Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 75.2% → 92.7%

Time: 21.6s

Alternatives: 20

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := \frac{y}{\frac{t + t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a\right)}{z}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-252}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (/ y (/ (+ t (* t (fma y (/ b t) a))) z))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -2e-158)
       t_1
       (if (<= t_1 2e-252)
         (/ (+ x (* y (/ z t))) (+ (* b (/ y t)) (+ a 1.0)))
         (if (<= t_1 5e+290)
           t_1
           (if (<= t_1 INFINITY) t_2 (/ (+ z (* x (/ t y))) b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = y / ((t + (t * fma(y, (b / t), a))) / z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -2e-158) {
		tmp = t_1;
	} else if (t_1 <= 2e-252) {
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	} else if (t_1 <= 5e+290) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (z + (x * (t / y))) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(y / Float64(Float64(t + Float64(t * fma(y, Float64(b / t), a))) / z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -2e-158)
		tmp = t_1;
	elseif (t_1 <= 2e-252)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (t_1 <= 5e+290)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(N[(t + N[(t * N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -2e-158], t$95$1, If[LessEqual[t$95$1, 2e-252], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+290], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 4.9999999999999998e290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 37.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 37.0%

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

      2. associate-*l/ 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-*l/ 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in x around 0 62.0%

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

      1. associate-/l* 87.1%

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

      2. distribute-lft-in 87.1%

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

      3. *-rgt-identity 87.1%

         \[\leadsto \frac{y}{\frac{\color{blue}{t} + t \cdot \left(\frac{y \cdot b}{t} + a\right)}{z}} \]

      4. associate-*r/ 83.7%

         \[\leadsto \frac{y}{\frac{t + t \cdot \left(\color{blue}{y \cdot \frac{b}{t}} + a\right)}{z}} \]

      5. fma-def 83.7%

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

   6. Simplified 83.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2.00000000000000013e-158 or 1.99999999999999989e-252 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999998e290

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   if -2.00000000000000013e-158 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.99999999999999989e-252

   1. Initial program 75.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 75.6%

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

      2. associate-*l/ 77.7%

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

      3. *-commutative 77.7%

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

      4. associate-*l/ 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in b around 0 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*r/ 86.4%

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

   6. Simplified 86.4%

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

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

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.2%

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

      3. *-commutative 0.2%

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

      4. associate-*l/ 8.0%

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

   3. Simplified 8.0%

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

   4. Taylor expanded in y around inf 76.3%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 76.3%

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

      2. times-frac 72.3%

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

      3. associate-*r* 88.0%

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

      4. unpow2 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in b around inf 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-*l/ 98.0%

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

      3. *-commutative 98.0%

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

   9. Simplified 98.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t + t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-158}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{-252}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{t + t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \]

Alternative 2: 89.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-252}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (/ z b)
     (if (<= t_1 -2e-158)
       t_1
       (if (<= t_1 2e-252)
         (/ (+ x (* y (/ z t))) (+ (* b (/ y t)) (+ a 1.0)))
         (if (<= t_1 5e+93)
           t_1
           (if (<= t_1 INFINITY)
             (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 (/ y (/ t b)))))
             (/ (+ z (* x (/ t y))) b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z / b;
	} else if (t_1 <= -2e-158) {
		tmp = t_1;
	} else if (t_1 <= 2e-252) {
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	} else if (t_1 <= 5e+93) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = (z + (x * (t / y))) / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z / b;
	} else if (t_1 <= -2e-158) {
		tmp = t_1;
	} else if (t_1 <= 2e-252) {
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	} else if (t_1 <= 5e+93) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = (z + (x * (t / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z / b
	elif t_1 <= -2e-158:
		tmp = t_1
	elif t_1 <= 2e-252:
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0))
	elif t_1 <= 5e+93:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))))
	else:
		tmp = (z + (x * (t / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z / b);
	elseif (t_1 <= -2e-158)
		tmp = t_1;
	elseif (t_1 <= 2e-252)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (t_1 <= 5e+93)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z / b;
	elseif (t_1 <= -2e-158)
		tmp = t_1;
	elseif (t_1 <= 2e-252)
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	elseif (t_1 <= 5e+93)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	else
		tmp = (z + (x * (t / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z / b), $MachinePrecision], If[LessEqual[t$95$1, -2e-158], t$95$1, If[LessEqual[t$95$1, 2e-252], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+93], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 33.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 33.2%

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

      2. associate-*l/ 55.6%

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

      3. *-commutative 55.6%

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

      4. associate-*l/ 55.4%

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

   3. Simplified 55.4%

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

   4. Taylor expanded in t around 0 82.7%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2.00000000000000013e-158 or 1.99999999999999989e-252 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000001e93

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   if -2.00000000000000013e-158 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.99999999999999989e-252

   1. Initial program 75.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 75.6%

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

      2. associate-*l/ 77.7%

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

      3. *-commutative 77.7%

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

      4. associate-*l/ 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in b around 0 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*r/ 86.4%

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

   6. Simplified 86.4%

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

   if 5.0000000000000001e93 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 72.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 72.0%

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

      2. associate-/l* 86.1%

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

      3. associate-*l/ 74.7%

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

      4. *-commutative 74.7%

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

      5. cancel-sign-sub 74.7%

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

      6. *-commutative 74.7%

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

      7. associate-*l/ 86.1%

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

      8. associate-+r- 86.1%

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

      9. associate-*l/ 74.7%

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

      10. *-commutative 74.7%

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

      11. cancel-sign-sub 74.7%

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

      12. *-commutative 74.7%

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

      13. associate-/r/ 86.1%

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

   3. Simplified 86.1%

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

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

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.2%

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

      3. *-commutative 0.2%

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

      4. associate-*l/ 8.0%

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

   3. Simplified 8.0%

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

   4. Taylor expanded in y around inf 76.3%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 76.3%

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

      2. times-frac 72.3%

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

      3. associate-*r* 88.0%

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

      4. unpow2 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in b around inf 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-*l/ 98.0%

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

      3. *-commutative 98.0%

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

   9. Simplified 98.0%

      \[\leadsto \color{blue}{\frac{z + x \cdot \frac{t}{y}}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-158}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{-252}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+93}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \]

Alternative 3: 80.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-16} \lor \neg \left(t \leq -7.8 \cdot 10^{-82} \lor \neg \left(t \leq -7 \cdot 10^{-167}\right) \land t \leq 2.35 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.1e-16)
         (not
          (or (<= t -7.8e-82) (and (not (<= t -7e-167)) (<= t 2.35e-167)))))
   (/ (+ x (* y (/ z t))) (+ (* b (/ y t)) (+ a 1.0)))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.1e-16) || !((t <= -7.8e-82) || (!(t <= -7e-167) && (t <= 2.35e-167)))) {
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.1d-16)) .or. (.not. (t <= (-7.8d-82)) .or. (.not. (t <= (-7d-167))) .and. (t <= 2.35d-167))) then
        tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0d0))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.1e-16) || !((t <= -7.8e-82) || (!(t <= -7e-167) && (t <= 2.35e-167)))) {
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.1e-16) or not ((t <= -7.8e-82) or (not (t <= -7e-167) and (t <= 2.35e-167))):
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.1e-16) || !((t <= -7.8e-82) || (!(t <= -7e-167) && (t <= 2.35e-167))))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.1e-16) || ~(((t <= -7.8e-82) || (~((t <= -7e-167)) && (t <= 2.35e-167)))))
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.1e-16], N[Not[Or[LessEqual[t, -7.8e-82], And[N[Not[LessEqual[t, -7e-167]], $MachinePrecision], LessEqual[t, 2.35e-167]]]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.10000000000000006e-16 or -7.79999999999999947e-82 < t < -6.9999999999999998e-167 or 2.34999999999999985e-167 < t

