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

Percentage Accurate: 75.2% → 91.2%

Time: 21.1s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{b} \cdot \frac{t}{y}\\ \mathbf{elif}\;t_1 \leq 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (* (/ y t) (/ z (fma y (/ b t) (+ a 1.0))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -2e-300)
       t_1
       (if (<= t_1 0.0)
         (* (/ (fma y (/ z t) x) b) (/ t y))
         (if (<= t_1 1e+303) t_1 (if (<= t_1 INFINITY) t_2 (/ z b))))))))

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) + ((y * b) / t));
	double t_2 = (y / t) * (z / fma(y, (b / t), (a + 1.0)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -2e-300) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (fma(y, (z / t), x) / b) * (t / y);
	} else if (t_1 <= 1e+303) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(Float64(y / t) * Float64(z / fma(y, Float64(b / t), Float64(a + 1.0))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -2e-300)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(y, Float64(z / t), x) / b) * Float64(t / y));
	elseif (t_1 <= 1e+303)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -2e-300], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision] / b), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+303], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, 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 45.2%

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

      1. *-commutative 45.2%

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

      2. associate-*l/ 62.4%

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

      3. +-rgt-identity 62.4%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 62.4%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 62.4%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 62.4%

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

      7. *-commutative 62.4%

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

      8. associate-*l/ 62.1%

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

   3. Simplified 62.1%

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

   4. Taylor expanded in x around 0 67.6%

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

      1. times-frac 91.1%

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

      2. associate-+r+ 91.1%

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

      3. +-commutative 91.1%

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

      4. *-commutative 91.1%

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

      5. associate-*r/ 85.2%

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

      6. +-commutative 85.2%

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

      7. fma-udef 85.2%

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

      8. +-commutative 85.2%

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

   6. Simplified 85.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2.00000000000000005e-300 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e303

   1. Initial program 98.6%

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

   if -2.00000000000000005e-300 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-*l/ 59.3%

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

      3. +-rgt-identity 59.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 59.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 59.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 59.3%

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

      7. *-commutative 59.3%

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

      8. associate-*l/ 72.8%

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

   3. Simplified 72.8%

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

      1. associate-*l/ 59.3%

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

      2. associate-/l* 72.9%

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

   5. Applied egg-rr 72.9%

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

   6. Taylor expanded in b around inf 49.1%

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

      1. associate-/l* 47.1%

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

      2. *-commutative 47.1%

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

   8. Simplified 47.1%

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

      1. times-frac 79.4%

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

      2. *-commutative 79.4%

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

      3. +-commutative 79.4%

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

      4. div-inv 79.4%

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

      5. fma-def 79.4%

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

      6. clear-num 79.4%

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

   10. Applied egg-rr 79.4%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.5%

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

      3. +-rgt-identity 0.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 0.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 0.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 0.5%

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

      7. *-commutative 0.5%

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

      8. associate-*l/ 17.3%

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

   3. Simplified 17.3%

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

   4. Taylor expanded in t around 0 100.0%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-300}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{b} \cdot \frac{t}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2: 87.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{b} \cdot \frac{t}{y}\\ \mathbf{elif}\;t_1 \leq 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 -2e-300)
     t_1
     (if (<= t_1 0.0)
       (* (/ (fma y (/ z t) x) b) (/ t y))
       (if (<= t_1 1e+303) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -2e-300) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (fma(y, (z / t), x) / b) * (t / y);
	} else if (t_1 <= 1e+303) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= -2e-300)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(y, Float64(z / t), x) / b) * Float64(t / y));
	elseif (t_1 <= 1e+303)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-300], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision] / b), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+303], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2.00000000000000005e-300 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e303

   1. Initial program 94.1%

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

   if -2.00000000000000005e-300 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-*l/ 59.3%

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

      3. +-rgt-identity 59.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 59.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 59.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 59.3%

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

      7. *-commutative 59.3%

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

      8. associate-*l/ 72.8%

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

   3. Simplified 72.8%

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

      1. associate-*l/ 59.3%

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

      2. associate-/l* 72.9%

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

   5. Applied egg-rr 72.9%

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

   6. Taylor expanded in b around inf 49.1%

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

      1. associate-/l* 47.1%

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

      2. *-commutative 47.1%

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

   8. Simplified 47.1%

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

      1. times-frac 79.4%

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

      2. *-commutative 79.4%

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

      3. +-commutative 79.4%

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

      4. div-inv 79.4%

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

      5. fma-def 79.4%

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

      6. clear-num 79.4%

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

   10. Applied egg-rr 79.4%

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

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

   1. Initial program 22.0%

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

      1. *-commutative 22.0%

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

      2. associate-*l/ 31.2%

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

      3. +-rgt-identity 31.2%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 31.2%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 31.2%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 31.2%

