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

Percentage Accurate: 75.3% → 91.2%

Time: 22.1s

Alternatives: 18

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.3% 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: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_3 := \frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-246}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{+303}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0))))
        (t_3 (* (/ y t) (/ z (fma y (/ b t) (+ a 1.0))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -5e-246)
       t_2
       (if (<= t_2 1e+303)
         (/ t_1 (+ (+ a 1.0) (* b (/ y t))))
         (if (<= t_2 INFINITY) t_3 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = (y / t) * (z / fma(y, (b / t), (a + 1.0)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -5e-246) {
		tmp = t_2;
	} else if (t_2 <= 1e+303) {
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_3 = Float64(Float64(y / t) * Float64(z / fma(y, Float64(b / t), Float64(a + 1.0))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -5e-246)
		tmp = t_2;
	elseif (t_2 <= 1e+303)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / t), $MachinePrecision] * N[(z / N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -5e-246], t$95$2, If[LessEqual[t$95$2, 1e+303], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, 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))) < -inf.0 or 1e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 26.9%

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

      1. associate-/l* 62.0%

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

      2. associate-/l* 61.8%

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

   3. Simplified 61.8%

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

   5. Taylor expanded in x around 0 45.0%

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

      1. times-frac 93.0%

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

      2. associate-+r+ 93.0%

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

      3. associate-*r/ 86.3%

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

      4. *-commutative 86.3%

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

      5. associate-/r/ 89.6%

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

      6. +-commutative 89.6%

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

      7. associate-/r/ 86.3%

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

      8. *-commutative 86.3%

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

      9. associate-*r/ 93.0%

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

      10. associate-*l/ 89.7%

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

      11. *-commutative 89.7%

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

      12. fma-define 89.7%

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

   7. Simplified 89.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.9999999999999997e-246

   1. Initial program 99.6%

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

   if -4.9999999999999997e-246 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e303

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      2. associate-/l* 87.6%

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

   4. Applied egg-rr 87.6%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.7%

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

      2. associate-/l* 25.1%

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

   3. Simplified 25.1%

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

   5. Taylor expanded in y around inf 88.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-246}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1 + \left(a + 1\right)}\\ t_4 := 1 + \left(a + t\_1\right)\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{t\_4} + \frac{y \cdot z}{t \cdot t\_4}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 (+ t_1 (+ a 1.0))))
        (t_4 (+ 1.0 (+ a t_1))))
   (if (<= t_3 -1e-262)
     (+ (/ x t_4) (/ (* y z) (* t t_4)))
     (if (<= t_3 2e+301)
       (/ t_2 (+ (+ a 1.0) (* b (/ y t))))
       (if (<= t_3 INFINITY)
         (* y (/ (/ z t) (+ 1.0 (fma y (/ b t) a))))
         (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / (t_1 + (a + 1.0));
	double t_4 = 1.0 + (a + t_1);
	double tmp;
	if (t_3 <= -1e-262) {
		tmp = (x / t_4) + ((y * z) / (t * t_4));
	} else if (t_3 <= 2e+301) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = y * ((z / t) / (1.0 + fma(y, (b / t), a)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / Float64(t_1 + Float64(a + 1.0)))
	t_4 = Float64(1.0 + Float64(a + t_1))
	tmp = 0.0
	if (t_3 <= -1e-262)
		tmp = Float64(Float64(x / t_4) + Float64(Float64(y * z) / Float64(t * t_4)));
	elseif (t_3 <= 2e+301)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif (t_3 <= Inf)
		tmp = Float64(y * Float64(Float64(z / t) / Float64(1.0 + fma(y, Float64(b / t), a))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-262], N[(N[(x / t$95$4), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / N[(t * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+301], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(y * N[(N[(z / t), $MachinePrecision] / N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $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))) < -1.00000000000000001e-262

   1. Initial program 91.5%

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

      1. associate-/l* 89.1%

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

      2. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in x around 0 92.6%

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

   if -1.00000000000000001e-262 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.00000000000000011e301

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-/l* 87.3%

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

   4. Applied egg-rr 87.3%

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

   if 2.00000000000000011e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 27.8%