   1. Initial program 85.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 85.2%

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

      2. associate-*l/ 88.8%

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

      3. *-commutative 88.8%

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

      4. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in b around 0 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*r/ 92.9%

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

   6. Simplified 92.9%

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

   if -4.10000000000000006e-16 < t < -7.79999999999999947e-82 or -6.9999999999999998e-167 < t < 2.34999999999999985e-167

   1. Initial program 55.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 55.0%

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

      2. associate-*l/ 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-*l/ 44.7%

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

   3. Simplified 44.7%

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

   4. Taylor expanded in y around inf 68.1%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 68.1%

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

      2. times-frac 65.1%

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

      3. associate-*r* 69.1%

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

      4. unpow2 69.1%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in b around inf 83.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-16} \lor \neg \left(t \leq -7.8 \cdot 10^{-82} \lor \neg \left(t \leq -7 \cdot 10^{-167}\right) \land t \leq 2.35 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 4: 80.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ t_2 := \frac{t_1}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ t_3 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-168}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t))))
        (t_2 (/ t_1 (+ (* b (/ y t)) (+ a 1.0))))
        (t_3 (/ (+ z (/ (* x t) y)) b)))
   (if (<= t -4.1e-16)
     t_2
     (if (<= t -1.05e-83)
       t_3
       (if (<= t -1.2e-166)
         t_2
         (if (<= t 3.6e-168) t_3 (/ t_1 (+ (* y (/ b t)) (+ a 1.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = t_1 / ((b * (y / t)) + (a + 1.0));
	double t_3 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -4.1e-16) {
		tmp = t_2;
	} else if (t <= -1.05e-83) {
		tmp = t_3;
	} else if (t <= -1.2e-166) {
		tmp = t_2;
	} else if (t <= 3.6e-168) {
		tmp = t_3;
	} else {
		tmp = t_1 / ((y * (b / t)) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    t_2 = t_1 / ((b * (y / t)) + (a + 1.0d0))
    t_3 = (z + ((x * t) / y)) / b
    if (t <= (-4.1d-16)) then
        tmp = t_2
    else if (t <= (-1.05d-83)) then
        tmp = t_3
    else if (t <= (-1.2d-166)) then
        tmp = t_2
    else if (t <= 3.6d-168) then
        tmp = t_3
    else
        tmp = t_1 / ((y * (b / t)) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = t_1 / ((b * (y / t)) + (a + 1.0));
	double t_3 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -4.1e-16) {
		tmp = t_2;
	} else if (t <= -1.05e-83) {
		tmp = t_3;
	} else if (t <= -1.2e-166) {
		tmp = t_2;
	} else if (t <= 3.6e-168) {
		tmp = t_3;
	} else {
		tmp = t_1 / ((y * (b / t)) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	t_2 = t_1 / ((b * (y / t)) + (a + 1.0))
	t_3 = (z + ((x * t) / y)) / b
	tmp = 0
	if t <= -4.1e-16:
		tmp = t_2
	elif t <= -1.05e-83:
		tmp = t_3
	elif t <= -1.2e-166:
		tmp = t_2
	elif t <= 3.6e-168:
		tmp = t_3
	else:
		tmp = t_1 / ((y * (b / t)) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	t_2 = Float64(t_1 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)))
	t_3 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (t <= -4.1e-16)
		tmp = t_2;
	elseif (t <= -1.05e-83)
		tmp = t_3;
	elseif (t <= -1.2e-166)
		tmp = t_2;
	elseif (t <= 3.6e-168)
		tmp = t_3;
	else
		tmp = Float64(t_1 / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	t_2 = t_1 / ((b * (y / t)) + (a + 1.0));
	t_3 = (z + ((x * t) / y)) / b;
	tmp = 0.0;
	if (t <= -4.1e-16)
		tmp = t_2;
	elseif (t <= -1.05e-83)
		tmp = t_3;
	elseif (t <= -1.2e-166)
		tmp = t_2;
	elseif (t <= 3.6e-168)
		tmp = t_3;
	else
		tmp = t_1 / ((y * (b / t)) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[t, -4.1e-16], t$95$2, If[LessEqual[t, -1.05e-83], t$95$3, If[LessEqual[t, -1.2e-166], t$95$2, If[LessEqual[t, 3.6e-168], t$95$3, N[(t$95$1 / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.10000000000000006e-16 or -1.0499999999999999e-83 < t < -1.1999999999999999e-166

   1. Initial program 90.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 90.6%

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

      2. associate-*l/ 93.2%

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

      3. *-commutative 93.2%

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

      4. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in b around 0 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*r/ 95.9%

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

   6. Simplified 95.9%

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

   if -4.10000000000000006e-16 < t < -1.0499999999999999e-83 or -1.1999999999999999e-166 < t < 3.5999999999999999e-168

   1. Initial program 55.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 55.0%

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

      2. associate-*l/ 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-*l/ 44.7%

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

   3. Simplified 44.7%

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

   4. Taylor expanded in y around inf 68.1%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 68.1%

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

      2. times-frac 65.1%

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

      3. associate-*r* 69.1%

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

      4. unpow2 69.1%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in b around inf 83.8%

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

   if 3.5999999999999999e-168 < t

   1. Initial program 81.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 81.7%

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

      2. associate-*l/ 86.0%

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

      3. *-commutative 86.0%

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

      4. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-83}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-166}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-168}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]

Alternative 5: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ t_2 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-167}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) (+ (* y (/ b t)) (+ a 1.0))))
        (t_2 (/ (+ z (/ (* x t) y)) b)))
   (if (<= t -4.1e-16)
     t_1
     (if (<= t -1.15e-83)
       t_2
       (if (<= t -1.7e-167)
         (/ (+ x (* y (/ z t))) (+ (* b (/ y t)) (+ a 1.0)))
         (if (<= t 3.6e-172) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	double t_2 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -4.1e-16) {
		tmp = t_1;
	} else if (t <= -1.15e-83) {
		tmp = t_2;
	} else if (t <= -1.7e-167) {
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	} else if (t <= 3.6e-172) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0d0))
    t_2 = (z + ((x * t) / y)) / b
    if (t <= (-4.1d-16)) then
        tmp = t_1
    else if (t <= (-1.15d-83)) then
        tmp = t_2
    else if (t <= (-1.7d-167)) then
        tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0d0))
    else if (t <= 3.6d-172) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	double t_2 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -4.1e-16) {
		tmp = t_1;
	} else if (t <= -1.15e-83) {
		tmp = t_2;
	} else if (t <= -1.7e-167) {
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	} else if (t <= 3.6e-172) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0))
	t_2 = (z + ((x * t) / y)) / b
	tmp = 0
	if t <= -4.1e-16:
		tmp = t_1
	elif t <= -1.15e-83:
		tmp = t_2
	elif t <= -1.7e-167:
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0))
	elif t <= 3.6e-172:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)))
	t_2 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (t <= -4.1e-16)
		tmp = t_1;
	elseif (t <= -1.15e-83)
		tmp = t_2;
	elseif (t <= -1.7e-167)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (t <= 3.6e-172)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	t_2 = (z + ((x * t) / y)) / b;
	tmp = 0.0;
	if (t <= -4.1e-16)
		tmp = t_1;
	elseif (t <= -1.15e-83)
		tmp = t_2;
	elseif (t <= -1.7e-167)
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	elseif (t <= 3.6e-172)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[t, -4.1e-16], t$95$1, If[LessEqual[t, -1.15e-83], t$95$2, If[LessEqual[t, -1.7e-167], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-172], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.10000000000000006e-16 or 3.60000000000000015e-172 < t