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

      7. *-commutative 31.2%

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

      8. associate-*l/ 40.1%

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

   3. Simplified 40.1%

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

   4. Taylor expanded in t around 0 79.4%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-300}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{b} \cdot \frac{t}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-114}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 -4e-295)
     t_1
     (if (<= t_1 1e-114)
       (/ (+ x (* y (/ z t))) (+ a (+ 1.0 (/ b (/ t y)))))
       (if (<= t_1 INFINITY)
         (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
         (/ z b))))))

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) + ((y * b) / t));
	double tmp;
	if (t_1 <= -4e-295) {
		tmp = t_1;
	} else if (t_1 <= 1e-114) {
		tmp = (x + (y * (z / t))) / (a + (1.0 + (b / (t / y))));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -4e-295) {
		tmp = t_1;
	} else if (t_1 <= 1e-114) {
		tmp = (x + (y * (z / t))) / (a + (1.0 + (b / (t / y))));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -4e-295:
		tmp = t_1
	elif t_1 <= 1e-114:
		tmp = (x + (y * (z / t))) / (a + (1.0 + (b / (t / y))))
	elif t_1 <= math.inf:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= -4e-295)
		tmp = t_1;
	elseif (t_1 <= 1e-114)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -4e-295)
		tmp = t_1;
	elseif (t_1 <= 1e-114)
		tmp = (x + (y * (z / t))) / (a + (1.0 + (b / (t / y))));
	elseif (t_1 <= Inf)
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-295], t$95$1, If[LessEqual[t$95$1, 1e-114], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.00000000000000024e-295

   1. Initial program 90.5%

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

   if -4.00000000000000024e-295 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.0000000000000001e-114

   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. *-commutative 70.5%

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

      2. associate-*l/ 71.8%

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

      3. +-rgt-identity 71.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 71.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 71.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 71.8%

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

      7. *-commutative 71.8%

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

      8. associate-*l/ 75.9%

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

   3. Simplified 75.9%

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

      1. associate-*l/ 71.8%

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

      2. associate-/l* 81.2%

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

   5. Applied egg-rr 81.2%

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

   if 1.0000000000000001e-114 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 85.2%

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

      1. associate-/l* 86.6%

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

      2. +-rgt-identity 86.6%

         \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      3. associate-+l+ 86.6%

         \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      4. associate-+r+ 86.6%

         \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      5. +-rgt-identity 86.6%

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

      6. associate-/l* 86.6%

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

   3. Simplified 86.6%

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

      1. associate-/r/ 88.9%

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

   5. Applied egg-rr 88.9%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.5%

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

      3. +-rgt-identity 0.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 0.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 0.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 0.5%

