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

Percentage Accurate: 74.8% → 90.1%

Time: 19.2s

Alternatives: 17

Speedup: 0.9×

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: 74.8% 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: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+299}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1} + \frac{x}{a + 1}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{\frac{t}{\frac{{b}^{2}}{z \cdot \left(a + 1\right)}} - \frac{t}{\frac{b}{x}}}{y}, \frac{z}{b}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 -4e+299)
     (+ (* (/ y t) (/ z (+ a 1.0))) (/ x (+ a 1.0)))
     (if (<= t_1 -5e-308)
       t_1
       (if (<= t_1 0.0)
         (fma
          -1.0
          (/ (- (/ t (/ (pow b 2.0) (* z (+ a 1.0)))) (/ t (/ b x))) y)
          (/ z b))
         (if (<= t_1 5e+262)
           t_1
           (if (<= t_1 INFINITY)
             (* (/ y t) (/ z (fma y (/ b t) (+ a 1.0))))
             (/ z 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 <= -4e+299) {
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0));
	} else if (t_1 <= -5e-308) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = fma(-1.0, (((t / (pow(b, 2.0) / (z * (a + 1.0)))) - (t / (b / x))) / y), (z / b));
	} else if (t_1 <= 5e+262) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / fma(y, (b / t), (a + 1.0)));
	} else {
		tmp = z / 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 <= -4e+299)
		tmp = Float64(Float64(Float64(y / t) * Float64(z / Float64(a + 1.0))) + Float64(x / Float64(a + 1.0)));
	elseif (t_1 <= -5e-308)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = fma(-1.0, Float64(Float64(Float64(t / Float64((b ^ 2.0) / Float64(z * Float64(a + 1.0)))) - Float64(t / Float64(b / x))) / y), Float64(z / b));
	elseif (t_1 <= 5e+262)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / fma(y, Float64(b / t), Float64(a + 1.0))));
	else
		tmp = Float64(z / 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]}, If[LessEqual[t$95$1, -4e+299], N[(N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-308], t$95$1, If[LessEqual[t$95$1, 0.0], N[(-1.0 * N[(N[(N[(t / N[(N[Power[b, 2.0], $MachinePrecision] / N[(z * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+262], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / 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))) < -4.0000000000000002e299

   1. Initial program 39.6%

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

   3. Taylor expanded in b around 0 39.1%

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

   4. Taylor expanded in x around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. times-frac 87.8%

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

   6. Simplified 87.8%

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

   if -4.0000000000000002e299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.99999999999999955e-308 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.00000000000000008e262

   1. Initial program 99.7%

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

   if -4.99999999999999955e-308 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 60.2%

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

   3. Taylor expanded in y around -inf 63.5%

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

      1. fma-def 63.5%

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

      2. distribute-lft-out-- 63.5%

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

      3. associate-/l* 65.9%

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

      4. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

   if 5.00000000000000008e262 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 55.2%

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

   3. Taylor expanded in x around 0 65.0%

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

      1. times-frac 94.8%

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

      2. associate-+r+ 94.8%

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

      3. +-commutative 94.8%

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

      4. +-commutative 94.8%

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

      5. associate-*l/ 94.8%

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

      6. *-commutative 94.8%

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

      7. fma-udef 94.8%

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

      8. +-commutative 94.8%

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

   5. Simplified 94.8%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf 88.0%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -4 \cdot 10^{+299}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1} + \frac{x}{a + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-308}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{\frac{t}{\frac{{b}^{2}}{z \cdot \left(a + 1\right)}} - \frac{t}{\frac{b}{x}}}{y}, \frac{z}{b}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+299}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1} + \frac{x}{a + 1}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 -4e+299)
     (+ (* (/ y t) (/ z (+ a 1.0))) (/ x (+ a 1.0)))
     (if (<= t_1 5e+262)
       t_1
       (if (<= t_1 INFINITY)
         (* (/ y t) (/ z (fma y (/ b t) (+ a 1.0))))
         (/ z 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 <= -4e+299) {
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0));
	} else if (t_1 <= 5e+262) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / fma(y, (b / t), (a + 1.0)));
	} else {
		tmp = z / 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 <= -4e+299)
		tmp = Float64(Float64(Float64(y / t) * Float64(z / Float64(a + 1.0))) + Float64(x / Float64(a + 1.0)));
	elseif (t_1 <= 5e+262)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / fma(y, Float64(b / t), Float64(a + 1.0))));
	else
		tmp = Float64(z / 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]}, If[LessEqual[t$95$1, -4e+299], N[(N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+262], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / 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))) < -4.0000000000000002e299

   1. Initial program 39.6%

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

   3. Taylor expanded in b around 0 39.1%

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

   4. Taylor expanded in x around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. times-frac 87.8%

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

   6. Simplified 87.8%

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

   if -4.0000000000000002e299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.00000000000000008e262

   1. Initial program 91.1%

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

   if 5.00000000000000008e262 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 55.2%

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

   3. Taylor expanded in x around 0 65.0%

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

      1. times-frac 94.8%

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

      2. associate-+r+ 94.8%

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

      3. +-commutative 94.8%

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

      4. +-commutative 94.8%

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

      5. associate-*l/ 94.8%

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

      6. *-commutative 94.8%

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

      7. fma-udef 94.8%

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

      8. +-commutative 94.8%

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

   5. Simplified 94.8%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf 88.0%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -4 \cdot 10^{+299}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1} + \frac{x}{a + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+299}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1} + \frac{x}{a + 1}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 -4e+299)
     (+ (* (/ y t) (/ z (+ a 1.0))) (/ x (+ a 1.0)))
     (if (<= t_1 INFINITY) t_1 (/ z 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 <= -4e+299) {
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z / 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 <= -4e+299) {
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z / 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 <= -4e+299:
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0))
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z / 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 <= -4e+299)
		tmp = Float64(Float64(Float64(y / t) * Float64(z / Float64(a + 1.0))) + Float64(x / Float64(a + 1.0)));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z / 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 <= -4e+299)
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z / 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, -4e+299], N[(N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.0000000000000002e299