   1. Initial program 84.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 84.6%

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

      2. associate-*l/ 89.1%

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

      3. *-commutative 89.1%

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

      4. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around 0 88.0%

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

      1. associate-/l* 93.6%

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

   6. Simplified 93.6%

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

   if -4.10000000000000006e-16 < t < -1.14999999999999995e-83 or -1.6999999999999999e-167 < t < 3.60000000000000015e-172

   1. Initial program 55.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 55.0%

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

      2. associate-*l/ 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-*l/ 44.7%

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

   3. Simplified 44.7%

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

   4. Taylor expanded in y around inf 68.1%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 68.1%

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

      2. times-frac 65.1%

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

      3. associate-*r* 69.1%

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

      4. unpow2 69.1%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in b around inf 83.8%

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

   if -1.14999999999999995e-83 < t < -1.6999999999999999e-167

   1. Initial program 92.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 92.8%

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

      2. associate-*l/ 86.1%

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

      3. *-commutative 86.1%

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

      4. associate-*l/ 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in b around 0 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-*r/ 86.0%

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

   6. Simplified 86.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-83}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-167}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-172}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]

Alternative 6: 80.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-167}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b)))
   (if (<= t -4.1e-16)
     (/ (+ x (/ y (/ t z))) (+ (* y (/ b t)) (+ a 1.0)))
     (if (<= t -9.2e-83)
       t_1
       (if (<= t -6.3e-167)
         (/ (+ x (* y (/ z t))) (+ (* b (/ y t)) (+ a 1.0)))
         (if (<= t 8e-80)
           t_1
           (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 (/ y (/ t b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -4.1e-16) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else if (t <= -9.2e-83) {
		tmp = t_1;
	} else if (t <= -6.3e-167) {
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	} else if (t <= 8e-80) {
		tmp = t_1;
	} else {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + ((x * t) / y)) / b
    if (t <= (-4.1d-16)) then
        tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0d0))
    else if (t <= (-9.2d-83)) then
        tmp = t_1
    else if (t <= (-6.3d-167)) then
        tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0d0))
    else if (t <= 8d-80) then
        tmp = t_1
    else
        tmp = (x + (z / (t / y))) / (a + (1.0d0 + (y / (t / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -4.1e-16) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else if (t <= -9.2e-83) {
		tmp = t_1;
	} else if (t <= -6.3e-167) {
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	} else if (t <= 8e-80) {
		tmp = t_1;
	} else {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	tmp = 0
	if t <= -4.1e-16:
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0))
	elif t <= -9.2e-83:
		tmp = t_1
	elif t <= -6.3e-167:
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0))
	elif t <= 8e-80:
		tmp = t_1
	else:
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (t <= -4.1e-16)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	elseif (t <= -9.2e-83)
		tmp = t_1;
	elseif (t <= -6.3e-167)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (t <= 8e-80)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	tmp = 0.0;
	if (t <= -4.1e-16)
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	elseif (t <= -9.2e-83)
		tmp = t_1;
	elseif (t <= -6.3e-167)
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	elseif (t <= 8e-80)
		tmp = t_1;
	else
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[t, -4.1e-16], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.2e-83], t$95$1, If[LessEqual[t, -6.3e-167], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-80], t$95$1, N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.10000000000000006e-16

   1. Initial program 90.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 90.0%

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

      2. associate-*l/ 94.9%

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

      3. *-commutative 94.9%

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

      4. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 93.3%

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

      1. associate-/l* 98.3%

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

   6. Simplified 98.3%

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

   if -4.10000000000000006e-16 < t < -9.19999999999999959e-83 or -6.3000000000000001e-167 < t < 7.99999999999999969e-80

   1. Initial program 55.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 55.7%

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

      2. associate-*l/ 51.2%

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

      3. *-commutative 51.2%

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

      4. associate-*l/ 48.1%

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

   3. Simplified 48.1%

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

   4. Taylor expanded in y around inf 64.1%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 64.1%

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

      2. times-frac 61.6%

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

      3. associate-*r* 65.0%

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

      4. unpow2 65.0%

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

   6. Simplified 65.0%

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

   7. Taylor expanded in b around inf 80.8%

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

   if -9.19999999999999959e-83 < t < -6.3000000000000001e-167

   1. Initial program 92.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 92.8%

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

      2. associate-*l/ 86.1%

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

      3. *-commutative 86.1%

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

      4. associate-*l/ 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in b around 0 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-*r/ 86.0%

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

   6. Simplified 86.0%

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

   if 7.99999999999999969e-80 < t

   1. Initial program 84.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 84.9%

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

      2. associate-/l* 89.9%

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

      3. associate-*l/ 95.8%

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

      4. *-commutative 95.8%

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

      5. cancel-sign-sub 95.8%

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

      6. *-commutative 95.8%

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

      7. associate-*l/ 89.9%

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

      8. associate-+r- 89.9%

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

      9. associate-*l/ 95.8%

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

      10. *-commutative 95.8%

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

      11. cancel-sign-sub 95.8%

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

      12. *-commutative 95.8%

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

      13. associate-/r/ 95.8%

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

   3. Simplified 95.8%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-167}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-80}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]

Alternative 7: 53.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{t + t \cdot a}\\ t_2 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-82}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-79}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y z) (+ t (* t a)))) (t_2 (/ x (+ a 1.0))))
   (if (<= t -9.6e+64)
     t_2
     (if (<= t -1e-15)
       t_1
       (if (<= t -1.05e-82)
         (/ z b)
         (if (<= t -7.5e-153) t_1 (if (<= t 9.2e-79) (/ z b) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * z) / (t + (t * a));
	double t_2 = x / (a + 1.0);
	double tmp;
	if (t <= -9.6e+64) {
		tmp = t_2;
	} else if (t <= -1e-15) {
		tmp = t_1;
	} else if (t <= -1.05e-82) {
		tmp = z / b;
	} else if (t <= -7.5e-153) {
		tmp = t_1;
	} else if (t <= 9.2e-79) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / (t + (t * a))
    t_2 = x / (a + 1.0d0)
    if (t <= (-9.6d+64)) then
        tmp = t_2
    else if (t <= (-1d-15)) then
        tmp = t_1
    else if (t <= (-1.05d-82)) then
        tmp = z / b
    else if (t <= (-7.5d-153)) then
        tmp = t_1
    else if (t <= 9.2d-79) then
        tmp = z / b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * z) / (t + (t * a));
	double t_2 = x / (a + 1.0);
	double tmp;
	if (t <= -9.6e+64) {
		tmp = t_2;
	} else if (t <= -1e-15) {
		tmp = t_1;
	} else if (t <= -1.05e-82) {
		tmp = z / b;
	} else if (t <= -7.5e-153) {
		tmp = t_1;
	} else if (t <= 9.2e-79) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * z) / (t + (t * a))
	t_2 = x / (a + 1.0)
	tmp = 0
	if t <= -9.6e+64:
		tmp = t_2
	elif t <= -1e-15:
		tmp = t_1
	elif t <= -1.05e-82:
		tmp = z / b
	elif t <= -7.5e-153:
		tmp = t_1
	elif t <= 9.2e-79:
		tmp = z / b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * z) / Float64(t + Float64(t * a)))
	t_2 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -9.6e+64)
		tmp = t_2;
	elseif (t <= -1e-15)
		tmp = t_1;
	elseif (t <= -1.05e-82)
		tmp = Float64(z / b);
	elseif (t <= -7.5e-153)
		tmp = t_1;
	elseif (t <= 9.2e-79)
		tmp = Float64(z / b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * z) / (t + (t * a));
	t_2 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -9.6e+64)
		tmp = t_2;
	elseif (t <= -1e-15)
		tmp = t_1;
	elseif (t <= -1.05e-82)
		tmp = z / b;
	elseif (t <= -7.5e-153)
		tmp = t_1;
	elseif (t <= 9.2e-79)
		tmp = z / b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / N[(t + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.6e+64], t$95$2, If[LessEqual[t, -1e-15], t$95$1, If[LessEqual[t, -1.05e-82], N[(z / b), $MachinePrecision], If[LessEqual[t, -7.5e-153], t$95$1, If[LessEqual[t, 9.2e-79], N[(z / b), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.59999999999999997e64 or 9.20000000000000047e-79 < t