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

      7. *-commutative 0.5%

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

      8. associate-*l/ 17.3%

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

   3. Simplified 17.3%

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

   4. Taylor expanded in t around 0 100.0%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -4 \cdot 10^{-295}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{-114}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + t \cdot \frac{\frac{x}{y}}{b}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;b \leq -1.16 \cdot 10^{+134}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{elif}\;b \leq 390000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+288}:\\ \;\;\;\;\frac{x}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* t (/ (/ x y) b))))
        (t_2 (/ (+ x (* y (/ z t))) (+ a 1.0))))
   (if (<= b -1.16e+134)
     (+ (/ z b) (* t (/ x (* y b))))
     (if (<= b 390000000000.0)
       t_2
       (if (<= b 2.35e+88)
         t_1
         (if (<= b 4.1e+103)
           t_2
           (if (<= b 6e+205)
             t_1
             (if (<= b 2.8e+288)
               (/ x (+ 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 = (z / b) + (t * ((x / y) / b));
	double t_2 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (b <= -1.16e+134) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else if (b <= 390000000000.0) {
		tmp = t_2;
	} else if (b <= 2.35e+88) {
		tmp = t_1;
	} else if (b <= 4.1e+103) {
		tmp = t_2;
	} else if (b <= 6e+205) {
		tmp = t_1;
	} else if (b <= 2.8e+288) {
		tmp = x / (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) :: tmp
    t_1 = (z / b) + (t * ((x / y) / b))
    t_2 = (x + (y * (z / t))) / (a + 1.0d0)
    if (b <= (-1.16d+134)) then
        tmp = (z / b) + (t * (x / (y * b)))
    else if (b <= 390000000000.0d0) then
        tmp = t_2
    else if (b <= 2.35d+88) then
        tmp = t_1
    else if (b <= 4.1d+103) then
        tmp = t_2
    else if (b <= 6d+205) then
        tmp = t_1
    else if (b <= 2.8d+288) then
        tmp = x / (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 = (z / b) + (t * ((x / y) / b));
	double t_2 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (b <= -1.16e+134) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else if (b <= 390000000000.0) {
		tmp = t_2;
	} else if (b <= 2.35e+88) {
		tmp = t_1;
	} else if (b <= 4.1e+103) {
		tmp = t_2;
	} else if (b <= 6e+205) {
		tmp = t_1;
	} else if (b <= 2.8e+288) {
		tmp = x / (a + (1.0 + (b * (y / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + (t * ((x / y) / b))
	t_2 = (x + (y * (z / t))) / (a + 1.0)
	tmp = 0
	if b <= -1.16e+134:
		tmp = (z / b) + (t * (x / (y * b)))
	elif b <= 390000000000.0:
		tmp = t_2
	elif b <= 2.35e+88:
		tmp = t_1
	elif b <= 4.1e+103:
		tmp = t_2
	elif b <= 6e+205:
		tmp = t_1
	elif b <= 2.8e+288:
		tmp = x / (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(z / b) + Float64(t * Float64(Float64(x / y) / b)))
	t_2 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (b <= -1.16e+134)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(x / Float64(y * b))));
	elseif (b <= 390000000000.0)
		tmp = t_2;
	elseif (b <= 2.35e+88)
		tmp = t_1;
	elseif (b <= 4.1e+103)
		tmp = t_2;
	elseif (b <= 6e+205)
		tmp = t_1;
	elseif (b <= 2.8e+288)
		tmp = Float64(x / Float64(a + Float64(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 = (z / b) + (t * ((x / y) / b));
	t_2 = (x + (y * (z / t))) / (a + 1.0);
	tmp = 0.0;
	if (b <= -1.16e+134)
		tmp = (z / b) + (t * (x / (y * b)));
	elseif (b <= 390000000000.0)
		tmp = t_2;
	elseif (b <= 2.35e+88)
		tmp = t_1;
	elseif (b <= 4.1e+103)
		tmp = t_2;
	elseif (b <= 6e+205)
		tmp = t_1;
	elseif (b <= 2.8e+288)
		tmp = x / (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[(z / b), $MachinePrecision] + N[(t * N[(N[(x / y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.16e+134], N[(N[(z / b), $MachinePrecision] + N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 390000000000.0], t$95$2, If[LessEqual[b, 2.35e+88], t$95$1, If[LessEqual[b, 4.1e+103], t$95$2, If[LessEqual[b, 6e+205], t$95$1, If[LessEqual[b, 2.8e+288], N[(x / N[(a + N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.16e134

   1. Initial program 61.9%

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

      1. *-commutative 61.9%

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

      2. associate-*l/ 63.6%

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

      3. +-rgt-identity 63.6%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 63.6%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 63.6%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 63.6%

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

      7. *-commutative 63.6%

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

      8. associate-*l/ 51.7%

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

   3. Simplified 51.7%

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

   4. Taylor expanded in t around 0 65.9%

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

   5. Taylor expanded in x around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-*r/ 70.9%

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

   7. Simplified 70.9%

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

   if -1.16e134 < b < 3.9e11 or 2.35000000000000004e88 < b < 4.1000000000000002e103

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-*l/ 86.0%

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

      3. +-rgt-identity 86.0%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 86.0%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 86.0%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 86.0%

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

      7. *-commutative 86.0%

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

      8. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in b around 0 76.3%

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

   if 3.9e11 < b < 2.35000000000000004e88 or 4.1000000000000002e103 < b < 5.9999999999999999e205

   1. Initial program 54.5%

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

      1. *-commutative 54.5%

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

      2. associate-*l/ 45.9%

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

      3. +-rgt-identity 45.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 45.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 45.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 45.9%

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

      7. *-commutative 45.9%

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

      8. associate-*l/ 57.5%

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

   3. Simplified 57.5%

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

   4. Taylor expanded in t around 0 62.0%

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

   5. Taylor expanded in x around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. associate-*r/ 71.5%

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

      3. associate-/r* 80.2%

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

   7. Simplified 80.2%

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

   if 5.9999999999999999e205 < b < 2.7999999999999998e288

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. associate-*l/ 89.3%

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

      3. +-rgt-identity 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

      1. associate-*l/ 89.3%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 79.8%