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

      1. associate-/l* 54.9%

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

      2. associate-/l* 54.7%

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

   3. Simplified 54.7%

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

   5. Taylor expanded in x around 0 49.1%

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

      1. associate-/l* 81.2%

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

      2. associate-+r+ 81.2%

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

      3. associate-*r/ 71.9%

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

      4. *-commutative 71.9%

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

      5. associate-/r/ 76.3%

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

      6. +-commutative 76.3%

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

      7. associate-/r/ 71.9%

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

      8. *-commutative 71.9%

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

      9. associate-*r/ 81.2%

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

      10. associate-*l/ 76.4%

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

      11. *-commutative 76.4%

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

      12. fma-define 76.4%

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

      13. +-commutative 76.4%

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

      14. associate-/r* 82.0%

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

      15. fma-undefine 82.0%

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

      16. associate-*r/ 82.2%

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

      17. associate-*l/ 72.8%

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

      18. associate-/r/ 81.8%

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

      19. associate-+r+ 81.8%

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

      20. +-commutative 81.8%

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

   7. Simplified 82.0%

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

   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. Step-by-step derivation

      1. associate-/l* 0.7%

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

      2. associate-/l* 25.1%

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

   3. Simplified 25.1%

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

   5. Taylor expanded in y around inf 88.2%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+29} \lor \neg \left(t \leq 9 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + {\left(t \cdot \left(\frac{1}{y \cdot z} + \frac{a}{y \cdot z}\right) + \frac{b}{z}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.45e+29) (not (<= t 9e-114)))
   (/ (+ x (/ y (/ t z))) (+ (* y (/ b t)) (+ a 1.0)))
   (+
    (/ x (+ 1.0 (+ a (/ (* y b) t))))
    (pow (+ (* t (+ (/ 1.0 (* y z)) (/ a (* y z)))) (/ b z)) -1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.45e+29) || !(t <= 9e-114)) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (x / (1.0 + (a + ((y * b) / t)))) + pow(((t * ((1.0 / (y * z)) + (a / (y * z)))) + (b / z)), -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.45d+29)) .or. (.not. (t <= 9d-114))) then
        tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0d0))
    else
        tmp = (x / (1.0d0 + (a + ((y * b) / t)))) + (((t * ((1.0d0 / (y * z)) + (a / (y * z)))) + (b / z)) ** (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.45e+29) || !(t <= 9e-114)) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (x / (1.0 + (a + ((y * b) / t)))) + Math.pow(((t * ((1.0 / (y * z)) + (a / (y * z)))) + (b / z)), -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.45e+29) or not (t <= 9e-114):
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = (x / (1.0 + (a + ((y * b) / t)))) + math.pow(((t * ((1.0 / (y * z)) + (a / (y * z)))) + (b / z)), -1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.45e+29) || !(t <= 9e-114))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))) + (Float64(Float64(t * Float64(Float64(1.0 / Float64(y * z)) + Float64(a / Float64(y * z)))) + Float64(b / z)) ^ -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.45e+29) || ~((t <= 9e-114)))
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = (x / (1.0 + (a + ((y * b) / t)))) + (((t * ((1.0 / (y * z)) + (a / (y * z)))) + (b / z)) ^ -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.45e+29], N[Not[LessEqual[t, 9e-114]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[Power[N[(N[(t * N[(N[(1.0 / N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45e29 or 8.99999999999999937e-114 < t

   1. Initial program 76.5%

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

      1. associate-/l* 83.6%

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

      2. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

      1. clear-num 73.3%

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

      2. un-div-inv 73.3%

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

   6. Applied egg-rr 93.6%

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

   if -1.45e29 < t < 8.99999999999999937e-114

   1. Initial program 70.4%

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

      1. associate-/l* 61.6%

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

      2. associate-/l* 54.4%

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

   3. Simplified 54.4%

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

   5. Taylor expanded in x around 0 76.6%

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

      1. clear-num 76.5%

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

      2. inv-pow 76.5%

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

      3. *-commutative 76.5%

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

      4. times-frac 61.4%

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

      5. associate-+r+ 61.4%

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

      6. *-commutative 61.4%

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

      7. *-un-lft-identity 61.4%

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

      8. associate-*l/ 60.6%

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

      9. +-commutative 60.6%

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

      10. associate-*l/ 61.4%

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

      11. *-un-lft-identity 61.4%

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

      12. *-commutative 61.4%

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

      13. associate-/l* 53.9%

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

      14. fma-define 53.9%

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

   7. Applied egg-rr 53.9%

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

   8. Taylor expanded in t around 0 86.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+29} \lor \neg \left(t \leq 9 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + {\left(t \cdot \left(\frac{1}{y \cdot z} + \frac{a}{y \cdot z}\right) + \frac{b}{z}\right)}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-246}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 10^{+303}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0)))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 t_1)))
   (if (<= t_3 (- INFINITY))
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t_3 -5e-246)
       t_3
       (if (<= t_3 1e+303) (/ t_2 (+ (+ a 1.0) (* b (/ y t)))) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_3 <= -5e-246) {
		tmp = t_3;
	} else if (t_3 <= 1e+303) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} 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 = ((y * b) / t) + (a + 1.0);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_3 <= -5e-246) {
		tmp = t_3;
	} else if (t_3 <= 1e+303) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = x + ((y * z) / t)
	t_3 = t_2 / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (x + (z * (y / t))) / t_1
	elif t_3 <= -5e-246:
		tmp = t_3
	elif t_3 <= 1e+303:
		tmp = t_2 / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t_3 <= -5e-246)
		tmp = t_3;
	elseif (t_3 <= 1e+303)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t_3 <= -5e-246)
		tmp = t_3;
	elseif (t_3 <= 1e+303)
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, -5e-246], t$95$3, If[LessEqual[t$95$3, 1e+303], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $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))) < -inf.0

   1. Initial program 32.6%

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

      1. *-commutative 32.6%

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

      2. associate-/l* 80.7%

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

   4. Applied egg-rr 80.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.9999999999999997e-246

   1. Initial program 99.6%

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

   if -4.9999999999999997e-246 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e303

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      2. associate-/l* 87.6%