   1. Initial program 86.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 86.3%

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

      2. associate-*l/ 91.0%

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

      3. *-commutative 91.0%

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

      4. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 65.9%

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

   if -9.59999999999999997e64 < t < -1.0000000000000001e-15 or -1.05e-82 < t < -7.5e-153

   1. Initial program 95.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 95.4%

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

      2. associate-/l* 91.5%

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

      3. associate-*l/ 91.5%

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

      4. *-commutative 91.5%

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

      5. cancel-sign-sub 91.5%

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

      6. *-commutative 91.5%

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

      7. associate-*l/ 91.5%

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

      8. associate-+r- 91.5%

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

      9. associate-*l/ 91.5%

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

      10. *-commutative 91.5%

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

      11. cancel-sign-sub 91.5%

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

      12. *-commutative 91.5%

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

      13. associate-/r/ 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in x around 0 70.1%

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

   5. Taylor expanded in t around inf 60.1%

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

      1. distribute-lft-in 60.1%

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

      2. *-rgt-identity 60.1%

         \[\leadsto \frac{y \cdot z}{\color{blue}{t} + t \cdot a} \]

   7. Simplified 60.1%

      \[\leadsto \frac{y \cdot z}{\color{blue}{t + t \cdot a}} \]

   if -1.0000000000000001e-15 < t < -1.05e-82 or -7.5e-153 < t < 9.20000000000000047e-79

   1. Initial program 56.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 56.6%

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

      2. associate-*l/ 52.3%

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

      3. *-commutative 52.3%

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

      4. associate-*l/ 48.3%

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

   3. Simplified 48.3%

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

   4. Taylor expanded in t around 0 68.1%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-15}:\\ \;\;\;\;\frac{y \cdot z}{t + t \cdot a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-82}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-153}:\\ \;\;\;\;\frac{y \cdot z}{t + t \cdot a}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-79}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 8: 53.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-16}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-85}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-153}:\\ \;\;\;\;\frac{y \cdot z}{t + t \cdot a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-75}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -2.8e+65)
     t_1
     (if (<= t -5e-16)
       (/ (* y (/ z t)) (+ a 1.0))
       (if (<= t -2.35e-85)
         (/ z b)
         (if (<= t -9.2e-153)
           (/ (* y z) (+ t (* t a)))
           (if (<= t 1.02e-75) (/ z b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.8e+65) {
		tmp = t_1;
	} else if (t <= -5e-16) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if (t <= -2.35e-85) {
		tmp = z / b;
	} else if (t <= -9.2e-153) {
		tmp = (y * z) / (t + (t * a));
	} else if (t <= 1.02e-75) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-2.8d+65)) then
        tmp = t_1
    else if (t <= (-5d-16)) then
        tmp = (y * (z / t)) / (a + 1.0d0)
    else if (t <= (-2.35d-85)) then
        tmp = z / b
    else if (t <= (-9.2d-153)) then
        tmp = (y * z) / (t + (t * a))
    else if (t <= 1.02d-75) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.8e+65) {
		tmp = t_1;
	} else if (t <= -5e-16) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if (t <= -2.35e-85) {
		tmp = z / b;
	} else if (t <= -9.2e-153) {
		tmp = (y * z) / (t + (t * a));
	} else if (t <= 1.02e-75) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -2.8e+65:
		tmp = t_1
	elif t <= -5e-16:
		tmp = (y * (z / t)) / (a + 1.0)
	elif t <= -2.35e-85:
		tmp = z / b
	elif t <= -9.2e-153:
		tmp = (y * z) / (t + (t * a))
	elif t <= 1.02e-75:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.8e+65)
		tmp = t_1;
	elseif (t <= -5e-16)
		tmp = Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0));
	elseif (t <= -2.35e-85)
		tmp = Float64(z / b);
	elseif (t <= -9.2e-153)
		tmp = Float64(Float64(y * z) / Float64(t + Float64(t * a)));
	elseif (t <= 1.02e-75)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.8e+65)
		tmp = t_1;
	elseif (t <= -5e-16)
		tmp = (y * (z / t)) / (a + 1.0);
	elseif (t <= -2.35e-85)
		tmp = z / b;
	elseif (t <= -9.2e-153)
		tmp = (y * z) / (t + (t * a));
	elseif (t <= 1.02e-75)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+65], t$95$1, If[LessEqual[t, -5e-16], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.35e-85], N[(z / b), $MachinePrecision], If[LessEqual[t, -9.2e-153], N[(N[(y * z), $MachinePrecision] / N[(t + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-75], N[(z / b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7999999999999999e65 or 1.01999999999999997e-75 < t

   1. Initial program 86.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 86.3%

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

      2. associate-*l/ 91.0%

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

      3. *-commutative 91.0%

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

      4. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 65.9%

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

   if -2.7999999999999999e65 < t < -5.0000000000000004e-16

   1. Initial program 92.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 92.4%

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

      2. associate-*l/ 92.4%

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

      3. *-commutative 92.4%

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

      4. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 92.4%

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

      1. associate-/l* 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in b around 0 77.8%

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

   8. Taylor expanded in x around 0 62.8%

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

      1. associate-*r/ 62.8%

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

   10. Simplified 62.8%

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

   if -5.0000000000000004e-16 < t < -2.35000000000000005e-85 or -9.19999999999999988e-153 < t < 1.01999999999999997e-75

   1. Initial program 56.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 56.6%

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

      2. associate-*l/ 52.3%

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

      3. *-commutative 52.3%

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

      4. associate-*l/ 48.3%

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

   3. Simplified 48.3%

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

   4. Taylor expanded in t around 0 68.1%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if -2.35000000000000005e-85 < t < -9.19999999999999988e-153

   1. Initial program 99.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 99.4%

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

      2. associate-/l* 99.4%

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

      3. associate-*l/ 99.2%

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

      4. *-commutative 99.2%

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

      5. cancel-sign-sub 99.2%

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

      6. *-commutative 99.2%

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

      7. associate-*l/ 99.4%

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

      8. associate-+r- 99.4%

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

      9. associate-*l/ 99.2%

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

      10. *-commutative 99.2%

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

      11. cancel-sign-sub 99.2%

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

      12. *-commutative 99.2%

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

      13. associate-/r/ 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in x around 0 60.9%

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

   5. Taylor expanded in t around inf 57.0%

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

      1. distribute-lft-in 57.0%

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

      2. *-rgt-identity 57.0%

         \[\leadsto \frac{y \cdot z}{\color{blue}{t} + t \cdot a} \]