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

      1. +-commutative 79.8%

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

      2. *-commutative 79.8%

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

      3. associate-+r+ 79.8%

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

      4. +-commutative 79.8%

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

      5. associate-*l/ 90.3%

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

      6. *-commutative 90.3%

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

   8. Simplified 90.3%

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

   if 2.7999999999999998e288 < b

   1. Initial program 1.7%

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

      1. *-commutative 1.7%

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

      2. associate-*l/ 0.7%

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

      3. +-rgt-identity 0.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 0.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 0.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 0.7%

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

      7. *-commutative 0.7%

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

      8. associate-*l/ 20.0%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in t around 0 80.7%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{+134}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{elif}\;b \leq 390000000000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+88}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{y}}{b}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+103}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+205}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{y}}{b}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+288}:\\ \;\;\;\;\frac{x}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 5: 64.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -4 \cdot 10^{+18}:\\ \;\;\;\;\frac{1}{\frac{a}{x} + \left(\frac{\frac{b}{t}}{\frac{x}{y}} + \frac{1}{x}\right)}\\ \mathbf{elif}\;a + 1 \leq 1600:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} + \frac{z}{t} \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ a 1.0) -4e+18)
   (/ 1.0 (+ (/ a x) (+ (/ (/ b t) (/ x y)) (/ 1.0 x))))
   (if (<= (+ a 1.0) 1600.0)
     (/ (+ x (* y (/ z t))) (+ 1.0 (/ (* y b) t)))
     (+ (/ x a) (* (/ z t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a + 1.0) <= -4e+18) {
		tmp = 1.0 / ((a / x) + (((b / t) / (x / y)) + (1.0 / x)));
	} else if ((a + 1.0) <= 1600.0) {
		tmp = (x + (y * (z / t))) / (1.0 + ((y * b) / t));
	} else {
		tmp = (x / a) + ((z / t) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a + 1.0d0) <= (-4d+18)) then
        tmp = 1.0d0 / ((a / x) + (((b / t) / (x / y)) + (1.0d0 / x)))
    else if ((a + 1.0d0) <= 1600.0d0) then
        tmp = (x + (y * (z / t))) / (1.0d0 + ((y * b) / t))
    else
        tmp = (x / a) + ((z / t) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a + 1.0) <= -4e+18) {
		tmp = 1.0 / ((a / x) + (((b / t) / (x / y)) + (1.0 / x)));
	} else if ((a + 1.0) <= 1600.0) {
		tmp = (x + (y * (z / t))) / (1.0 + ((y * b) / t));
	} else {
		tmp = (x / a) + ((z / t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a + 1.0) <= -4e+18:
		tmp = 1.0 / ((a / x) + (((b / t) / (x / y)) + (1.0 / x)))
	elif (a + 1.0) <= 1600.0:
		tmp = (x + (y * (z / t))) / (1.0 + ((y * b) / t))
	else:
		tmp = (x / a) + ((z / t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a + 1.0) <= -4e+18)
		tmp = Float64(1.0 / Float64(Float64(a / x) + Float64(Float64(Float64(b / t) / Float64(x / y)) + Float64(1.0 / x))));
	elseif (Float64(a + 1.0) <= 1600.0)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(Float64(x / a) + Float64(Float64(z / t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a + 1.0) <= -4e+18)
		tmp = 1.0 / ((a / x) + (((b / t) / (x / y)) + (1.0 / x)));
	elseif ((a + 1.0) <= 1600.0)
		tmp = (x + (y * (z / t))) / (1.0 + ((y * b) / t));
	else
		tmp = (x / a) + ((z / t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a + 1.0), $MachinePrecision], -4e+18], N[(1.0 / N[(N[(a / x), $MachinePrecision] + N[(N[(N[(b / t), $MachinePrecision] / N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 1600.0], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 a 1) < -4e18

   1. Initial program 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-*l/ 83.5%

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

      3. +-rgt-identity 83.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 83.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 83.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 83.5%

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

      7. *-commutative 83.5%

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

      8. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

      1. associate-*l/ 83.5%

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

      2. associate-/l* 85.0%

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

   5. Applied egg-rr 85.0%

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

   6. Taylor expanded in x around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-+r+ 62.3%

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

      4. +-commutative 62.3%

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

      5. associate-*l/ 63.9%

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

      6. *-commutative 63.9%

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

   8. Simplified 63.9%

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

      1. clear-num 63.7%

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

      2. inv-pow 63.7%

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

      3. *-commutative 63.7%

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

      4. associate-*l/ 62.1%

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

      5. associate-*r/ 62.1%

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

      6. +-commutative 62.1%

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

      7. fma-udef 62.1%

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

   10. Applied egg-rr 62.1%

       \[\leadsto \color{blue}{{\left(\frac{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}{x}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 62.1%