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

   4. Applied egg-rr 87.6%

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

   if 1e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.0%

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

      1. associate-/l* 24.4%

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

      2. associate-/l* 37.5%

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

   3. Simplified 37.5%

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

   5. Taylor expanded in y around inf 71.6%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-246}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1 + \left(a + 1\right)}\\ t_4 := 1 + \left(a + t\_1\right)\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{t\_4} + \frac{y \cdot z}{t \cdot t\_4}\\ \mathbf{elif}\;t\_3 \leq 10^{+303}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 (+ t_1 (+ a 1.0))))
        (t_4 (+ 1.0 (+ a t_1))))
   (if (<= t_3 -1e-262)
     (+ (/ x t_4) (/ (* y z) (* t t_4)))
     (if (<= t_3 1e+303) (/ t_2 (+ (+ a 1.0) (* b (/ y t)))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / (t_1 + (a + 1.0));
	double t_4 = 1.0 + (a + t_1);
	double tmp;
	if (t_3 <= -1e-262) {
		tmp = (x / t_4) + ((y * z) / (t * t_4));
	} else if (t_3 <= 1e+303) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y * b) / t
    t_2 = x + ((y * z) / t)
    t_3 = t_2 / (t_1 + (a + 1.0d0))
    t_4 = 1.0d0 + (a + t_1)
    if (t_3 <= (-1d-262)) then
        tmp = (x / t_4) + ((y * z) / (t * t_4))
    else if (t_3 <= 1d+303) then
        tmp = t_2 / ((a + 1.0d0) + (b * (y / t)))
    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 t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / (t_1 + (a + 1.0));
	double t_4 = 1.0 + (a + t_1);
	double tmp;
	if (t_3 <= -1e-262) {
		tmp = (x / t_4) + ((y * z) / (t * t_4));
	} else if (t_3 <= 1e+303) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = x + ((y * z) / t)
	t_3 = t_2 / (t_1 + (a + 1.0))
	t_4 = 1.0 + (a + t_1)
	tmp = 0
	if t_3 <= -1e-262:
		tmp = (x / t_4) + ((y * z) / (t * t_4))
	elif t_3 <= 1e+303:
		tmp = t_2 / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / Float64(t_1 + Float64(a + 1.0)))
	t_4 = Float64(1.0 + Float64(a + t_1))
	tmp = 0.0
	if (t_3 <= -1e-262)
		tmp = Float64(Float64(x / t_4) + Float64(Float64(y * z) / Float64(t * t_4)));
	elseif (t_3 <= 1e+303)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / (t_1 + (a + 1.0));
	t_4 = 1.0 + (a + t_1);
	tmp = 0.0;
	if (t_3 <= -1e-262)
		tmp = (x / t_4) + ((y * z) / (t * t_4));
	elseif (t_3 <= 1e+303)
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-262], N[(N[(x / t$95$4), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / N[(t * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+303], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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))) < -1.00000000000000001e-262

   1. Initial program 91.5%

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

      1. associate-/l* 89.1%

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

      2. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in x around 0 92.6%

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

   if -1.00000000000000001e-262 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e303

   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. Step-by-step derivation

      1. *-commutative 83.7%

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

      2. associate-/l* 87.4%

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

   4. Applied egg-rr 87.4%

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

   if 1e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.0%

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

      1. associate-/l* 24.4%

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

      2. associate-/l* 37.5%

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

   3. Simplified 37.5%

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

   5. Taylor expanded in y around inf 71.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-56}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) (+ a 1.0))))
   (if (<= t -2.7e-18)
     t_1
     (if (<= t -8.4e-47)
       (/ x (+ 1.0 (+ a (* b (/ y t)))))
       (if (<= t -5.7e-56)
         (/ (+ x (* y (/ z t))) (+ a 1.0))
         (if (<= t -3.2e-106)
           (/ z b)
           (if (<= t 3.5e-159)
             (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
             (if (<= t 3.4e-59) (/ x (+ 1.0 (+ a (/ (* y b) t)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (t <= -2.7e-18) {
		tmp = t_1;
	} else if (t <= -8.4e-47) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else if (t <= -5.7e-56) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= -3.2e-106) {
		tmp = z / b;
	} else if (t <= 3.5e-159) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= 3.4e-59) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / (a + 1.0d0)
    if (t <= (-2.7d-18)) then
        tmp = t_1
    else if (t <= (-8.4d-47)) then
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    else if (t <= (-5.7d-56)) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else if (t <= (-3.2d-106)) then
        tmp = z / b
    else if (t <= 3.5d-159) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else if (t <= 3.4d-59) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (t <= -2.7e-18) {
		tmp = t_1;
	} else if (t <= -8.4e-47) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else if (t <= -5.7e-56) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= -3.2e-106) {
		tmp = z / b;
	} else if (t <= 3.5e-159) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= 3.4e-59) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / (a + 1.0)
	tmp = 0
	if t <= -2.7e-18:
		tmp = t_1
	elif t <= -8.4e-47:
		tmp = x / (1.0 + (a + (b * (y / t))))
	elif t <= -5.7e-56:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	elif t <= -3.2e-106:
		tmp = z / b
	elif t <= 3.5e-159:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	elif t <= 3.4e-59:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.7e-18)
		tmp = t_1;
	elseif (t <= -8.4e-47)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	elseif (t <= -5.7e-56)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	elseif (t <= -3.2e-106)
		tmp = Float64(z / b);
	elseif (t <= 3.5e-159)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	elseif (t <= 3.4e-59)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.7e-18)
		tmp = t_1;
	elseif (t <= -8.4e-47)
		tmp = x / (1.0 + (a + (b * (y / t))));
	elseif (t <= -5.7e-56)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	elseif (t <= -3.2e-106)
		tmp = z / b;
	elseif (t <= 3.5e-159)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	elseif (t <= 3.4e-59)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e-18], t$95$1, If[LessEqual[t, -8.4e-47], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.7e-56], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.2e-106], N[(z / b), $MachinePrecision], If[LessEqual[t, 3.5e-159], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-59], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.69999999999999989e-18 or 3.40000000000000018e-59 < t