   1. Initial program 39.6%

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

   3. Taylor expanded in b around 0 39.1%

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

   4. Taylor expanded in x around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. times-frac 87.8%

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

   6. Simplified 87.8%

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

   if -4.0000000000000002e299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 87.9%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf 88.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -4 \cdot 10^{+299}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1} + \frac{x}{a + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ t_2 := \frac{x}{a} + \frac{z}{t \cdot \frac{a}{y}}\\ t_3 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -2.35 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-305}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-256}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-189}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* (/ t b) (/ x y))))
        (t_2 (+ (/ x a) (/ z (* t (/ a y)))))
        (t_3 (+ x (/ y (/ t z)))))
   (if (<= a -2.35e+26)
     t_2
     (if (<= a -1.8e-10)
       t_1
       (if (<= a -9.5e-305)
         t_3
         (if (<= a 8.8e-256)
           (/ z b)
           (if (<= a 2.1e-189)
             (+ x (/ (* y z) t))
             (if (<= a 1.15e-156)
               t_1
               (if (<= a 2.2e-58) t_3 (if (<= a 2e+69) (/ z b) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / b) * (x / y));
	double t_2 = (x / a) + (z / (t * (a / y)));
	double t_3 = x + (y / (t / z));
	double tmp;
	if (a <= -2.35e+26) {
		tmp = t_2;
	} else if (a <= -1.8e-10) {
		tmp = t_1;
	} else if (a <= -9.5e-305) {
		tmp = t_3;
	} else if (a <= 8.8e-256) {
		tmp = z / b;
	} else if (a <= 2.1e-189) {
		tmp = x + ((y * z) / t);
	} else if (a <= 1.15e-156) {
		tmp = t_1;
	} else if (a <= 2.2e-58) {
		tmp = t_3;
	} else if (a <= 2e+69) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (z / b) + ((t / b) * (x / y))
    t_2 = (x / a) + (z / (t * (a / y)))
    t_3 = x + (y / (t / z))
    if (a <= (-2.35d+26)) then
        tmp = t_2
    else if (a <= (-1.8d-10)) then
        tmp = t_1
    else if (a <= (-9.5d-305)) then
        tmp = t_3
    else if (a <= 8.8d-256) then
        tmp = z / b
    else if (a <= 2.1d-189) then
        tmp = x + ((y * z) / t)
    else if (a <= 1.15d-156) then
        tmp = t_1
    else if (a <= 2.2d-58) then
        tmp = t_3
    else if (a <= 2d+69) 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 = (z / b) + ((t / b) * (x / y));
	double t_2 = (x / a) + (z / (t * (a / y)));
	double t_3 = x + (y / (t / z));
	double tmp;
	if (a <= -2.35e+26) {
		tmp = t_2;
	} else if (a <= -1.8e-10) {
		tmp = t_1;
	} else if (a <= -9.5e-305) {
		tmp = t_3;
	} else if (a <= 8.8e-256) {
		tmp = z / b;
	} else if (a <= 2.1e-189) {
		tmp = x + ((y * z) / t);
	} else if (a <= 1.15e-156) {
		tmp = t_1;
	} else if (a <= 2.2e-58) {
		tmp = t_3;
	} else if (a <= 2e+69) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t / b) * (x / y))
	t_2 = (x / a) + (z / (t * (a / y)))
	t_3 = x + (y / (t / z))
	tmp = 0
	if a <= -2.35e+26:
		tmp = t_2
	elif a <= -1.8e-10:
		tmp = t_1
	elif a <= -9.5e-305:
		tmp = t_3
	elif a <= 8.8e-256:
		tmp = z / b
	elif a <= 2.1e-189:
		tmp = x + ((y * z) / t)
	elif a <= 1.15e-156:
		tmp = t_1
	elif a <= 2.2e-58:
		tmp = t_3
	elif a <= 2e+69:
		tmp = z / b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)))
	t_2 = Float64(Float64(x / a) + Float64(z / Float64(t * Float64(a / y))))
	t_3 = Float64(x + Float64(y / Float64(t / z)))
	tmp = 0.0
	if (a <= -2.35e+26)
		tmp = t_2;
	elseif (a <= -1.8e-10)
		tmp = t_1;
	elseif (a <= -9.5e-305)
		tmp = t_3;
	elseif (a <= 8.8e-256)
		tmp = Float64(z / b);
	elseif (a <= 2.1e-189)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 1.15e-156)
		tmp = t_1;
	elseif (a <= 2.2e-58)
		tmp = t_3;
	elseif (a <= 2e+69)
		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 = (z / b) + ((t / b) * (x / y));
	t_2 = (x / a) + (z / (t * (a / y)));
	t_3 = x + (y / (t / z));
	tmp = 0.0;
	if (a <= -2.35e+26)
		tmp = t_2;
	elseif (a <= -1.8e-10)
		tmp = t_1;
	elseif (a <= -9.5e-305)
		tmp = t_3;
	elseif (a <= 8.8e-256)
		tmp = z / b;
	elseif (a <= 2.1e-189)
		tmp = x + ((y * z) / t);
	elseif (a <= 1.15e-156)
		tmp = t_1;
	elseif (a <= 2.2e-58)
		tmp = t_3;
	elseif (a <= 2e+69)
		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[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / a), $MachinePrecision] + N[(z / N[(t * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.35e+26], t$95$2, If[LessEqual[a, -1.8e-10], t$95$1, If[LessEqual[a, -9.5e-305], t$95$3, If[LessEqual[a, 8.8e-256], N[(z / b), $MachinePrecision], If[LessEqual[a, 2.1e-189], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-156], t$95$1, If[LessEqual[a, 2.2e-58], t$95$3, If[LessEqual[a, 2e+69], N[(z / b), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.3499999999999999e26 or 2.0000000000000001e69 < a