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

   12. Simplified 62.1%

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

   13. Taylor expanded in a around 0 61.9%

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

       1. +-commutative 61.9%

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

       2. associate-+l+ 61.9%

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

       3. times-frac 68.3%

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

       4. associate-*r/ 62.0%

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

       5. associate-/l* 68.4%

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

   15. Simplified 68.4%

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

   if -4e18 < (+.f64 a 1) < 1600

   1. Initial program 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-*l/ 72.5%

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

      3. +-rgt-identity 72.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 72.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 72.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 72.5%

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

      7. *-commutative 72.5%

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

      8. associate-*l/ 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in a around 0 72.1%

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

   if 1600 < (+.f64 a 1)

   1. Initial program 75.2%

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

      1. *-commutative 75.2%

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

      2. associate-*l/ 76.7%

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

      3. +-rgt-identity 76.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 76.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 76.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 76.7%

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

      7. *-commutative 76.7%

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

      8. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in a around inf 66.8%

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

   5. Taylor expanded in x around 0 64.9%

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

      1. times-frac 71.2%

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

   7. Simplified 71.2%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -4 \cdot 10^{+18}:\\ \;\;\;\;\frac{1}{\frac{a}{x} + \left(\frac{\frac{b}{t}}{\frac{x}{y}} + \frac{1}{x}\right)}\\ \mathbf{elif}\;a + 1 \leq 1600:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} + \frac{z}{t} \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-125} \lor \neg \left(t \leq 6.2 \cdot 10^{-150}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.02e-125) (not (<= t 6.2e-150)))
   (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
   (+ (/ z b) (/ (* x t) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.02e-125) || !(t <= 6.2e-150)) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.02d-125)) .or. (.not. (t <= 6.2d-150))) then
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    else
        tmp = (z / b) + ((x * t) / (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.02e-125) || !(t <= 6.2e-150)) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.02e-125) or not (t <= 6.2e-150):
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.02e-125) || !(t <= 6.2e-150))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.02e-125) || ~((t <= 6.2e-150)))
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.02e-125], N[Not[LessEqual[t, 6.2e-150]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.02e-125 or 6.19999999999999996e-150 < t

   1. Initial program 81.6%

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

      1. associate-/l* 83.2%

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

      2. +-rgt-identity 83.2%

         \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      3. associate-+l+ 83.2%

         \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      4. associate-+r+ 83.2%

         \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      5. +-rgt-identity 83.2%

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

      6. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

      1. associate-/r/ 88.7%

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

   5. Applied egg-rr 88.7%

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

   if -1.02e-125 < t < 6.19999999999999996e-150

   1. Initial program 57.3%

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

      1. *-commutative 57.3%

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

      2. associate-*l/ 55.5%

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

      3. +-rgt-identity 55.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 55.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 55.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 55.5%

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

      7. *-commutative 55.5%

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

      8. associate-*l/ 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in t around 0 53.4%

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

   5. Taylor expanded in x around inf 73.9%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-125} \lor \neg \left(t \leq 6.2 \cdot 10^{-150}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 7: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-150}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.5e-229)
   (/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* y (/ b t)))))
   (if (<= t 7e-150)
     (+ (/ z b) (/ (* x t) (* y b)))
     (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e-229) {
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	} else if (t <= 7e-150) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.5d-229)) then
        tmp = (x + (y * (z / t))) / (a + (1.0d0 + (y * (b / t))))
    else if (t <= 7d-150) then
        tmp = (z / b) + ((x * t) / (y * b))
    else
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e-229) {
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	} else if (t <= 7e-150) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.5e-229:
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))))
	elif t <= 7e-150:
		tmp = (z / b) + ((x * t) / (y * b))
	else:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.5e-229)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + Float64(1.0 + Float64(y * Float64(b / t)))));
	elseif (t <= 7e-150)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.5e-229)
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	elseif (t <= 7e-150)
		tmp = (z / b) + ((x * t) / (y * b));
	else
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.5e-229], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-150], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.4999999999999999e-229

   1. Initial program 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-*l/ 84.7%

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

      3. +-rgt-identity 84.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 84.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 84.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 84.7%

