.7%

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

      8. unsub-neg 79.7%

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

   7. Simplified 79.7%

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

      1. div-sub 79.7%

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

   9. Applied egg-rr 79.7%

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

   10. Taylor expanded in z around inf 85.1%

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

       1. mul-1-neg 85.1%

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

       2. associate-/r* 85.1%

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

       3. +-commutative 85.1%

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

       4. distribute-neg-frac2 85.1%

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

       5. neg-sub0 85.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{\color{blue}{0 - \left(x + 1\right)}} \]

       6. +-commutative 85.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{0 - \color{blue}{\left(1 + x\right)}} \]

       7. associate--r+ 85.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{\color{blue}{\left(0 - 1\right) - x}} \]

       8. metadata-eval 85.1%

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

   12. Simplified 85.1%

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

   if -1.2600000000000001e-51 < z < 7.99999999999999942e-76

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 83.1%

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

   if 7.99999999999999942e-76 < z

   1. Initial program 86.1%

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

      1. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in z around inf 83.1%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{y}{t}}{-1 - x}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-76}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-57} \lor \neg \left(z \leq 1.9 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e-57) (not (<= z 1.9e-99)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x 1.0) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e-57) || !(z <= 1.9e-99)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + 1.0) / (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 <= (-7.5d-57)) .or. (.not. (z <= 1.9d-99))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + 1.0d0) / (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 <= -7.5e-57) || !(z <= 1.9e-99)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + 1.0) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e-57) or not (z <= 1.9e-99):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + 1.0) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e-57) || !(z <= 1.9e-99))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + 1.0) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e-57) || ~((z <= 1.9e-99)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + 1.0) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e-57], N[Not[LessEqual[z, 1.9e-99]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999973e-57 or 1.8999999999999998e-99 < z

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in z around inf 83.8%

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

   if -7.49999999999999973e-57 < z < 1.8999999999999998e-99

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 76.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-57} \lor \neg \left(z \leq 1.9 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{y}{t}}{-1 - x}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{-97}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e-54)
   (- (/ x (+ x 1.0)) (/ (/ y t) (- -1.0 x)))
   (if (<= z 1.14e-97) (/ (+ x 1.0) (+ x 1.0)) (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e-54) {
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	} else if (z <= 1.14e-97) {
		tmp = (x + 1.0) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.7d-54)) then
        tmp = (x / (x + 1.0d0)) - ((y / t) / ((-1.0d0) - x))
    else if (z <= 1.14d-97) then
        tmp = (x + 1.0d0) / (x + 1.0d0)
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e-54) {
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	} else if (z <= 1.14e-97) {
		tmp = (x + 1.0) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e-54:
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x))
	elif z <= 1.14e-97:
		tmp = (x + 1.0) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e-54)
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(y / t) / Float64(-1.0 - x)));
	elseif (z <= 1.14e-97)
		tmp = Float64(Float64(x + 1.0) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.7e-54)
		tmp = (x / (x + 1.0)) - ((y / t) / (-1.0 - x));
	elseif (z <= 1.14e-97)
		tmp = (x + 1.0) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e-54], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(y / t), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.14e-97], N[(N[(x + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999994e-54

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in t around -inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. unsub-neg 79.7%

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

      3. sub-neg 79.7%

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

      4. mul-1-neg 79.7%

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

      5. remove-double-neg 79.7%

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

      6. +-commutative 79.7%

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

      7. mul-1-neg 79.7%

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

      8. unsub-neg 79.7%

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

   7. Simplified 79.7%

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

      1. div-sub 79.7%

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

   9. Applied egg-rr 79.7%

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

   10. Taylor expanded in z around inf 85.1%

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

       1. mul-1-neg 85.1%

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

       2. associate-/r* 85.1%

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

       3. +-commutative 85.1%

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

       4. distribute-neg-frac2 85.1%

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

       5. neg-sub0 85.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{\color{blue}{0 - \left(x + 1\right)}} \]

       6. +-commutative 85.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{0 - \color{blue}{\left(1 + x\right)}} \]