   1. Initial program 78.1%

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

   3. Taylor expanded in x around 0 78.3%

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

   4. Taylor expanded in a around inf 70.1%

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

      1. times-frac 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in a around inf 65.6%

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

      1. clear-num 65.5%

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

      2. frac-times 69.4%

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

      3. *-un-lft-identity 69.4%

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

   9. Applied egg-rr 69.4%

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

   if -2.3499999999999999e26 < a < -1.8e-10 or 2.10000000000000016e-189 < a < 1.15e-156

   1. Initial program 61.9%

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

   3. Taylor expanded in b around inf 53.9%

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

   4. Taylor expanded in t around 0 83.7%

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

      1. times-frac 91.0%

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

   6. Simplified 91.0%

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

   if -1.8e-10 < a < -9.49999999999999902e-305 or 1.15e-156 < a < 2.20000000000000006e-58

   1. Initial program 87.4%

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

   3. Taylor expanded in b around 0 68.2%

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

   4. Taylor expanded in a around 0 68.2%

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

      1. associate-/l* 70.9%

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

   6. Simplified 70.9%

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

   if -9.49999999999999902e-305 < a < 8.80000000000000039e-256 or 2.20000000000000006e-58 < a < 2.0000000000000001e69

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf 66.3%

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

   if 8.80000000000000039e-256 < a < 2.10000000000000016e-189

   1. Initial program 81.5%

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

   3. Taylor expanded in b around 0 74.7%

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

   4. Taylor expanded in a around 0 74.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{a} + \frac{z}{t \cdot \frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-305}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-256}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-189}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-156}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} + \frac{z}{t \cdot \frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a} + \frac{z}{t \cdot \frac{a}{y}}\\ t_2 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_3 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-305}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-256}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-189}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x a) (/ z (* t (/ a y)))))
        (t_2 (+ (/ z b) (/ (* x t) (* y b))))
        (t_3 (+ x (/ y (/ t z)))))
   (if (<= a -1.8e+26)
     t_1
     (if (<= a -2.8e-7)
       (+ (/ z b) (* (/ t b) (/ x y)))
       (if (<= a -2.7e-305)
         t_3
         (if (<= a 8.8e-256)
           (/ z b)
           (if (<= a 1.25e-189)
             (+ x (/ (* y z) t))
             (if (<= a 2.25e-157)
               t_2
               (if (<= a 4.8e-64) t_3 (if (<= a 8.8e+70) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) + (z / (t * (a / y)));
	double t_2 = (z / b) + ((x * t) / (y * b));
	double t_3 = x + (y / (t / z));
	double tmp;
	if (a <= -1.8e+26) {
		tmp = t_1;
	} else if (a <= -2.8e-7) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else if (a <= -2.7e-305) {
		tmp = t_3;
	} else if (a <= 8.8e-256) {
		tmp = z / b;
	} else if (a <= 1.25e-189) {
		tmp = x + ((y * z) / t);
	} else if (a <= 2.25e-157) {
		tmp = t_2;
	} else if (a <= 4.8e-64) {
		tmp = t_3;
	} else if (a <= 8.8e+70) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (x / a) + (z / (t * (a / y)))
    t_2 = (z / b) + ((x * t) / (y * b))
    t_3 = x + (y / (t / z))
    if (a <= (-1.8d+26)) then
        tmp = t_1
    else if (a <= (-2.8d-7)) then
        tmp = (z / b) + ((t / b) * (x / y))
    else if (a <= (-2.7d-305)) then
        tmp = t_3
    else if (a <= 8.8d-256) then
        tmp = z / b
    else if (a <= 1.25d-189) then
        tmp = x + ((y * z) / t)
    else if (a <= 2.25d-157) then
        tmp = t_2
    else if (a <= 4.8d-64) then
        tmp = t_3
    else if (a <= 8.8d+70) 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 / a) + (z / (t * (a / y)));
	double t_2 = (z / b) + ((x * t) / (y * b));
	double t_3 = x + (y / (t / z));
	double tmp;
	if (a <= -1.8e+26) {
		tmp = t_1;
	} else if (a <= -2.8e-7) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else if (a <= -2.7e-305) {
		tmp = t_3;
	} else if (a <= 8.8e-256) {
		tmp = z / b;
	} else if (a <= 1.25e-189) {
		tmp = x + ((y * z) / t);
	} else if (a <= 2.25e-157) {
		tmp = t_2;
	} else if (a <= 4.8e-64) {
		tmp = t_3;
	} else if (a <= 8.8e+70) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) + (z / (t * (a / y)))
	t_2 = (z / b) + ((x * t) / (y * b))
	t_3 = x + (y / (t / z))
	tmp = 0
	if a <= -1.8e+26:
		tmp = t_1
	elif a <= -2.8e-7:
		tmp = (z / b) + ((t / b) * (x / y))
	elif a <= -2.7e-305:
		tmp = t_3
	elif a <= 8.8e-256:
		tmp = z / b
	elif a <= 1.25e-189:
		tmp = x + ((y * z) / t)
	elif a <= 2.25e-157:
		tmp = t_2
	elif a <= 4.8e-64:
		tmp = t_3
	elif a <= 8.8e+70:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) + Float64(z / Float64(t * Float64(a / y))))
	t_2 = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)))
	t_3 = Float64(x + Float64(y / Float64(t / z)))
	tmp = 0.0
	if (a <= -1.8e+26)
		tmp = t_1;
	elseif (a <= -2.8e-7)
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	elseif (a <= -2.7e-305)
		tmp = t_3;
	elseif (a <= 8.8e-256)
		tmp = Float64(z / b);
	elseif (a <= 1.25e-189)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (a <= 2.25e-157)
		tmp = t_2;
	elseif (a <= 4.8e-64)
		tmp = t_3;
	elseif (a <= 8.8e+70)
		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 / a) + (z / (t * (a / y)));
	t_2 = (z / b) + ((x * t) / (y * b));
	t_3 = x + (y / (t / z));
	tmp = 0.0;
	if (a <= -1.8e+26)
		tmp = t_1;
	elseif (a <= -2.8e-7)
		tmp = (z / b) + ((t / b) * (x / y));
	elseif (a <= -2.7e-305)
		tmp = t_3;
	elseif (a <= 8.8e-256)
		tmp = z / b;
	elseif (a <= 1.25e-189)
		tmp = x + ((y * z) / t);
	elseif (a <= 2.25e-157)
		tmp = t_2;
	elseif (a <= 4.8e-64)
		tmp = t_3;
	elseif (a <= 8.8e+70)
		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 / a), $MachinePrecision] + N[(z / N[(t * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+26], t$95$1, If[LessEqual[a, -2.8e-7], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.7e-305], t$95$3, If[LessEqual[a, 8.8e-256], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.25e-189], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-157], t$95$2, If[LessEqual[a, 4.8e-64], t$95$3, If[LessEqual[a, 8.8e+70], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.80000000000000012e26 or 8.80000000000000003e70 < a