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

      7. *-commutative 84.7%

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

      8. associate-*l/ 84.7%

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

   3. Simplified 84.7%

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

   if -7.4999999999999999e-229 < t < 6.9999999999999996e-150

   1. Initial program 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*l/ 48.9%

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

      3. +-rgt-identity 48.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 48.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 48.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 48.9%

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

      7. *-commutative 48.9%

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

      8. associate-*l/ 38.4%

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

   3. Simplified 38.4%

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

   4. Taylor expanded in t around 0 61.1%

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

   5. Taylor expanded in x around inf 79.8%

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

   if 6.9999999999999996e-150 < 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* 79.2%

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

      2. +-rgt-identity 79.2%

         \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      3. associate-+l+ 79.2%

         \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      4. associate-+r+ 79.2%

         \[\leadsto \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      5. +-rgt-identity 79.2%

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

      6. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

      1. associate-/r/ 87.6%

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

   5. Applied egg-rr 87.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-150}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]

Alternative 8: 54.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -1.32 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-268}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1650:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) a)))
   (if (<= a -1.32e+17)
     t_1
     (if (<= a -6.5e-111)
       (/ z b)
       (if (<= a -2.5e-268)
         (+ x (/ y (/ t z)))
         (if (<= a 1650.0) (/ x (+ 1.0 (/ (* 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;
	double tmp;
	if (a <= -1.32e+17) {
		tmp = t_1;
	} else if (a <= -6.5e-111) {
		tmp = z / b;
	} else if (a <= -2.5e-268) {
		tmp = x + (y / (t / z));
	} else if (a <= 1650.0) {
		tmp = x / (1.0 + ((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
    if (a <= (-1.32d+17)) then
        tmp = t_1
    else if (a <= (-6.5d-111)) then
        tmp = z / b
    else if (a <= (-2.5d-268)) then
        tmp = x + (y / (t / z))
    else if (a <= 1650.0d0) then
        tmp = x / (1.0d0 + ((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;
	double tmp;
	if (a <= -1.32e+17) {
		tmp = t_1;
	} else if (a <= -6.5e-111) {
		tmp = z / b;
	} else if (a <= -2.5e-268) {
		tmp = x + (y / (t / z));
	} else if (a <= 1650.0) {
		tmp = x / (1.0 + ((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
	tmp = 0
	if a <= -1.32e+17:
		tmp = t_1
	elif a <= -6.5e-111:
		tmp = z / b
	elif a <= -2.5e-268:
		tmp = x + (y / (t / z))
	elif a <= 1650.0:
		tmp = x / (1.0 + ((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))) / a)
	tmp = 0.0
	if (a <= -1.32e+17)
		tmp = t_1;
	elseif (a <= -6.5e-111)
		tmp = Float64(z / b);
	elseif (a <= -2.5e-268)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (a <= 1650.0)
		tmp = Float64(x / Float64(1.0 + 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;
	tmp = 0.0;
	if (a <= -1.32e+17)
		tmp = t_1;
	elseif (a <= -6.5e-111)
		tmp = z / b;
	elseif (a <= -2.5e-268)
		tmp = x + (y / (t / z));
	elseif (a <= 1650.0)
		tmp = x / (1.0 + ((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] / a), $MachinePrecision]}, If[LessEqual[a, -1.32e+17], t$95$1, If[LessEqual[a, -6.5e-111], N[(z / b), $MachinePrecision], If[LessEqual[a, -2.5e-268], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1650.0], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.32e17 or 1650 < a

   1. Initial program 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-*l/ 79.8%

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

      3. +-rgt-identity 79.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 79.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 79.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 79.8%

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

      7. *-commutative 79.8%

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

      8. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in a around inf 67.0%

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

   if -1.32e17 < a < -6.49999999999999974e-111

   1. Initial program 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-*l/ 68.7%

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

      3. +-rgt-identity 68.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 68.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 68.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 68.7%

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

      7. *-commutative 68.7%

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

      8. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in t around 0 56.4%

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

   if -6.49999999999999974e-111 < a < -2.5e-268

   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. *-commutative 78.1%

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

      2. associate-*l/ 80.8%

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

      3. +-rgt-identity 80.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 80.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 80.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 80.8%

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

      7. *-commutative 80.8%

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

      8. associate-*l/ 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in b around 0 72.7%

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

   5. Taylor expanded in a around 0 72.6%

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

      1. associate-/l* 72.7%

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

   7. Simplified 72.7%

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

   if -2.5e-268 < a < 1650

   1. Initial program 73.1%

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

      1. *-commutative 73.1%

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

      2. associate-*l/ 70.9%

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

      3. +-rgt-identity 70.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 70.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 70.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 70.9%