   7. Simplified 57.0%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-16}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-85}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-153}:\\ \;\;\;\;\frac{y \cdot z}{t + t \cdot a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-75}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 9: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-15}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-85}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-153}:\\ \;\;\;\;\frac{z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.02e+65)
     t_1
     (if (<= t -5e-15)
       (/ (* y (/ z t)) (+ a 1.0))
       (if (<= t -2.05e-85)
         (/ z b)
         (if (<= t -7.5e-153)
           (/ (* z (/ y t)) (+ a 1.0))
           (if (<= t 5.8e-78) (/ z b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.02e+65) {
		tmp = t_1;
	} else if (t <= -5e-15) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if (t <= -2.05e-85) {
		tmp = z / b;
	} else if (t <= -7.5e-153) {
		tmp = (z * (y / t)) / (a + 1.0);
	} else if (t <= 5.8e-78) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-1.02d+65)) then
        tmp = t_1
    else if (t <= (-5d-15)) then
        tmp = (y * (z / t)) / (a + 1.0d0)
    else if (t <= (-2.05d-85)) then
        tmp = z / b
    else if (t <= (-7.5d-153)) then
        tmp = (z * (y / t)) / (a + 1.0d0)
    else if (t <= 5.8d-78) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.02e+65) {
		tmp = t_1;
	} else if (t <= -5e-15) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if (t <= -2.05e-85) {
		tmp = z / b;
	} else if (t <= -7.5e-153) {
		tmp = (z * (y / t)) / (a + 1.0);
	} else if (t <= 5.8e-78) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.02e+65:
		tmp = t_1
	elif t <= -5e-15:
		tmp = (y * (z / t)) / (a + 1.0)
	elif t <= -2.05e-85:
		tmp = z / b
	elif t <= -7.5e-153:
		tmp = (z * (y / t)) / (a + 1.0)
	elif t <= 5.8e-78:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.02e+65)
		tmp = t_1;
	elseif (t <= -5e-15)
		tmp = Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0));
	elseif (t <= -2.05e-85)
		tmp = Float64(z / b);
	elseif (t <= -7.5e-153)
		tmp = Float64(Float64(z * Float64(y / t)) / Float64(a + 1.0));
	elseif (t <= 5.8e-78)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.02e+65)
		tmp = t_1;
	elseif (t <= -5e-15)
		tmp = (y * (z / t)) / (a + 1.0);
	elseif (t <= -2.05e-85)
		tmp = z / b;
	elseif (t <= -7.5e-153)
		tmp = (z * (y / t)) / (a + 1.0);
	elseif (t <= 5.8e-78)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e+65], t$95$1, If[LessEqual[t, -5e-15], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.05e-85], N[(z / b), $MachinePrecision], If[LessEqual[t, -7.5e-153], N[(N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-78], N[(z / b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.02000000000000005e65 or 5.8000000000000001e-78 < t

   1. Initial program 86.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 86.3%

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

      2. associate-*l/ 91.0%

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

      3. *-commutative 91.0%

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

      4. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 65.9%

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

   if -1.02000000000000005e65 < t < -4.99999999999999999e-15

   1. Initial program 92.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 92.4%

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

      2. associate-*l/ 92.4%

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

      3. *-commutative 92.4%

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

      4. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 92.4%

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

      1. associate-/l* 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in b around 0 77.8%

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

   8. Taylor expanded in x around 0 62.8%

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

      1. associate-*r/ 62.8%

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

   10. Simplified 62.8%

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

   if -4.99999999999999999e-15 < t < -2.04999999999999997e-85 or -7.5e-153 < t < 5.8000000000000001e-78

   1. Initial program 56.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 56.6%

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

      2. associate-*l/ 52.3%

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

      3. *-commutative 52.3%

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

      4. associate-*l/ 48.3%

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

   3. Simplified 48.3%

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

   4. Taylor expanded in t around 0 68.1%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if -2.04999999999999997e-85 < t < -7.5e-153

   1. Initial program 99.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 99.4%

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

      2. associate-*l/ 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in z around 0 80.4%

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

      1. associate-/l* 70.9%

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

   6. Simplified 70.9%

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

   7. Taylor expanded in b around 0 56.3%

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

   8. Taylor expanded in x around 0 57.0%

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

      1. associate-*l/ 57.2%

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

      2. *-commutative 57.2%

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

   10. Simplified 57.2%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-15}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-85}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-153}:\\ \;\;\;\;\frac{z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 10: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-14}:\\ \;\;\;\;\frac{-z}{\frac{t \cdot \left(-1 - a\right)}{y}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.8e+64)
   (/ x (+ a 1.0))
   (if (<= t -1.02e-14)
     (/ (- z) (/ (* t (- -1.0 a)) y))
     (if (<= t 1.2e-76)
       (/ (+ z (/ (* x t) y)) b)
       (/ x (+ (/ (* y b) t) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.8e+64) {
		tmp = x / (a + 1.0);
	} else if (t <= -1.02e-14) {
		tmp = -z / ((t * (-1.0 - a)) / y);
	} else if (t <= 1.2e-76) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9.8d+64)) then
        tmp = x / (a + 1.0d0)
    else if (t <= (-1.02d-14)) then
        tmp = -z / ((t * ((-1.0d0) - a)) / y)
    else if (t <= 1.2d-76) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / (((y * b) / t) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.8e+64) {
		tmp = x / (a + 1.0);
	} else if (t <= -1.02e-14) {
		tmp = -z / ((t * (-1.0 - a)) / y);
	} else if (t <= 1.2e-76) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.8e+64:
		tmp = x / (a + 1.0)
	elif t <= -1.02e-14:
		tmp = -z / ((t * (-1.0 - a)) / y)
	elif t <= 1.2e-76:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / (((y * b) / t) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.8e+64)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (t <= -1.02e-14)
		tmp = Float64(Float64(-z) / Float64(Float64(t * Float64(-1.0 - a)) / y));
	elseif (t <= 1.2e-76)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.8e+64)
		tmp = x / (a + 1.0);
	elseif (t <= -1.02e-14)
		tmp = -z / ((t * (-1.0 - a)) / y);
	elseif (t <= 1.2e-76)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / (((y * b) / t) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.8e+64], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.02e-14], N[((-z) / N[(N[(t * N[(-1.0 - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-76], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.8000000000000005e64

   1. Initial program 89.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 89.3%

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

      2. associate-*l/ 95.7%

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

      3. *-commutative 95.7%

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

      4. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 85.0%

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

   if -9.8000000000000005e64 < t < -1.02e-14

   1. Initial program 92.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 92.4%

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

      2. associate-/l* 85.4%

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

      3. associate-*l/ 85.6%

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

      4. *-commutative 85.6%

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

      5. cancel-sign-sub 85.6%

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

      6. *-commutative 85.6%

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

      7. associate-*l/ 85.4%

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

      8. associate-+r- 85.4%

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

      9. associate-*l/ 85.6%

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

      10. *-commutative 85.6%

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

      11. cancel-sign-sub 85.6%

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

      12. *-commutative 85.6%

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

      13. associate-/r/ 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in x around 0 77.3%

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

   5. Taylor expanded in t around inf 62.5%

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

      1. distribute-lft-in 62.5%

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

      2. *-rgt-identity 62.5%

         \[\leadsto \frac{y \cdot z}{\color{blue}{t} + t \cdot a} \]

   7. Simplified 62.5%

      \[\leadsto \frac{y \cdot z}{\color{blue}{t + t \cdot a}} \]

   8. Taylor expanded in t around -inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. distribute-neg-frac 62.5%

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

      3. distribute-rgt-neg-out 62.5%

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

      4. *-commutative 62.5%

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

      5. *-commutative 62.5%

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

      6. sub-neg 62.5%

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

      7. metadata-eval 62.5%

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

      8. distribute-lft-in 62.5%

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

      9. neg-mul-1 62.5%

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

      10. distribute-rgt-neg-in 62.5%

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

      11. *-commutative 62.5%

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

      12. neg-mul-1 62.5%

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

      13. distribute-neg-in 62.5%

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

      14. fma-udef 62.5%

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

      15. associate-/l* 62.8%

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

   10. Simplified 62.8%

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

   if -1.02e-14 < t < 1.20000000000000007e-76

   1. Initial program 60.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 60.8%

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

      2. associate-*l/ 56.0%

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

      3. *-commutative 56.0%

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

      4. associate-*l/ 50.5%

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

   3. Simplified 50.5%

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

   4. Taylor expanded in y around inf 60.4%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 60.4%

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

      2. times-frac 58.2%

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

      3. associate-*r* 61.1%

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

      4. unpow2 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in b around inf 75.8%