   1. Initial program 78.1%

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

   3. Taylor expanded in x around 0 78.3%

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

   4. Taylor expanded in a around inf 70.1%

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

      1. times-frac 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in a around inf 65.6%

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

      1. clear-num 65.5%

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

      2. frac-times 69.4%

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

      3. *-un-lft-identity 69.4%

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

   9. Applied egg-rr 69.4%

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

   if -1.80000000000000012e26 < a < -2.80000000000000019e-7

   1. Initial program 66.4%

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

   3. Taylor expanded in b around inf 65.2%

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

   4. Taylor expanded in t around 0 81.3%

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

      1. times-frac 97.5%

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

   6. Simplified 97.5%

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

   if -2.80000000000000019e-7 < a < -2.6999999999999999e-305 or 2.24999999999999999e-157 < a < 4.79999999999999997e-64

   1. Initial program 87.4%

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

   3. Taylor expanded in b around 0 68.2%

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

   4. Taylor expanded in a around 0 68.2%

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

      1. associate-/l* 70.9%

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

   6. Simplified 70.9%

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

   if -2.6999999999999999e-305 < a < 8.80000000000000039e-256

   1. Initial program 47.7%

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

   3. Taylor expanded in y around inf 90.9%

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

   if 8.80000000000000039e-256 < a < 1.2499999999999999e-189

   1. Initial program 81.5%

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

   3. Taylor expanded in b around 0 74.7%

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

   4. Taylor expanded in a around 0 74.7%

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

   if 1.2499999999999999e-189 < a < 2.24999999999999999e-157 or 4.79999999999999997e-64 < a < 8.80000000000000003e70

   1. Initial program 55.9%

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

   3. Taylor expanded in b around inf 47.3%

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

   4. Taylor expanded in t around 0 70.9%

      \[\leadsto \color{blue}{\frac{z}{b} + \frac{t \cdot x}{b \cdot y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{a} + \frac{z}{t \cdot \frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-305}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-256}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-189}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} + \frac{z}{t \cdot \frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ t_2 := \frac{x}{a} + \frac{z}{t \cdot \frac{a}{y}}\\ \mathbf{if}\;a \leq -22000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-255}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+67}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ t z)))) (t_2 (+ (/ x a) (/ z (* t (/ a y))))))
   (if (<= a -22000000000.0)
     t_2
     (if (<= a -1e-304)
       t_1
       (if (<= a 1.75e-255)
         (/ z b)
         (if (<= a 2.2e-58) t_1 (if (<= a 2.15e+67) (/ z b) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y / (t / z));
	double t_2 = (x / a) + (z / (t * (a / y)));
	double tmp;
	if (a <= -22000000000.0) {
		tmp = t_2;
	} else if (a <= -1e-304) {
		tmp = t_1;
	} else if (a <= 1.75e-255) {
		tmp = z / b;
	} else if (a <= 2.2e-58) {
		tmp = t_1;
	} else if (a <= 2.15e+67) {
		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 = x + (y / (t / z))
    t_2 = (x / a) + (z / (t * (a / y)))
    if (a <= (-22000000000.0d0)) then
        tmp = t_2
    else if (a <= (-1d-304)) then
        tmp = t_1
    else if (a <= 1.75d-255) then
        tmp = z / b
    else if (a <= 2.2d-58) then
        tmp = t_1
    else if (a <= 2.15d+67) 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 = x + (y / (t / z));
	double t_2 = (x / a) + (z / (t * (a / y)));
	double tmp;
	if (a <= -22000000000.0) {
		tmp = t_2;
	} else if (a <= -1e-304) {
		tmp = t_1;
	} else if (a <= 1.75e-255) {
		tmp = z / b;
	} else if (a <= 2.2e-58) {
		tmp = t_1;
	} else if (a <= 2.15e+67) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y / (t / z))
	t_2 = (x / a) + (z / (t * (a / y)))
	tmp = 0
	if a <= -22000000000.0:
		tmp = t_2
	elif a <= -1e-304:
		tmp = t_1
	elif a <= 1.75e-255:
		tmp = z / b
	elif a <= 2.2e-58:
		tmp = t_1
	elif a <= 2.15e+67:
		tmp = z / b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y / Float64(t / z)))
	t_2 = Float64(Float64(x / a) + Float64(z / Float64(t * Float64(a / y))))
	tmp = 0.0
	if (a <= -22000000000.0)
		tmp = t_2;
	elseif (a <= -1e-304)
		tmp = t_1;
	elseif (a <= 1.75e-255)
		tmp = Float64(z / b);
	elseif (a <= 2.2e-58)
		tmp = t_1;
	elseif (a <= 2.15e+67)
		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 = x + (y / (t / z));
	t_2 = (x / a) + (z / (t * (a / y)));
	tmp = 0.0;
	if (a <= -22000000000.0)
		tmp = t_2;
	elseif (a <= -1e-304)
		tmp = t_1;
	elseif (a <= 1.75e-255)
		tmp = z / b;
	elseif (a <= 2.2e-58)
		tmp = t_1;
	elseif (a <= 2.15e+67)
		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[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / a), $MachinePrecision] + N[(z / N[(t * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -22000000000.0], t$95$2, If[LessEqual[a, -1e-304], t$95$1, If[LessEqual[a, 1.75e-255], N[(z / b), $MachinePrecision], If[LessEqual[a, 2.2e-58], t$95$1, If[LessEqual[a, 2.15e+67], N[(z / b), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2e10 or 2.1500000000000001e67 < a