   1. Initial program 74.2%

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

      1. associate-/l* 81.4%

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

      2. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around 0 73.2%

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

      1. clear-num 73.1%

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

      2. un-div-inv 73.2%

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

   7. Applied egg-rr 73.2%

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

   if -2.69999999999999989e-18 < t < -8.4000000000000003e-47

   1. Initial program 99.3%

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

      1. associate-/l* 99.3%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 86.0%

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

      1. associate-/l* 86.3%

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

   7. Applied egg-rr 86.3%

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

   if -8.4000000000000003e-47 < t < -5.6999999999999998e-56

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

   if -5.6999999999999998e-56 < t < -3.2e-106

   1. Initial program 63.6%

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

      1. associate-/l* 63.2%

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

      2. associate-/l* 51.3%

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

   3. Simplified 51.3%

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

   5. Taylor expanded in y around inf 88.0%

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

   if -3.2e-106 < t < 3.50000000000000002e-159

   1. Initial program 65.1%

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

      1. associate-/l* 53.9%

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

      2. associate-/l* 46.5%

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

   3. Simplified 46.5%

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

   5. Taylor expanded in x around 0 56.8%

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

   6. Taylor expanded in t around 0 75.7%

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

   if 3.50000000000000002e-159 < t < 3.40000000000000018e-59

   1. Initial program 89.1%

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

      1. associate-/l* 81.8%

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

      2. associate-/l* 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in x around inf 74.7%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-56}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.38 \cdot 10^{-164}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ a 1.0))))
   (if (<= t -2.65e-18)
     t_1
     (if (<= t -1.12e-46)
       (/ x (+ 1.0 (+ a (* b (/ y t)))))
       (if (<= t -1.5e-56)
         t_1
         (if (<= t 1.38e-164)
           (/ z b)
           (if (<= t 2.25e-57) (/ x (+ 1.0 (+ a (/ (* y b) t)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -2.65e-18) {
		tmp = t_1;
	} else if (t <= -1.12e-46) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else if (t <= -1.5e-56) {
		tmp = t_1;
	} else if (t <= 1.38e-164) {
		tmp = z / b;
	} else if (t <= 2.25e-57) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / (a + 1.0d0)
    if (t <= (-2.65d-18)) then
        tmp = t_1
    else if (t <= (-1.12d-46)) then
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    else if (t <= (-1.5d-56)) then
        tmp = t_1
    else if (t <= 1.38d-164) then
        tmp = z / b
    else if (t <= 2.25d-57) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -2.65e-18) {
		tmp = t_1;
	} else if (t <= -1.12e-46) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else if (t <= -1.5e-56) {
		tmp = t_1;
	} else if (t <= 1.38e-164) {
		tmp = z / b;
	} else if (t <= 2.25e-57) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / (a + 1.0)
	tmp = 0
	if t <= -2.65e-18:
		tmp = t_1
	elif t <= -1.12e-46:
		tmp = x / (1.0 + (a + (b * (y / t))))
	elif t <= -1.5e-56:
		tmp = t_1
	elif t <= 1.38e-164:
		tmp = z / b
	elif t <= 2.25e-57:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.65e-18)
		tmp = t_1;
	elseif (t <= -1.12e-46)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	elseif (t <= -1.5e-56)
		tmp = t_1;
	elseif (t <= 1.38e-164)
		tmp = Float64(z / b);
	elseif (t <= 2.25e-57)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.65e-18)
		tmp = t_1;
	elseif (t <= -1.12e-46)
		tmp = x / (1.0 + (a + (b * (y / t))));
	elseif (t <= -1.5e-56)
		tmp = t_1;
	elseif (t <= 1.38e-164)
		tmp = z / b;
	elseif (t <= 2.25e-57)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.65e-18], t$95$1, If[LessEqual[t, -1.12e-46], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e-56], t$95$1, If[LessEqual[t, 1.38e-164], N[(z / b), $MachinePrecision], If[LessEqual[t, 2.25e-57], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.65000000000000015e-18 or -1.11999999999999997e-46 < t < -1.49999999999999995e-56 or 2.24999999999999986e-57 < t

   1. Initial program 74.8%

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

      1. associate-/l* 81.8%

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

      2. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in y around 0 73.7%

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

   if -2.65000000000000015e-18 < t < -1.11999999999999997e-46

   1. Initial program 99.3%

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

      1. associate-/l* 99.3%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 86.0%