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

   if 1.20000000000000007e-76 < t

   1. Initial program 84.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 84.9%

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

      2. associate-/l* 89.9%

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

      3. associate-*l/ 95.8%

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

      4. *-commutative 95.8%

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

      5. cancel-sign-sub 95.8%

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

      6. *-commutative 95.8%

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

      7. associate-*l/ 89.9%

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

      8. associate-+r- 89.9%

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

      9. associate-*l/ 95.8%

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

      10. *-commutative 95.8%

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

      11. cancel-sign-sub 95.8%

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

      12. *-commutative 95.8%

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

      13. associate-/r/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 70.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-14}:\\ \;\;\;\;\frac{-z}{\frac{t \cdot \left(-1 - a\right)}{y}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \]

Alternative 11: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-78}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.3e-15)
   (/ (+ x (/ y (/ t z))) (+ a 1.0))
   (if (<= t 5e-78)
     (/ (+ z (/ (* x t) y)) b)
     (* x (/ 1.0 (+ a (+ 1.0 (* y (/ b t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.3e-15) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (t <= 5e-78) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x * (1.0 / (a + (1.0 + (y * (b / t)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.3d-15)) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else if (t <= 5d-78) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x * (1.0d0 / (a + (1.0d0 + (y * (b / t)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.3e-15) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (t <= 5e-78) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x * (1.0 / (a + (1.0 + (y * (b / t)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.3e-15:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	elif t <= 5e-78:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x * (1.0 / (a + (1.0 + (y * (b / t)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.3e-15)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	elseif (t <= 5e-78)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x * Float64(1.0 / Float64(a + Float64(1.0 + Float64(y * Float64(b / t))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.3e-15)
		tmp = (x + (y / (t / z))) / (a + 1.0);
	elseif (t <= 5e-78)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x * (1.0 / (a + (1.0 + (y * (b / t)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.3e-15], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-78], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x * N[(1.0 / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2999999999999997e-15

   1. Initial program 90.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 90.0%

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

      2. associate-*l/ 94.9%

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

      3. *-commutative 94.9%

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

      4. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 93.3%

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

      1. associate-/l* 98.3%

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

   6. Simplified 98.3%

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

   7. Taylor expanded in b around 0 87.9%

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

   if -4.2999999999999997e-15 < t < 4.9999999999999996e-78

   1. Initial program 60.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 60.8%

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

      2. associate-*l/ 56.0%

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

      3. *-commutative 56.0%

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

      4. associate-*l/ 50.5%

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

   3. Simplified 50.5%

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

   4. Taylor expanded in y around inf 60.4%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 60.4%

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

      2. times-frac 58.2%

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

      3. associate-*r* 61.1%

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

      4. unpow2 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in b around inf 75.8%

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

   if 4.9999999999999996e-78 < t

   1. Initial program 84.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 84.9%

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

      2. associate-/l* 89.9%

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

      3. associate-*l/ 95.8%

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

      4. *-commutative 95.8%

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

      5. cancel-sign-sub 95.8%

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

      6. *-commutative 95.8%

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

      7. associate-*l/ 89.9%

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

      8. associate-+r- 89.9%

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

      9. associate-*l/ 95.8%

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

      10. *-commutative 95.8%

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

      11. cancel-sign-sub 95.8%

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

      12. *-commutative 95.8%

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

      13. associate-/r/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 70.9%

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

      1. div-inv 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-*l/ 74.7%

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

      4. +-commutative 74.7%

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

      5. +-commutative 74.7%

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

      6. associate-+l+ 74.7%

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

      7. *-commutative 74.7%

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

   6. Applied egg-rr 74.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-78}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \end{array} \]

Alternative 12: 58.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.04 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-14}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 122000000000:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.04e+65)
     t_1
     (if (<= t -1.65e-14)
       (/ (* y (/ z t)) (+ a 1.0))
       (if (<= t 122000000000.0) (/ (+ z (* x (/ t y))) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.04e+65) {
		tmp = t_1;
	} else if (t <= -1.65e-14) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if (t <= 122000000000.0) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-1.04d+65)) then
        tmp = t_1
    else if (t <= (-1.65d-14)) then
        tmp = (y * (z / t)) / (a + 1.0d0)
    else if (t <= 122000000000.0d0) then
        tmp = (z + (x * (t / y))) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.04e+65) {
		tmp = t_1;
	} else if (t <= -1.65e-14) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if (t <= 122000000000.0) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.04e+65:
		tmp = t_1
	elif t <= -1.65e-14:
		tmp = (y * (z / t)) / (a + 1.0)
	elif t <= 122000000000.0:
		tmp = (z + (x * (t / y))) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.04e+65)
		tmp = t_1;
	elseif (t <= -1.65e-14)
		tmp = Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0));
	elseif (t <= 122000000000.0)
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.04e+65)
		tmp = t_1;
	elseif (t <= -1.65e-14)
		tmp = (y * (z / t)) / (a + 1.0);
	elseif (t <= 122000000000.0)
		tmp = (z + (x * (t / y))) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.04e+65], t$95$1, If[LessEqual[t, -1.65e-14], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 122000000000.0], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.03999999999999999e65 or 1.22e11 < t

   1. Initial program 86.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 86.6%

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

      2. associate-*l/ 92.1%

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

      3. *-commutative 92.1%

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

      4. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 69.2%

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

   if -1.03999999999999999e65 < t < -1.6499999999999999e-14

   1. Initial program 92.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 92.4%

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

      2. associate-*l/ 92.4%

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

      3. *-commutative 92.4%

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

      4. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 92.4%

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

      1. associate-/l* 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in b around 0 77.8%

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

   8. Taylor expanded in x around 0 62.8%

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

      1. associate-*r/ 62.8%

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

   10. Simplified 62.8%

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

   if -1.6499999999999999e-14 < t < 1.22e11

   1. Initial program 64.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 64.5%

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

      2. associate-*l/ 60.5%

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

      3. *-commutative 60.5%

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

      4. associate-*l/ 55.8%

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

   3. Simplified 55.8%

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

   4. Taylor expanded in y around inf 57.6%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 57.6%

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

      2. times-frac 55.7%

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

      3. associate-*r* 59.0%

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

      4. unpow2 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in b around inf 72.3%

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

      1. +-commutative 72.3%

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

      2. associate-*l/ 70.7%

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

      3. *-commutative 70.7%

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

   9. Simplified 70.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.04 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-14}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 122000000000:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 13: 59.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.12 \cdot 10^{-13}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 320000000:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -9e+66)
     t_1
     (if (<= t -2.12e-13)
       (/ (* y (/ z t)) (+ a 1.0))
       (if (<= t 320000000.0) (/ (+ z (/ (* x t) y)) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -9e+66) {
		tmp = t_1;
	} else if (t <= -2.12e-13) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if (t <= 320000000.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-9d+66)) then
        tmp = t_1
    else if (t <= (-2.12d-13)) then
        tmp = (y * (z / t)) / (a + 1.0d0)
    else if (t <= 320000000.0d0) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -9e+66) {
		tmp = t_1;
	} else if (t <= -2.12e-13) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if (t <= 320000000.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -9e+66:
		tmp = t_1
	elif t <= -2.12e-13:
		tmp = (y * (z / t)) / (a + 1.0)
	elif t <= 320000000.0:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -9e+66)
		tmp = t_1;
	elseif (t <= -2.12e-13)
		tmp = Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0));
	elseif (t <= 320000000.0)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -9e+66)
		tmp = t_1;
	elseif (t <= -2.12e-13)
		tmp = (y * (z / t)) / (a + 1.0);
	elseif (t <= 320000000.0)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+66], t$95$1, If[LessEqual[t, -2.12e-13], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 320000000.0], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.9999999999999997e66 or 3.2e8 < t