   1. Initial program 77.8%

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

   3. Taylor expanded in x around 0 78.1%

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

   4. Taylor expanded in a around inf 68.6%

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

      1. times-frac 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in a around inf 64.1%

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

      1. clear-num 64.0%

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

      2. frac-times 67.8%

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

      3. *-un-lft-identity 67.8%

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

   9. Applied egg-rr 67.8%

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

   if -2.2e10 < a < -9.99999999999999971e-305 or 1.74999999999999989e-255 < a < 2.20000000000000006e-58

   1. Initial program 83.7%

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

   3. Taylor expanded in b around 0 63.4%

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

   4. Taylor expanded in a around 0 63.4%

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

      1. associate-/l* 64.5%

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

   6. Simplified 64.5%

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

   if -9.99999999999999971e-305 < a < 1.74999999999999989e-255 or 2.20000000000000006e-58 < a < 2.1500000000000001e67

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf 66.3%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -22000000000:\\ \;\;\;\;\frac{x}{a} + \frac{z}{t \cdot \frac{a}{y}}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-304}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-255}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+67}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} + \frac{z}{t \cdot \frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1450 \lor \neg \left(b \leq 1.3 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1450.0) (not (<= b 1.3e+105)))
   (+ (/ z b) (/ x (+ (+ a (/ (* y b) t)) 1.0)))
   (/ (+ x (* z (/ y t))) (+ (+ a (* y (/ b t))) 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1450.0) || !(b <= 1.3e+105)) {
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0));
	} else {
		tmp = (x + (z * (y / t))) / ((a + (y * (b / t))) + 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 ((b <= (-1450.0d0)) .or. (.not. (b <= 1.3d+105))) then
        tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0d0))
    else
        tmp = (x + (z * (y / t))) / ((a + (y * (b / t))) + 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 ((b <= -1450.0) || !(b <= 1.3e+105)) {
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0));
	} else {
		tmp = (x + (z * (y / t))) / ((a + (y * (b / t))) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1450.0) or not (b <= 1.3e+105):
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0))
	else:
		tmp = (x + (z * (y / t))) / ((a + (y * (b / t))) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1450.0) || !(b <= 1.3e+105))
		tmp = Float64(Float64(z / b) + Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 1.0)));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(a + Float64(y * Float64(b / t))) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1450.0) || ~((b <= 1.3e+105)))
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0));
	else
		tmp = (x + (z * (y / t))) / ((a + (y * (b / t))) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1450.0], N[Not[LessEqual[b, 1.3e+105]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1450 or 1.3000000000000001e105 < b

   1. Initial program 60.2%

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

   3. Taylor expanded in x around 0 59.7%

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

   4. Taylor expanded in y around inf 84.5%

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

   if -1450 < b < 1.3000000000000001e105

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-/l* 87.7%

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

      3. +-commutative 87.7%

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

      4. associate-+l+ 87.7%

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

      5. associate-*r/ 87.7%

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

      6. *-commutative 87.7%

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

   3. Simplified 87.7%

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

      1. div-inv 87.6%

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

      2. clear-num 87.7%

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

   6. Applied egg-rr 87.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1450 \lor \neg \left(b \leq 1.3 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -400 \lor \neg \left(b \leq 8 \cdot 10^{+97}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -400.0) (not (<= b 8e+97)))
   (+ (/ z b) (/ x (+ (+ a (/ (* y b) t)) 1.0)))
   (/ (+ x (/ z (/ t y))) (+ (+ a (/ y (/ t b))) 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -400.0) || !(b <= 8e+97)) {
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0));
	} else {
		tmp = (x + (z / (t / y))) / ((a + (y / (t / b))) + 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 ((b <= (-400.0d0)) .or. (.not. (b <= 8d+97))) then
        tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0d0))
    else
        tmp = (x + (z / (t / y))) / ((a + (y / (t / b))) + 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 ((b <= -400.0) || !(b <= 8e+97)) {
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0));
	} else {
		tmp = (x + (z / (t / y))) / ((a + (y / (t / b))) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -400.0) or not (b <= 8e+97):
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0))
	else:
		tmp = (x + (z / (t / y))) / ((a + (y / (t / b))) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -400.0) || !(b <= 8e+97))
		tmp = Float64(Float64(z / b) + Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 1.0)));
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(a + Float64(y / Float64(t / b))) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -400.0) || ~((b <= 8e+97)))
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0));
	else
		tmp = (x + (z / (t / y))) / ((a + (y / (t / b))) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -400.0], N[Not[LessEqual[b, 8e+97]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -400 or 8.0000000000000006e97 < b