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

      1. associate-/l* 86.3%

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

   7. Applied egg-rr 86.3%

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

   if -1.49999999999999995e-56 < t < 1.38000000000000003e-164

   1. Initial program 64.6%

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

      1. associate-/l* 55.4%

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

      2. associate-/l* 47.4%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in y around inf 62.5%

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

   if 1.38000000000000003e-164 < t < 2.24999999999999986e-57

   1. Initial program 89.5%

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

      1. associate-/l* 79.1%

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

      2. associate-/l* 68.5%

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

   3. Simplified 68.5%

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

   5. Taylor expanded in x around inf 71.9%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{-18}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 1.38 \cdot 10^{-164}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.92 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-57}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-168}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) (+ a 1.0))))
   (if (<= t -2.15e-17)
     t_1
     (if (<= t -1.92e-47)
       (/ x (+ 1.0 (+ a (* b (/ y t)))))
       (if (<= t -9.6e-57)
         (/ (+ x (* y (/ z t))) (+ a 1.0))
         (if (<= t 2.9e-168)
           (/ z b)
           (if (<= t 1.12e-55) (/ x (+ 1.0 (+ a (/ (* y b) t)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (t <= -2.15e-17) {
		tmp = t_1;
	} else if (t <= -1.92e-47) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else if (t <= -9.6e-57) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= 2.9e-168) {
		tmp = z / b;
	} else if (t <= 1.12e-55) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / (a + 1.0d0)
    if (t <= (-2.15d-17)) then
        tmp = t_1
    else if (t <= (-1.92d-47)) then
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    else if (t <= (-9.6d-57)) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else if (t <= 2.9d-168) then
        tmp = z / b
    else if (t <= 1.12d-55) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (t <= -2.15e-17) {
		tmp = t_1;
	} else if (t <= -1.92e-47) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else if (t <= -9.6e-57) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= 2.9e-168) {
		tmp = z / b;
	} else if (t <= 1.12e-55) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / (a + 1.0)
	tmp = 0
	if t <= -2.15e-17:
		tmp = t_1
	elif t <= -1.92e-47:
		tmp = x / (1.0 + (a + (b * (y / t))))
	elif t <= -9.6e-57:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	elif t <= 2.9e-168:
		tmp = z / b
	elif t <= 1.12e-55:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.15e-17)
		tmp = t_1;
	elseif (t <= -1.92e-47)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	elseif (t <= -9.6e-57)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	elseif (t <= 2.9e-168)
		tmp = Float64(z / b);
	elseif (t <= 1.12e-55)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.15e-17)
		tmp = t_1;
	elseif (t <= -1.92e-47)
		tmp = x / (1.0 + (a + (b * (y / t))));
	elseif (t <= -9.6e-57)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	elseif (t <= 2.9e-168)
		tmp = z / b;
	elseif (t <= 1.12e-55)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e-17], t$95$1, If[LessEqual[t, -1.92e-47], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.6e-57], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-168], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.12e-55], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.15000000000000012e-17 or 1.11999999999999997e-55 < t

   1. Initial program 74.2%

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

      1. associate-/l* 81.4%

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

      2. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around 0 73.2%

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

      1. clear-num 73.1%

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

      2. un-div-inv 73.2%

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

   7. Applied egg-rr 73.2%

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

   if -2.15000000000000012e-17 < t < -1.92e-47

   1. Initial program 99.3%

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

      1. associate-/l* 99.3%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 86.0%

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

      1. associate-/l* 86.3%

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

   7. Applied egg-rr 86.3%

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

   if -1.92e-47 < t < -9.60000000000000025e-57

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

   if -9.60000000000000025e-57 < t < 2.8999999999999998e-168

   1. Initial program 64.6%

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

      1. associate-/l* 55.4%

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

      2. associate-/l* 47.4%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in y around inf 62.5%

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

   if 2.8999999999999998e-168 < t < 1.11999999999999997e-55

   1. Initial program 89.5%

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

      1. associate-/l* 79.1%

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

      2. associate-/l* 68.5%

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

   3. Simplified 68.5%

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

   5. Taylor expanded in x around inf 71.9%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-17}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq -1.92 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-57}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-168}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1} + y \cdot \frac{\frac{z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-160}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x (+ a 1.0)) (* y (/ (/ z t) (+ a 1.0))))))
   (if (<= t -8.5e-56)
     t_1
     (if (<= t 1.45e-160)
       (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
       (if (<= t 3.8e-64) (/ x (+ 1.0 (+ a (/ (* y b) t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a + 1.0)) + (y * ((z / t) / (a + 1.0)));
	double tmp;
	if (t <= -8.5e-56) {
		tmp = t_1;
	} else if (t <= 1.45e-160) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= 3.8e-64) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / (a + 1.0d0)) + (y * ((z / t) / (a + 1.0d0)))
    if (t <= (-8.5d-56)) then
        tmp = t_1
    else if (t <= 1.45d-160) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else if (t <= 3.8d-64) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a + 1.0)) + (y * ((z / t) / (a + 1.0)));
	double tmp;
	if (t <= -8.5e-56) {
		tmp = t_1;
	} else if (t <= 1.45e-160) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= 3.8e-64) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a + 1.0)) + (y * ((z / t) / (a + 1.0)))
	tmp = 0
	if t <= -8.5e-56:
		tmp = t_1
	elif t <= 1.45e-160:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	elif t <= 3.8e-64:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a + 1.0)) + Float64(y * Float64(Float64(z / t) / Float64(a + 1.0))))
	tmp = 0.0
	if (t <= -8.5e-56)
		tmp = t_1;
	elseif (t <= 1.45e-160)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	elseif (t <= 3.8e-64)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (a + 1.0)) + (y * ((z / t) / (a + 1.0)));
	tmp = 0.0;
	if (t <= -8.5e-56)
		tmp = t_1;
	elseif (t <= 1.45e-160)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	elseif (t <= 3.8e-64)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(z / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e-56], t$95$1, If[LessEqual[t, 1.45e-160], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-64], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.49999999999999932e-56 or 3.8000000000000002e-64 < t