   1. Initial program 86.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 86.6%

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

      2. associate-*l/ 92.1%

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

      3. *-commutative 92.1%

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

      4. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 69.2%

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

   if -8.9999999999999997e66 < t < -2.1200000000000001e-13

   1. Initial program 92.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 92.4%

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

      2. associate-*l/ 92.4%

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

      3. *-commutative 92.4%

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

      4. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 92.4%

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

      1. associate-/l* 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in b around 0 77.8%

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

   8. Taylor expanded in x around 0 62.8%

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

      1. associate-*r/ 62.8%

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

   10. Simplified 62.8%

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

   if -2.1200000000000001e-13 < t < 3.2e8

   1. Initial program 64.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 64.5%

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

      2. associate-*l/ 60.5%

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

      3. *-commutative 60.5%

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

      4. associate-*l/ 55.8%

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

   3. Simplified 55.8%

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

   4. Taylor expanded in y around inf 57.6%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 57.6%

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

      2. times-frac 55.7%

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

      3. associate-*r* 59.0%

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

      4. unpow2 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in b around inf 72.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -2.12 \cdot 10^{-13}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 320000000:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 14: 59.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-14}:\\ \;\;\;\;\frac{-z}{\frac{t \cdot \left(-1 - a\right)}{y}}\\ \mathbf{elif}\;t \leq 1350000000:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -9.6e+64)
     t_1
     (if (<= t -1e-14)
       (/ (- z) (/ (* t (- -1.0 a)) y))
       (if (<= t 1350000000.0) (/ (+ z (/ (* x t) y)) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -9.6e+64) {
		tmp = t_1;
	} else if (t <= -1e-14) {
		tmp = -z / ((t * (-1.0 - a)) / y);
	} else if (t <= 1350000000.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-9.6d+64)) then
        tmp = t_1
    else if (t <= (-1d-14)) then
        tmp = -z / ((t * ((-1.0d0) - a)) / y)
    else if (t <= 1350000000.0d0) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -9.6e+64) {
		tmp = t_1;
	} else if (t <= -1e-14) {
		tmp = -z / ((t * (-1.0 - a)) / y);
	} else if (t <= 1350000000.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -9.6e+64:
		tmp = t_1
	elif t <= -1e-14:
		tmp = -z / ((t * (-1.0 - a)) / y)
	elif t <= 1350000000.0:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -9.6e+64)
		tmp = t_1;
	elseif (t <= -1e-14)
		tmp = Float64(Float64(-z) / Float64(Float64(t * Float64(-1.0 - a)) / y));
	elseif (t <= 1350000000.0)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -9.6e+64)
		tmp = t_1;
	elseif (t <= -1e-14)
		tmp = -z / ((t * (-1.0 - a)) / y);
	elseif (t <= 1350000000.0)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.6e+64], t$95$1, If[LessEqual[t, -1e-14], N[((-z) / N[(N[(t * N[(-1.0 - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1350000000.0], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.59999999999999997e64 or 1.35e9 < t

   1. Initial program 86.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 86.6%

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

      2. associate-*l/ 92.1%

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

      3. *-commutative 92.1%

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

      4. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 69.2%

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

   if -9.59999999999999997e64 < t < -9.99999999999999999e-15

   1. Initial program 92.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 92.4%

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

      2. associate-/l* 85.4%

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

      3. associate-*l/ 85.6%

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

      4. *-commutative 85.6%

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

      5. cancel-sign-sub 85.6%

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

      6. *-commutative 85.6%

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

      7. associate-*l/ 85.4%

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

      8. associate-+r- 85.4%

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

      9. associate-*l/ 85.6%

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

      10. *-commutative 85.6%

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

      11. cancel-sign-sub 85.6%

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

      12. *-commutative 85.6%

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

      13. associate-/r/ 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in x around 0 77.3%

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

   5. Taylor expanded in t around inf 62.5%

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

      1. distribute-lft-in 62.5%

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

      2. *-rgt-identity 62.5%

         \[\leadsto \frac{y \cdot z}{\color{blue}{t} + t \cdot a} \]

   7. Simplified 62.5%

      \[\leadsto \frac{y \cdot z}{\color{blue}{t + t \cdot a}} \]

   8. Taylor expanded in t around -inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. distribute-neg-frac 62.5%

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

      3. distribute-rgt-neg-out 62.5%

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

      4. *-commutative 62.5%

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

      5. *-commutative 62.5%

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

      6. sub-neg 62.5%

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

      7. metadata-eval 62.5%

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

      8. distribute-lft-in 62.5%

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

      9. neg-mul-1 62.5%

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

      10. distribute-rgt-neg-in 62.5%

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

      11. *-commutative 62.5%

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

      12. neg-mul-1 62.5%

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

      13. distribute-neg-in 62.5%

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

      14. fma-udef 62.5%

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

      15. associate-/l* 62.8%

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

   10. Simplified 62.8%

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

   if -9.99999999999999999e-15 < t < 1.35e9

   1. Initial program 64.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 64.5%

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

      2. associate-*l/ 60.5%

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

      3. *-commutative 60.5%

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

      4. associate-*l/ 55.8%

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

   3. Simplified 55.8%

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

   4. Taylor expanded in y around inf 57.6%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 57.6%

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

      2. times-frac 55.7%

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

      3. associate-*r* 59.0%

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

      4. unpow2 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in b around inf 72.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-14}:\\ \;\;\;\;\frac{-z}{\frac{t \cdot \left(-1 - a\right)}{y}}\\ \mathbf{elif}\;t \leq 1350000000:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 15: 69.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-14} \lor \neg \left(t \leq 1.5 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.35e-14) (not (<= t 1.5e-51)))
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.35e-14) || !(t <= 1.5e-51)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.35d-14)) .or. (.not. (t <= 1.5d-51))) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.35e-14) || !(t <= 1.5e-51)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.35e-14) or not (t <= 1.5e-51):
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.35e-14) || !(t <= 1.5e-51))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.35e-14) || ~((t <= 1.5e-51)))
		tmp = (x + (y * (z / t))) / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.35e-14], N[Not[LessEqual[t, 1.5e-51]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3499999999999999e-14 or 1.50000000000000001e-51 < t

   1. Initial program 86.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 86.4%

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

      2. associate-*l/ 90.9%

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

      3. *-commutative 90.9%

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

      4. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in b around 0 79.7%

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

   if -1.3499999999999999e-14 < t < 1.50000000000000001e-51

   1. Initial program 62.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 62.6%

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

      2. associate-*l/ 58.0%

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

      3. *-commutative 58.0%

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

      4. associate-*l/ 52.8%

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

   3. Simplified 52.8%

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

   4. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 60.3%

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

      2. times-frac 58.3%

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

      3. associate-*r* 61.0%

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

      4. unpow2 61.0%

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

   6. Simplified 61.0%

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

   7. Taylor expanded in b around inf 75.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-14} \lor \neg \left(t \leq 1.5 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 16: 69.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-50}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.2e-15)
   (/ (+ x (/ y (/ t z))) (+ a 1.0))
   (if (<= t 1.85e-50)
     (/ (+ z (/ (* x t) y)) b)
     (/ (+ x (* y (/ z t))) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e-15) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (t <= 1.85e-50) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.2d-15)) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else if (t <= 1.85d-50) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e-15) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (t <= 1.85e-50) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.2e-15:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	elif t <= 1.85e-50:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.2e-15)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	elseif (t <= 1.85e-50)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.2e-15)
		tmp = (x + (y / (t / z))) / (a + 1.0);
	elseif (t <= 1.85e-50)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.2e-15], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-50], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.19999999999999986e-15