   1. Initial program 60.2%

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

   3. Taylor expanded in x around 0 59.7%

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

   4. Taylor expanded in y around inf 84.5%

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

   if -400 < b < 8.0000000000000006e97

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-/l* 87.7%

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

      3. +-commutative 87.7%

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

      4. associate-+l+ 87.7%

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

      5. associate-*r/ 87.7%

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

      6. *-commutative 87.7%

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

   3. Simplified 87.7%

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

      1. associate-*l/ 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-/l* 87.7%

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

   6. Applied egg-rr 87.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -400 \lor \neg \left(b \leq 8 \cdot 10^{+97}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ t_2 := \frac{t_1}{a}\\ \mathbf{if}\;a \leq -22000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-256}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ t z)))) (t_2 (/ t_1 a)))
   (if (<= a -22000000000.0)
     t_2
     (if (<= a -1.1e-306)
       t_1
       (if (<= a 8e-256)
         (/ z b)
         (if (<= a 1.28e-61) t_1 (if (<= a 1.2e+69) (/ z b) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y / (t / z));
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -22000000000.0) {
		tmp = t_2;
	} else if (a <= -1.1e-306) {
		tmp = t_1;
	} else if (a <= 8e-256) {
		tmp = z / b;
	} else if (a <= 1.28e-61) {
		tmp = t_1;
	} else if (a <= 1.2e+69) {
		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 = x + (y / (t / z))
    t_2 = t_1 / a
    if (a <= (-22000000000.0d0)) then
        tmp = t_2
    else if (a <= (-1.1d-306)) then
        tmp = t_1
    else if (a <= 8d-256) then
        tmp = z / b
    else if (a <= 1.28d-61) then
        tmp = t_1
    else if (a <= 1.2d+69) 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 = x + (y / (t / z));
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -22000000000.0) {
		tmp = t_2;
	} else if (a <= -1.1e-306) {
		tmp = t_1;
	} else if (a <= 8e-256) {
		tmp = z / b;
	} else if (a <= 1.28e-61) {
		tmp = t_1;
	} else if (a <= 1.2e+69) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y / (t / z))
	t_2 = t_1 / a
	tmp = 0
	if a <= -22000000000.0:
		tmp = t_2
	elif a <= -1.1e-306:
		tmp = t_1
	elif a <= 8e-256:
		tmp = z / b
	elif a <= 1.28e-61:
		tmp = t_1
	elif a <= 1.2e+69:
		tmp = z / b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y / Float64(t / z)))
	t_2 = Float64(t_1 / a)
	tmp = 0.0
	if (a <= -22000000000.0)
		tmp = t_2;
	elseif (a <= -1.1e-306)
		tmp = t_1;
	elseif (a <= 8e-256)
		tmp = Float64(z / b);
	elseif (a <= 1.28e-61)
		tmp = t_1;
	elseif (a <= 1.2e+69)
		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 = x + (y / (t / z));
	t_2 = t_1 / a;
	tmp = 0.0;
	if (a <= -22000000000.0)
		tmp = t_2;
	elseif (a <= -1.1e-306)
		tmp = t_1;
	elseif (a <= 8e-256)
		tmp = z / b;
	elseif (a <= 1.28e-61)
		tmp = t_1;
	elseif (a <= 1.2e+69)
		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[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / a), $MachinePrecision]}, If[LessEqual[a, -22000000000.0], t$95$2, If[LessEqual[a, -1.1e-306], t$95$1, If[LessEqual[a, 8e-256], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.28e-61], t$95$1, If[LessEqual[a, 1.2e+69], N[(z / b), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2e10 or 1.2000000000000001e69 < a

   1. Initial program 77.8%

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

   3. Taylor expanded in b around 0 63.1%

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

   4. Taylor expanded in a around inf 63.1%

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

      1. associate-/l* 64.9%

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

   6. Simplified 64.9%

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

   if -2.2e10 < a < -1.10000000000000008e-306 or 7.99999999999999982e-256 < a < 1.28000000000000009e-61

   1. Initial program 83.7%

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

   3. Taylor expanded in b around 0 63.4%

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

   4. Taylor expanded in a around 0 63.4%

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

      1. associate-/l* 64.5%

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

   6. Simplified 64.5%

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

   if -1.10000000000000008e-306 < a < 7.99999999999999982e-256 or 1.28000000000000009e-61 < a < 1.2000000000000001e69

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf 66.3%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -22000000000:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-306}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-256}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{t}{y} \cdot \frac{a + 1}{z}}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+217}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* (/ t y) (/ (+ a 1.0) z)))))
   (if (<= z -1.65e+217)
     (/ z b)
     (if (<= z -3.5e+118)
       t_1
       (if (<= z 2.8e+69)
         (/ x (+ (+ a (/ (* y b) t)) 1.0))
         (if (<= z 4e+136) (+ (/ z b) (/ (* x t) (* y b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 / ((t / y) * ((a + 1.0) / z));
	double tmp;
	if (z <= -1.65e+217) {
		tmp = z / b;
	} else if (z <= -3.5e+118) {
		tmp = t_1;
	} else if (z <= 2.8e+69) {
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	} else if (z <= 4e+136) {
		tmp = (z / b) + ((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 = 1.0d0 / ((t / y) * ((a + 1.0d0) / z))
    if (z <= (-1.65d+217)) then
        tmp = z / b
    else if (z <= (-3.5d+118)) then
        tmp = t_1
    else if (z <= 2.8d+69) then
        tmp = x / ((a + ((y * b) / t)) + 1.0d0)
    else if (z <= 4d+136) then
        tmp = (z / b) + ((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 = 1.0 / ((t / y) * ((a + 1.0) / z));
	double tmp;
	if (z <= -1.65e+217) {
		tmp = z / b;
	} else if (z <= -3.5e+118) {
		tmp = t_1;
	} else if (z <= 2.8e+69) {
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	} else if (z <= 4e+136) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 / ((t / y) * ((a + 1.0) / z))
	tmp = 0
	if z <= -1.65e+217:
		tmp = z / b
	elif z <= -3.5e+118:
		tmp = t_1
	elif z <= 2.8e+69:
		tmp = x / ((a + ((y * b) / t)) + 1.0)
	elif z <= 4e+136:
		tmp = (z / b) + ((x * t) / (y * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 / Float64(Float64(t / y) * Float64(Float64(a + 1.0) / z)))
	tmp = 0.0
	if (z <= -1.65e+217)
		tmp = Float64(z / b);
	elseif (z <= -3.5e+118)
		tmp = t_1;
	elseif (z <= 2.8e+69)
		tmp = Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 1.0));
	elseif (z <= 4e+136)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 / ((t / y) * ((a + 1.0) / z));
	tmp = 0.0;
	if (z <= -1.65e+217)
		tmp = z / b;
	elseif (z <= -3.5e+118)
		tmp = t_1;
	elseif (z <= 2.8e+69)
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	elseif (z <= 4e+136)
		tmp = (z / b) + ((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[(1.0 / N[(N[(t / y), $MachinePrecision] * N[(N[(a + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+217], N[(z / b), $MachinePrecision], If[LessEqual[z, -3.5e+118], t$95$1, If[LessEqual[z, 2.8e+69], N[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+136], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.65e217