   1. Initial program 75.9%

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

      1. associate-/l* 82.6%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in y around 0 71.1%

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

   6. Taylor expanded in x around 0 64.1%

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

      1. +-commutative 64.1%

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

      2. associate-/l* 69.0%

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

      3. associate-/r* 73.0%

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

   8. Simplified 73.0%

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

   if -8.49999999999999932e-56 < t < 1.45e-160

   1. Initial program 65.0%

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

      1. associate-/l* 54.8%

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

      2. associate-/l* 46.9%

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

   3. Simplified 46.9%

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

   5. Taylor expanded in x around 0 57.5%

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

   6. Taylor expanded in t around 0 74.6%

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

   if 1.45e-160 < t < 3.8000000000000002e-64

   1. Initial program 89.1%

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

      1. associate-/l* 81.8%

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

      2. associate-/l* 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in x around inf 74.7%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{a + 1} + y \cdot \frac{\frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-160}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1} + y \cdot \frac{\frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{-12}:\\ \;\;\;\;t\_1 + z \cdot \frac{\frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-155}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y \cdot \frac{\frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -3.9e-12)
     (+ t_1 (* z (/ (/ y t) (+ a 1.0))))
     (if (<= t 9.6e-155)
       (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
       (if (<= t 2e-62)
         (/ x (+ 1.0 (+ a (/ (* y b) t))))
         (+ t_1 (* y (/ (/ z t) (+ a 1.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -3.9e-12) {
		tmp = t_1 + (z * ((y / t) / (a + 1.0)));
	} else if (t <= 9.6e-155) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= 2e-62) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1 + (y * ((z / t) / (a + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-3.9d-12)) then
        tmp = t_1 + (z * ((y / t) / (a + 1.0d0)))
    else if (t <= 9.6d-155) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else if (t <= 2d-62) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1 + (y * ((z / t) / (a + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -3.9e-12) {
		tmp = t_1 + (z * ((y / t) / (a + 1.0)));
	} else if (t <= 9.6e-155) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= 2e-62) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1 + (y * ((z / t) / (a + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -3.9e-12:
		tmp = t_1 + (z * ((y / t) / (a + 1.0)))
	elif t <= 9.6e-155:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	elif t <= 2e-62:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1 + (y * ((z / t) / (a + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -3.9e-12)
		tmp = Float64(t_1 + Float64(z * Float64(Float64(y / t) / Float64(a + 1.0))));
	elseif (t <= 9.6e-155)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	elseif (t <= 2e-62)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(t_1 + Float64(y * Float64(Float64(z / t) / Float64(a + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -3.9e-12)
		tmp = t_1 + (z * ((y / t) / (a + 1.0)));
	elseif (t <= 9.6e-155)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	elseif (t <= 2e-62)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1 + (y * ((z / t) / (a + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e-12], N[(t$95$1 + N[(z * N[(N[(y / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e-155], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-62], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * N[(N[(z / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.89999999999999994e-12

   1. Initial program 65.9%

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

      1. associate-/l* 73.4%

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

      2. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in y around 0 69.3%

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

   6. Taylor expanded in x around 0 58.3%

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

      1. associate-/l* 66.1%

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

   8. Applied egg-rr 66.1%

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

      1. associate-*r/ 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-*r/ 65.7%

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

      4. associate-/r* 71.6%

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

   10. Simplified 71.6%

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

   if -3.89999999999999994e-12 < t < 9.600000000000001e-155

   1. Initial program 69.6%

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

      1. associate-/l* 60.8%

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

      2. associate-/l* 54.0%

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

   3. Simplified 54.0%

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

   5. Taylor expanded in x around 0 57.4%

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

   6. Taylor expanded in t around 0 72.2%

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

   if 9.600000000000001e-155 < t < 2.0000000000000001e-62

   1. Initial program 89.1%

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

      1. associate-/l* 81.8%

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

      2. associate-/l* 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in x around inf 74.7%