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

      7. *-commutative 70.9%

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

      8. associate-*l/ 70.7%

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

   3. Simplified 70.7%

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

      1. associate-*l/ 70.9%

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

      2. associate-/l* 72.1%

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

   5. Applied egg-rr 72.1%

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

   6. Taylor expanded in x around inf 53.8%

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

      1. +-commutative 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-+r+ 53.8%

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

      4. +-commutative 53.8%

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

      5. associate-*l/ 54.9%

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

      6. *-commutative 54.9%

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

   8. Simplified 54.9%

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

   9. Taylor expanded in a around 0 53.3%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+17}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-268}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1650:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]

Alternative 9: 54.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -14500000000000:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-111}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1650:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ t z)))))
   (if (<= a -14500000000000.0)
     (/ t_1 a)
     (if (<= a -8e-111)
       (/ z b)
       (if (<= a -9.5e-268)
         t_1
         (if (<= a 1650.0)
           (/ x (+ 1.0 (/ (* y b) t)))
           (/ (+ x (* y (/ z t))) a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y / (t / z));
	double tmp;
	if (a <= -14500000000000.0) {
		tmp = t_1 / a;
	} else if (a <= -8e-111) {
		tmp = z / b;
	} else if (a <= -9.5e-268) {
		tmp = t_1;
	} else if (a <= 1650.0) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = (x + (y * (z / t))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (t / z))
    if (a <= (-14500000000000.0d0)) then
        tmp = t_1 / a
    else if (a <= (-8d-111)) then
        tmp = z / b
    else if (a <= (-9.5d-268)) then
        tmp = t_1
    else if (a <= 1650.0d0) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else
        tmp = (x + (y * (z / t))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y / (t / z));
	double tmp;
	if (a <= -14500000000000.0) {
		tmp = t_1 / a;
	} else if (a <= -8e-111) {
		tmp = z / b;
	} else if (a <= -9.5e-268) {
		tmp = t_1;
	} else if (a <= 1650.0) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = (x + (y * (z / t))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y / (t / z))
	tmp = 0
	if a <= -14500000000000.0:
		tmp = t_1 / a
	elif a <= -8e-111:
		tmp = z / b
	elif a <= -9.5e-268:
		tmp = t_1
	elif a <= 1650.0:
		tmp = x / (1.0 + ((y * b) / t))
	else:
		tmp = (x + (y * (z / t))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y / Float64(t / z)))
	tmp = 0.0
	if (a <= -14500000000000.0)
		tmp = Float64(t_1 / a);
	elseif (a <= -8e-111)
		tmp = Float64(z / b);
	elseif (a <= -9.5e-268)
		tmp = t_1;
	elseif (a <= 1650.0)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y / (t / z));
	tmp = 0.0;
	if (a <= -14500000000000.0)
		tmp = t_1 / a;
	elseif (a <= -8e-111)
		tmp = z / b;
	elseif (a <= -9.5e-268)
		tmp = t_1;
	elseif (a <= 1650.0)
		tmp = x / (1.0 + ((y * b) / t));
	else
		tmp = (x + (y * (z / t))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -14500000000000.0], N[(t$95$1 / a), $MachinePrecision], If[LessEqual[a, -8e-111], N[(z / b), $MachinePrecision], If[LessEqual[a, -9.5e-268], t$95$1, If[LessEqual[a, 1650.0], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.45e13

   1. Initial program 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-*l/ 83.5%

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

      3. +-rgt-identity 83.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 83.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 83.5%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 83.5%

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

      7. *-commutative 83.5%

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

      8. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

      1. associate-*l/ 83.5%

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

      2. associate-/l* 85.0%

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

   5. Applied egg-rr 85.0%

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

   6. Taylor expanded in a around inf 63.8%

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

      1. associate-/l* 67.2%

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

   8. Simplified 67.2%

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

   if -1.45e13 < a < -8.00000000000000071e-111

   1. Initial program 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-*l/ 68.7%

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

      3. +-rgt-identity 68.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 68.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 68.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 68.7%

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

      7. *-commutative 68.7%

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

      8. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in t around 0 56.4%

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

   if -8.00000000000000071e-111 < a < -9.50000000000000007e-268

   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. *-commutative 78.1%

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

      2. associate-*l/ 80.8%

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

      3. +-rgt-identity 80.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 80.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 80.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 80.8%