   1. Initial program 57.1%

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

   3. Taylor expanded in y around inf 59.0%

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

   if -1.65e217 < z < -3.50000000000000016e118 or 4.00000000000000023e136 < z

   1. Initial program 63.5%

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

   3. Taylor expanded in b around 0 59.7%

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

      1. clear-num 59.6%

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

      2. inv-pow 59.6%

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

      3. associate-/l* 63.4%

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

   5. Applied egg-rr 63.4%

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

      1. unpow-1 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in x around 0 44.0%

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

      1. times-frac 56.5%

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

      2. *-commutative 56.5%

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

   10. Simplified 56.5%

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

   if -3.50000000000000016e118 < z < 2.79999999999999982e69

   1. Initial program 85.6%

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

   3. Taylor expanded in x around inf 72.9%

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

   if 2.79999999999999982e69 < z < 4.00000000000000023e136

   1. Initial program 62.9%

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

   3. Taylor expanded in b around inf 39.0%

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

   4. Taylor expanded in t around 0 63.8%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+217}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+118}:\\ \;\;\;\;\frac{1}{\frac{t}{y} \cdot \frac{a + 1}{z}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{t}{y} \cdot \frac{a + 1}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+72} \lor \neg \left(b \leq 6.5 \cdot 10^{+191}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1} + \frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.6e+72) (not (<= b 6.5e+191)))
   (+ (/ z b) (/ (* x t) (* y b)))
   (+ (* (/ y t) (/ z (+ a 1.0))) (/ x (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+72) || !(b <= 6.5e+191)) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (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 ((b <= (-3.6d+72)) .or. (.not. (b <= 6.5d+191))) then
        tmp = (z / b) + ((x * t) / (y * b))
    else
        tmp = ((y / t) * (z / (a + 1.0d0))) + (x / (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 ((b <= -3.6e+72) || !(b <= 6.5e+191)) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.6e+72) or not (b <= 6.5e+191):
		tmp = (z / b) + ((x * t) / (y * b))
	else:
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.6e+72) || !(b <= 6.5e+191))
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	else
		tmp = Float64(Float64(Float64(y / t) * Float64(z / Float64(a + 1.0))) + Float64(x / Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.6e+72) || ~((b <= 6.5e+191)))
		tmp = (z / b) + ((x * t) / (y * b));
	else
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.6e+72], N[Not[LessEqual[b, 6.5e+191]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.60000000000000035e72 or 6.50000000000000008e191 < b

   1. Initial program 57.7%

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

   3. Taylor expanded in b around inf 45.1%

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

   4. Taylor expanded in t around 0 68.8%

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

   if -3.60000000000000035e72 < b < 6.50000000000000008e191

   1. Initial program 84.8%

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

   3. Taylor expanded in b around 0 74.8%

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

   4. Taylor expanded in x around 0 74.8%

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

      1. +-commutative 74.8%

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

      2. times-frac 79.7%

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

   6. Simplified 79.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+72} \lor \neg \left(b \leq 6.5 \cdot 10^{+191}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1} + \frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-8} \lor \neg \left(b \leq 45000\right):\\ \;\;\;\;\frac{z}{b} + \frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1} + \frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.5e-8) (not (<= b 45000.0)))
   (+ (/ z b) (/ x (+ (+ a (/ (* y b) t)) 1.0)))
   (+ (* (/ y t) (/ z (+ a 1.0))) (/ x (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.5e-8) || !(b <= 45000.0)) {
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0));
	} else {
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (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 ((b <= (-8.5d-8)) .or. (.not. (b <= 45000.0d0))) then
        tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0d0))
    else
        tmp = ((y / t) * (z / (a + 1.0d0))) + (x / (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 ((b <= -8.5e-8) || !(b <= 45000.0)) {
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0));
	} else {
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8.5e-8) or not (b <= 45000.0):
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0))
	else:
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.5e-8) || !(b <= 45000.0))
		tmp = Float64(Float64(z / b) + Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 1.0)));
	else
		tmp = Float64(Float64(Float64(y / t) * Float64(z / Float64(a + 1.0))) + Float64(x / Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8.5e-8) || ~((b <= 45000.0)))
		tmp = (z / b) + (x / ((a + ((y * b) / t)) + 1.0));
	else
		tmp = ((y / t) * (z / (a + 1.0))) + (x / (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.5e-8], N[Not[LessEqual[b, 45000.0]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.49999999999999935e-8 or 45000 < b

   1. Initial program 62.9%

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

   3. Taylor expanded in x around 0 61.7%

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

   4. Taylor expanded in y around inf 83.3%

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

   if -8.49999999999999935e-8 < b < 45000

   1. Initial program 86.8%

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

   3. Taylor expanded in b around 0 77.9%

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

   4. Taylor expanded in x around 0 79.2%

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

      1. +-commutative 79.2%

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

      2. times-frac 83.2%

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

   6. Simplified 83.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-8} \lor \neg \left(b \leq 45000\right):\\ \;\;\;\;\frac{z}{b} + \frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1} + \frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+69} \lor \neg \left(b \leq 8.4 \cdot 10^{+191}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5e+69) (not (<= b 8.4e+191)))
   (+ (/ z b) (/ (* x t) (* y b)))
   (/ (+ x (* z (/ y t))) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5e+69) || !(b <= 8.4e+191)) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = (x + (z * (y / 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 ((b <= (-5d+69)) .or. (.not. (b <= 8.4d+191))) then
        tmp = (z / b) + ((x * t) / (y * b))
    else
        tmp = (x + (z * (y / 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 ((b <= -5e+69) || !(b <= 8.4e+191)) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5e+69) or not (b <= 8.4e+191):
		tmp = (z / b) + ((x * t) / (y * b))
	else:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5e+69) || !(b <= 8.4e+191))
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5e+69) || ~((b <= 8.4e+191)))
		tmp = (z / b) + ((x * t) / (y * b));
	else
		tmp = (x + (z * (y / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5e+69], N[Not[LessEqual[b, 8.4e+191]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.00000000000000036e69 or 8.4000000000000003e191 < b