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

   if 2.0000000000000001e-62 < t

   1. Initial program 81.3%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around 0 77.0%

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

   6. Taylor expanded in x around 0 72.5%

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

      1. +-commutative 72.5%

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

      2. associate-/l* 74.1%

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

      3. associate-/r* 78.4%

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

   8. Simplified 78.4%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{a + 1} + z \cdot \frac{\frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-155}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1} + y \cdot \frac{\frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-165} \lor \neg \left(t \leq 4.8 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.2e-165) (not (<= t 4.8e-115)))
   (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))
   (/ (* y z) (+ (* y b) (* t (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e-165) || !(t <= 4.8e-115)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.2d-165)) .or. (.not. (t <= 4.8d-115))) then
        tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0d0))
    else
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e-165) || !(t <= 4.8e-115)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.2e-165) or not (t <= 4.8e-115):
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.2e-165) || !(t <= 4.8e-115))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.2e-165) || ~((t <= 4.8e-115)))
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.2e-165], N[Not[LessEqual[t, 4.8e-115]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.20000000000000015e-165 or 4.80000000000000042e-115 < t

   1. Initial program 78.4%

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

      1. associate-/l* 82.7%

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

      2. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   if -5.20000000000000015e-165 < t < 4.80000000000000042e-115

   1. Initial program 62.4%

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

      1. associate-/l* 51.0%

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

      2. associate-/l* 40.9%

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

   3. Simplified 40.9%

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

   5. Taylor expanded in x around 0 52.3%

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

   6. Taylor expanded in t around 0 73.9%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-165} \lor \neg \left(t \leq 4.8 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-168} \lor \neg \left(t \leq 1.2 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6e-168) (not (<= t 1.2e-114)))
   (/ (+ x (/ y (/ t z))) (+ (* y (/ b t)) (+ a 1.0)))
   (/ (* y z) (+ (* y b) (* t (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6e-168) || !(t <= 1.2e-114)) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-6d-168)) .or. (.not. (t <= 1.2d-114))) then
        tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0d0))
    else
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6e-168) || !(t <= 1.2e-114)) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6e-168) or not (t <= 1.2e-114):
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6e-168) || !(t <= 1.2e-114))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6e-168) || ~((t <= 1.2e-114)))
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6e-168], N[Not[LessEqual[t, 1.2e-114]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.99999999999999983e-168 or 1.2000000000000001e-114 < t

   1. Initial program 78.4%

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

      1. associate-/l* 82.7%

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

      2. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

      1. clear-num 66.1%

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

      2. un-div-inv 66.1%

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

   6. Applied egg-rr 89.8%

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

   if -5.99999999999999983e-168 < t < 1.2000000000000001e-114

   1. Initial program 62.4%

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

      1. associate-/l* 51.0%

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

      2. associate-/l* 40.9%

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

   3. Simplified 40.9%

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

   5. Taylor expanded in x around 0 52.3%

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

   6. Taylor expanded in t around 0 73.9%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-168} \lor \neg \left(t \leq 1.2 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+41} \lor \neg \left(t \leq 8.2 \cdot 10^{-166}\right):\\ \;\;\;\;z \cdot \frac{y}{t} + \frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.05e+41) (not (<= t 8.2e-166)))
   (+ (* z (/ y t)) (/ 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 <= -1.05e+41) || !(t <= 8.2e-166)) {
		tmp = (z * (y / t)) + (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 <= (-1.05d+41)) .or. (.not. (t <= 8.2d-166))) then
        tmp = (z * (y / t)) + (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 <= -1.05e+41) || !(t <= 8.2e-166)) {
		tmp = (z * (y / t)) + (x / (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.05e+41) or not (t <= 8.2e-166):
		tmp = (z * (y / t)) + (x / (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.05e+41) || !(t <= 8.2e-166))
		tmp = Float64(Float64(z * Float64(y / t)) + 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 <= -1.05e+41) || ~((t <= 8.2e-166)))
		tmp = (z * (y / t)) + (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, -1.05e+41], N[Not[LessEqual[t, 8.2e-166]], $MachinePrecision]], N[(N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e41 or 8.1999999999999995e-166 < t

   1. Initial program 76.2%

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

      1. associate-/l* 81.1%

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

      2. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around 0 69.9%

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

   6. Taylor expanded in x around 0 64.6%

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

   7. Taylor expanded in a around 0 54.8%

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

      1. *-commutative 54.8%

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

      2. associate-/l* 58.1%

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

   9. Simplified 58.1%

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

   if -1.05e41 < t < 8.1999999999999995e-166

   1. Initial program 70.5%

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

      1. associate-/l* 63.7%

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

      2. associate-/l* 57.8%

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

   3. Simplified 57.8%

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

   5. Taylor expanded in y around inf 55.7%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+41} \lor \neg \left(t \leq 8.2 \cdot 10^{-166}\right):\\ \;\;\;\;z \cdot \frac{y}{t} + \frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-56} \lor \neg \left(t \leq 4.3 \cdot 10^{-172}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.8e-56) (not (<= t 4.3e-172)))
   (/ x (+ 1.0 (+ a (* b (/ y t)))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.8e-56) || !(t <= 4.3e-172)) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} 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 <= (-2.8d-56)) .or. (.not. (t <= 4.3d-172))) then
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    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 <= -2.8e-56) || !(t <= 4.3e-172)) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.8e-56) or not (t <= 4.3e-172):
		tmp = x / (1.0 + (a + (b * (y / t))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.8e-56) || !(t <= 4.3e-172))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	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 <= -2.8e-56) || ~((t <= 4.3e-172)))
		tmp = x / (1.0 + (a + (b * (y / t))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.8e-56], N[Not[LessEqual[t, 4.3e-172]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999993e-56 or 4.2999999999999997e-172 < t