   1. Initial program 90.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 90.0%

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

      2. associate-*l/ 94.9%

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

      3. *-commutative 94.9%

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

      4. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 93.3%

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

      1. associate-/l* 98.3%

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

   6. Simplified 98.3%

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

   7. Taylor expanded in b around 0 87.9%

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

   if -2.19999999999999986e-15 < t < 1.85e-50

   1. Initial program 62.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 62.6%

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

      2. associate-*l/ 58.0%

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

      3. *-commutative 58.0%

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

      4. associate-*l/ 52.8%

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

   3. Simplified 52.8%

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

   4. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{\left(\frac{t \cdot x}{y \cdot b} + \frac{z}{b}\right) - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 60.3%

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

      2. times-frac 58.3%

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

      3. associate-*r* 61.0%

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

      4. unpow2 61.0%

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

   6. Simplified 61.0%

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

   7. Taylor expanded in b around inf 75.1%

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

   if 1.85e-50 < t

   1. Initial program 84.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 84.1%

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

      2. associate-*l/ 88.3%

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

      3. *-commutative 88.3%

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

      4. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in b around 0 74.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-50}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]

Alternative 17: 54.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+67} \lor \neg \left(t \leq 10^{-75}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.1e+67) (not (<= t 1e-75))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.1e+67) || !(t <= 1e-75)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.1d+67)) .or. (.not. (t <= 1d-75))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.1e+67) || !(t <= 1e-75)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.1e+67) or not (t <= 1e-75):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.1e+67) || !(t <= 1e-75))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.1e+67) || ~((t <= 1e-75)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.1e+67], N[Not[LessEqual[t, 1e-75]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.09999999999999979e67 or 9.9999999999999996e-76 < t

   1. Initial program 86.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 86.9%

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

      2. associate-*l/ 91.0%

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

      3. *-commutative 91.0%

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

      4. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 66.4%

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

   if -4.09999999999999979e67 < t < 9.9999999999999996e-76

   1. Initial program 63.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 63.8%

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

      2. associate-*l/ 60.4%

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

      3. *-commutative 60.4%

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

      4. associate-*l/ 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in t around 0 58.0%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+67} \lor \neg \left(t \leq 10^{-75}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 18: 41.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 0.22:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.1e+67) (/ x a) (if (<= t 0.22) (/ z b) (- x (* x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.1e+67) {
		tmp = x / a;
	} else if (t <= 0.22) {
		tmp = z / b;
	} else {
		tmp = x - (x * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.1d+67)) then
        tmp = x / a
    else if (t <= 0.22d0) then
        tmp = z / b
    else
        tmp = x - (x * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.1e+67) {
		tmp = x / a;
	} else if (t <= 0.22) {
		tmp = z / b;
	} else {
		tmp = x - (x * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.1e+67:
		tmp = x / a
	elif t <= 0.22:
		tmp = z / b
	else:
		tmp = x - (x * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.1e+67)
		tmp = Float64(x / a);
	elseif (t <= 0.22)
		tmp = Float64(z / b);
	else
		tmp = Float64(x - Float64(x * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.1e+67)
		tmp = x / a;
	elseif (t <= 0.22)
		tmp = z / b;
	else
		tmp = x - (x * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.1e+67], N[(x / a), $MachinePrecision], If[LessEqual[t, 0.22], N[(z / b), $MachinePrecision], N[(x - N[(x * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.09999999999999979e67

   1. Initial program 91.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 91.3%

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

      2. associate-/l* 95.6%

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

      3. associate-*l/ 99.9%

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

      4. *-commutative 99.9%

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

      5. cancel-sign-sub 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-*l/ 95.6%

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

      8. associate-+r- 95.6%

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

      9. associate-*l/ 99.9%

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

      10. *-commutative 99.9%

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

      11. cancel-sign-sub 99.9%

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

      12. *-commutative 99.9%

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

      13. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 85.3%

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

   5. Taylor expanded in a around inf 49.1%

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

   if -4.09999999999999979e67 < t < 0.220000000000000001

   1. Initial program 66.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 66.5%

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

      2. associate-*l/ 63.5%

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

      3. *-commutative 63.5%

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

      4. associate-*l/ 59.4%

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

   3. Simplified 59.4%

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

   4. Taylor expanded in t around 0 54.4%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if 0.220000000000000001 < t

   1. Initial program 85.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 85.2%

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

      2. associate-*l/ 90.1%

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

      3. *-commutative 90.1%

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

      4. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around inf 59.3%

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

   5. Taylor expanded in a around 0 35.2%

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

      1. +-commutative 35.2%

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

      2. mul-1-neg 35.2%

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

      3. unsub-neg 35.2%

         \[\leadsto \color{blue}{x - a \cdot x} \]

   7. Simplified 35.2%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 0.22:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot a\\ \end{array} \]

Alternative 19: 42.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-71}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.4e+67) (/ x a) (if (<= t 3.3e-71) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.4e+67) {
		tmp = x / a;
	} else if (t <= 3.3e-71) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.4d+67)) then
        tmp = x / a
    else if (t <= 3.3d-71) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.4e+67) {
		tmp = x / a;
	} else if (t <= 3.3e-71) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.4e+67:
		tmp = x / a
	elif t <= 3.3e-71:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.4e+67)
		tmp = Float64(x / a);
	elseif (t <= 3.3e-71)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.4e+67)
		tmp = x / a;
	elseif (t <= 3.3e-71)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.4e+67], N[(x / a), $MachinePrecision], If[LessEqual[t, 3.3e-71], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e67 or 3.3000000000000002e-71 < t

   1. Initial program 86.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 86.7%

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

      2. associate-/l* 91.6%

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

      3. associate-*l/ 97.1%

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

      4. *-commutative 97.1%

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

      5. cancel-sign-sub 97.1%

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

      6. *-commutative 97.1%

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

      7. associate-*l/ 91.6%

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

      8. associate-+r- 91.6%

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

      9. associate-*l/ 97.1%

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

      10. *-commutative 97.1%

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

      11. cancel-sign-sub 97.1%

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

      12. *-commutative 97.1%

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

      13. associate-/r/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around inf 75.1%

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

   5. Taylor expanded in a around inf 35.1%

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

   if -4.4e67 < t < 3.3000000000000002e-71

   1. Initial program 64.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 64.4%

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

      2. associate-*l/ 61.1%

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

      3. *-commutative 61.1%

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

      4. associate-*l/ 56.4%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in t around 0 57.9%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-71}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 20: 25.5% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / a), $MachinePrecision]

Derivation

1. Initial program 76.5%

   \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
2. Step-by-step derivation

   1. *-commutative 76.5%

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

   2. associate-/l* 76.3%

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

   3. associate-*l/ 77.6%

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

   4. *-commutative 77.6%

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

   5. cancel-sign-sub 77.6%

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

   6. *-commutative 77.6%

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

   7. associate-*l/ 76.3%

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

   8. associate-+r- 76.3%

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

   9. associate-*l/ 77.6%

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

   10. *-commutative 77.6%

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

   11. cancel-sign-sub 77.6%

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

   12. *-commutative 77.6%

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

   13. associate-/r/ 76.0%

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

3. Simplified 76.0%

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

4. Taylor expanded in x around inf 55.7%

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

5. Taylor expanded in a around inf 24.1%

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

6. Final simplification 24.1%

   \[\leadsto \frac{x}{a} \]

Developer target: 78.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))