       7. associate--r+ 85.1%

          \[\leadsto \frac{x}{x + 1} - \frac{\frac{y}{t}}{\color{blue}{\left(0 - 1\right) - x}} \]

       8. metadata-eval 85.1%

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

   12. Simplified 85.1%

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

   if -1.69999999999999994e-54 < z < 1.14e-97

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 76.9%

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

   if 1.14e-97 < z

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 82.1%

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

Alternative 9: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-158} \lor \neg \left(x \leq 2.5 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.6e-158) (not (<= x 2.5e-53)))
   (/ (+ x 1.0) (+ x 1.0))
   (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.6e-158) || !(x <= 2.5e-53)) {
		tmp = (x + 1.0) / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.6d-158)) .or. (.not. (x <= 2.5d-53))) then
        tmp = (x + 1.0d0) / (x + 1.0d0)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.6e-158) || !(x <= 2.5e-53)) {
		tmp = (x + 1.0) / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.6e-158) or not (x <= 2.5e-53):
		tmp = (x + 1.0) / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.6e-158) || !(x <= 2.5e-53))
		tmp = Float64(Float64(x + 1.0) / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.6e-158) || ~((x <= 2.5e-53)))
		tmp = (x + 1.0) / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.6e-158], N[Not[LessEqual[x, 2.5e-53]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.59999999999999991e-158 or 2.5e-53 < 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 z around 0 78.2%

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

   if -3.59999999999999991e-158 < x < 2.5e-53

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t around -inf 74.6%

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

      1. mul-1-neg 74.6%

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

      2. unsub-neg 74.6%

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

      3. sub-neg 74.6%

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

      4. mul-1-neg 74.6%

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

      5. remove-double-neg 74.6%

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

      6. +-commutative 74.6%

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

      7. mul-1-neg 74.6%

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

      8. unsub-neg 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in x around 0 56.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-158} \lor \neg \left(x \leq 2.5 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-54} \lor \neg \left(x \leq 1.45 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.5e-54) (not (<= x 1.45e-54))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e-54) || !(x <= 1.45e-54)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-9.5d-54)) .or. (.not. (x <= 1.45d-54))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e-54) || !(x <= 1.45e-54)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9.5e-54) or not (x <= 1.45e-54):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9.5e-54) || !(x <= 1.45e-54))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -9.5e-54) || ~((x <= 1.45e-54)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9.5e-54], N[Not[LessEqual[x, 1.45e-54]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4999999999999994e-54 or 1.45000000000000007e-54 < x

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in t around inf 81.2%

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

      1. +-commutative 81.2%

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

   7. Simplified 81.2%

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

   if -9.4999999999999994e-54 < x < 1.45000000000000007e-54

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in t around -inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. unsub-neg 69.4%

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

      3. sub-neg 69.4%

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

      4. mul-1-neg 69.4%

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

      5. remove-double-neg 69.4%

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

      6. +-commutative 69.4%

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

      7. mul-1-neg 69.4%

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

      8. unsub-neg 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in x around 0 49.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-54} \lor \neg \left(x \leq 1.45 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 25.2% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \frac{y}{t} \end{array} \]

FPCore

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

C

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

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 = y / t
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return Float64(y / t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(y / t), $MachinePrecision]

Derivation

1. Initial program 88.0%

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

   1. *-commutative 88.0%

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

3. Simplified 88.0%

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

5. Taylor expanded in t around -inf 54.0%

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

   1. mul-1-neg 54.0%

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

   2. unsub-neg 54.0%

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

   3. sub-neg 54.0%

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

   4. mul-1-neg 54.0%

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

   5. remove-double-neg 54.0%

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

   6. +-commutative 54.0%

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

   7. mul-1-neg 54.0%

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

   8. unsub-neg 54.0%

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

7. Simplified 54.0%

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

8. Taylor expanded in x around 0 20.9%

   \[\leadsto \color{blue}{\frac{y}{t}} \]
9. Add Preprocessing

Developer target: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024111 
(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)))