   1. Initial program 78.1%

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

      1. associate-/l* 82.1%

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

      2. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in x around inf 61.4%

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

      1. associate-/l* 64.2%

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

   7. Applied egg-rr 64.2%

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

   if -2.79999999999999993e-56 < t < 4.2999999999999997e-172

   1. Initial program 64.6%

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

      1. associate-/l* 55.4%

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

      2. associate-/l* 47.4%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in y around inf 62.5%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-56} \lor \neg \left(t \leq 4.3 \cdot 10^{-172}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.5e-107)
   (/ z b)
   (if (<= y 4.2e-210) x (if (<= y 4.2e-101) (/ x a) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.5e-107) {
		tmp = z / b;
	} else if (y <= 4.2e-210) {
		tmp = x;
	} else if (y <= 4.2e-101) {
		tmp = x / a;
	} 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 (y <= (-4.5d-107)) then
        tmp = z / b
    else if (y <= 4.2d-210) then
        tmp = x
    else if (y <= 4.2d-101) then
        tmp = x / a
    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 (y <= -4.5e-107) {
		tmp = z / b;
	} else if (y <= 4.2e-210) {
		tmp = x;
	} else if (y <= 4.2e-101) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.5e-107:
		tmp = z / b
	elif y <= 4.2e-210:
		tmp = x
	elif y <= 4.2e-101:
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.5e-107)
		tmp = Float64(z / b);
	elseif (y <= 4.2e-210)
		tmp = x;
	elseif (y <= 4.2e-101)
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.5e-107)
		tmp = z / b;
	elseif (y <= 4.2e-210)
		tmp = x;
	elseif (y <= 4.2e-101)
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.5e-107], N[(z / b), $MachinePrecision], If[LessEqual[y, 4.2e-210], x, If[LessEqual[y, 4.2e-101], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000016e-107 or 4.20000000000000031e-101 < y

   1. Initial program 59.9%

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

      1. associate-/l* 64.8%

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

      2. associate-/l* 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in y around inf 50.3%

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

   if -4.50000000000000016e-107 < y < 4.20000000000000032e-210

   1. Initial program 97.0%

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

      1. associate-/l* 90.7%

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

      2. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in a around 0 54.0%

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

   6. Taylor expanded in y around 0 45.5%

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

   if 4.20000000000000032e-210 < y < 4.20000000000000031e-101

   1. Initial program 99.7%

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

      1. associate-/l* 84.4%

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

      2. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in x around inf 62.7%

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

   6. Taylor expanded in a around inf 41.1%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-56} \lor \neg \left(t \leq 1.38 \cdot 10^{-164}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.3e-56) (not (<= t 1.38e-164))) (/ 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 <= -3.3e-56) || !(t <= 1.38e-164)) {
		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 <= (-3.3d-56)) .or. (.not. (t <= 1.38d-164))) 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 <= -3.3e-56) || !(t <= 1.38e-164)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.3e-56) or not (t <= 1.38e-164):
		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 <= -3.3e-56) || !(t <= 1.38e-164))
		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 <= -3.3e-56) || ~((t <= 1.38e-164)))
		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, -3.3e-56], N[Not[LessEqual[t, 1.38e-164]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.29999999999999984e-56 or 1.38000000000000003e-164 < t

   1. Initial program 78.1%

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

      1. associate-/l* 82.1%

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

      2. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in y around 0 53.6%

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

   if -3.29999999999999984e-56 < t < 1.38000000000000003e-164

   1. Initial program 64.6%

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

      1. associate-/l* 55.4%

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

      2. associate-/l* 47.4%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in y around inf 62.5%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-56} \lor \neg \left(t \leq 1.38 \cdot 10^{-164}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 41.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \lor \neg \left(a \leq 6.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.65) (not (<= a 6.2e-16))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.65) || !(a <= 6.2e-16)) {
		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 <= (-1.65d0)) .or. (.not. (a <= 6.2d-16))) 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 <= -1.65) || !(a <= 6.2e-16)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.65) or not (a <= 6.2e-16):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.65) || !(a <= 6.2e-16))
		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 <= -1.65) || ~((a <= 6.2e-16)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.65], N[Not[LessEqual[a, 6.2e-16]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.6499999999999999 or 6.2000000000000002e-16 < a

   1. Initial program 67.2%

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

      1. associate-/l* 67.2%

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

      2. associate-/l* 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in x around inf 44.2%

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

   6. Taylor expanded in a around inf 36.7%

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

   if -1.6499999999999999 < a < 6.2000000000000002e-16

   1. Initial program 82.6%

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

      1. associate-/l* 81.9%

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

      2. associate-/l* 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in a around 0 80.9%

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

   6. Taylor expanded in y around 0 43.0%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \lor \neg \left(a \leq 6.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 20.2% 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 73.7%

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

   1. associate-/l* 73.4%

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

   2. associate-/l* 75.3%

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

3. Simplified 75.3%

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

5. Taylor expanded in a around 0 47.1%

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

6. Taylor expanded in y around 0 20.4%

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

7. Final simplification 20.4%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 79.6% accurate, 0.5× 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 2024043 
(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))))