   1. Initial program 57.7%

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

   3. Taylor expanded in b around inf 45.1%

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

   4. Taylor expanded in t around 0 68.8%

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

   if -5.00000000000000036e69 < b < 8.4000000000000003e191

   1. Initial program 84.8%

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

   3. Taylor expanded in b around 0 74.8%

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

      1. associate-/l* 75.1%

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

      2. associate-/r/ 77.1%

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

   5. Applied egg-rr 77.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+69} \lor \neg \left(b \leq 8.4 \cdot 10^{+191}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 40.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -22000000000:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-255}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -22000000000.0)
   (/ x a)
   (if (<= a -7.5e-303)
     x
     (if (<= a 1.75e-255)
       (/ z b)
       (if (<= a 5.5e-200) x (if (<= a 1.08e+71) (/ z b) (/ x a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -22000000000.0) {
		tmp = x / a;
	} else if (a <= -7.5e-303) {
		tmp = x;
	} else if (a <= 1.75e-255) {
		tmp = z / b;
	} else if (a <= 5.5e-200) {
		tmp = x;
	} else if (a <= 1.08e+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 (a <= (-22000000000.0d0)) then
        tmp = x / a
    else if (a <= (-7.5d-303)) then
        tmp = x
    else if (a <= 1.75d-255) then
        tmp = z / b
    else if (a <= 5.5d-200) then
        tmp = x
    else if (a <= 1.08d+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 (a <= -22000000000.0) {
		tmp = x / a;
	} else if (a <= -7.5e-303) {
		tmp = x;
	} else if (a <= 1.75e-255) {
		tmp = z / b;
	} else if (a <= 5.5e-200) {
		tmp = x;
	} else if (a <= 1.08e+71) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -22000000000.0:
		tmp = x / a
	elif a <= -7.5e-303:
		tmp = x
	elif a <= 1.75e-255:
		tmp = z / b
	elif a <= 5.5e-200:
		tmp = x
	elif a <= 1.08e+71:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -22000000000.0)
		tmp = Float64(x / a);
	elseif (a <= -7.5e-303)
		tmp = x;
	elseif (a <= 1.75e-255)
		tmp = Float64(z / b);
	elseif (a <= 5.5e-200)
		tmp = x;
	elseif (a <= 1.08e+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 (a <= -22000000000.0)
		tmp = x / a;
	elseif (a <= -7.5e-303)
		tmp = x;
	elseif (a <= 1.75e-255)
		tmp = z / b;
	elseif (a <= 5.5e-200)
		tmp = x;
	elseif (a <= 1.08e+71)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -22000000000.0], N[(x / a), $MachinePrecision], If[LessEqual[a, -7.5e-303], x, If[LessEqual[a, 1.75e-255], N[(z / b), $MachinePrecision], If[LessEqual[a, 5.5e-200], x, If[LessEqual[a, 1.08e+71], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2e10 or 1.08e71 < a

   1. Initial program 77.8%

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

   3. Taylor expanded in y around 0 50.9%

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

   4. Taylor expanded in a around inf 50.9%

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

   if -2.2e10 < a < -7.49999999999999972e-303 or 1.74999999999999989e-255 < a < 5.4999999999999996e-200

   1. Initial program 86.3%

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

   3. Taylor expanded in y around 0 51.4%

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

   4. Taylor expanded in a around 0 51.4%

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

   if -7.49999999999999972e-303 < a < 1.74999999999999989e-255 or 5.4999999999999996e-200 < a < 1.08e71

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf 56.5%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -22000000000:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-255}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-80} \lor \neg \left(t \leq 1.45 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.36e-80) (not (<= t 1.45e-88))) (/ 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 <= -1.36e-80) || !(t <= 1.45e-88)) {
		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 <= (-1.36d-80)) .or. (.not. (t <= 1.45d-88))) 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 <= -1.36e-80) || !(t <= 1.45e-88)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.36e-80) or not (t <= 1.45e-88):
		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 <= -1.36e-80) || !(t <= 1.45e-88))
		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 <= -1.36e-80) || ~((t <= 1.45e-88)))
		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, -1.36e-80], N[Not[LessEqual[t, 1.45e-88]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3599999999999999e-80 or 1.4500000000000001e-88 < t

   1. Initial program 83.5%

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

   3. Taylor expanded in y around 0 57.4%

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

   if -1.3599999999999999e-80 < t < 1.4500000000000001e-88

   1. Initial program 64.9%

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

   3. Taylor expanded in y around inf 53.6%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-80} \lor \neg \left(t \leq 1.45 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -22000000000 \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -22000000000.0) (not (<= a 1.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -22000000000.0) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	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 ((a <= (-22000000000.0d0)) .or. (.not. (a <= 1.0d0))) then
        tmp = x / a
    else
        tmp = x
    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 ((a <= -22000000000.0) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -22000000000.0) or not (a <= 1.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -22000000000.0) || !(a <= 1.0))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -22000000000.0) || ~((a <= 1.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -22000000000.0], N[Not[LessEqual[a, 1.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -2.2e10 or 1 < a

   1. Initial program 74.8%

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

   3. Taylor expanded in y around 0 46.8%

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

   4. Taylor expanded in a around inf 46.3%

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

   if -2.2e10 < a < 1

   1. Initial program 78.4%

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

   3. Taylor expanded in y around 0 40.3%

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

   4. Taylor expanded in a around 0 39.8%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -22000000000 \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 19.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.4%

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

3. Taylor expanded in y around 0 43.8%

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

4. Taylor expanded in a around 0 20.3%

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

5. Final simplification 20.3%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 79.7% 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 2024019 
(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))))