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

      7. *-commutative 80.8%

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

      8. associate-*l/ 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in b around 0 72.7%

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

   5. Taylor expanded in a around 0 72.6%

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

      1. associate-/l* 72.7%

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

   7. Simplified 72.7%

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

   if -9.50000000000000007e-268 < a < 1650

   1. Initial program 73.1%

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

      1. *-commutative 73.1%

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

      2. associate-*l/ 70.9%

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

      3. +-rgt-identity 70.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 70.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 70.9%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 70.9%

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

      7. *-commutative 70.9%

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

      8. associate-*l/ 70.7%

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

   3. Simplified 70.7%

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

      1. associate-*l/ 70.9%

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

      2. associate-/l* 72.1%

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

   5. Applied egg-rr 72.1%

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

   6. Taylor expanded in x around inf 53.8%

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

      1. +-commutative 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-+r+ 53.8%

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

      4. +-commutative 53.8%

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

      5. associate-*l/ 54.9%

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

      6. *-commutative 54.9%

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

   8. Simplified 54.9%

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

   9. Taylor expanded in a around 0 53.3%

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

   if 1650 < a

   1. Initial program 75.2%

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

      1. *-commutative 75.2%

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

      2. associate-*l/ 76.7%

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

      3. +-rgt-identity 76.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 76.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 76.7%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 76.7%

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

      7. *-commutative 76.7%

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

      8. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in a around inf 66.8%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -14500000000000:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-111}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-268}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1650:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]

Alternative 10: 59.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-30} \lor \neg \left(y \leq 3.2 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.8e-30) (not (<= y 3.2e-24)))
   (+ (/ z b) (* t (/ x (* y b))))
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.8e-30) || !(y <= 3.2e-24)) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.8d-30)) .or. (.not. (y <= 3.2d-24))) then
        tmp = (z / b) + (t * (x / (y * b)))
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.8e-30) || !(y <= 3.2e-24)) {
		tmp = (z / b) + (t * (x / (y * b)));
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.8e-30) or not (y <= 3.2e-24):
		tmp = (z / b) + (t * (x / (y * b)))
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.8e-30) || !(y <= 3.2e-24))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(x / Float64(y * b))));
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.8e-30) || ~((y <= 3.2e-24)))
		tmp = (z / b) + (t * (x / (y * b)));
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.8e-30], N[Not[LessEqual[y, 3.2e-24]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999978e-30 or 3.20000000000000012e-24 < y

   1. Initial program 59.0%

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

      1. *-commutative 59.0%

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

      2. associate-*l/ 62.8%

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

      3. +-rgt-identity 62.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 62.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 62.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 62.8%

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

      7. *-commutative 62.8%

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

      8. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in t around 0 46.6%

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

   5. Taylor expanded in x around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-*r/ 55.6%

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

   7. Simplified 55.6%

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

   if -5.79999999999999978e-30 < y < 3.20000000000000012e-24

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l/ 89.3%

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

      3. +-rgt-identity 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-*l/ 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around inf 68.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-30} \lor \neg \left(y \leq 3.2 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 11: 60.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-28} \lor \neg \left(y \leq 3.8 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.8e-28) (not (<= y 3.8e-26)))
   (+ (/ z b) (* t (/ (/ x y) b)))
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.8e-28) || !(y <= 3.8e-26)) {
		tmp = (z / b) + (t * ((x / y) / b));
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.8d-28)) .or. (.not. (y <= 3.8d-26))) then
        tmp = (z / b) + (t * ((x / y) / b))
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.8e-28) || !(y <= 3.8e-26)) {
		tmp = (z / b) + (t * ((x / y) / b));
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.8e-28) or not (y <= 3.8e-26):
		tmp = (z / b) + (t * ((x / y) / b))
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.8e-28) || !(y <= 3.8e-26))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / y) / b)));
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.8e-28) || ~((y <= 3.8e-26)))
		tmp = (z / b) + (t * ((x / y) / b));
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.8e-28], N[Not[LessEqual[y, 3.8e-26]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8000000000000001e-28 or 3.80000000000000015e-26 < y

   1. Initial program 59.0%

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

      1. *-commutative 59.0%

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

      2. associate-*l/ 62.8%

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

      3. +-rgt-identity 62.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 62.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 62.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 62.8%

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

      7. *-commutative 62.8%

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

      8. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in t around 0 46.6%

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

   5. Taylor expanded in x around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-*r/ 55.6%

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

      3. associate-/r* 59.0%

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

   7. Simplified 59.0%

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

   if -6.8000000000000001e-28 < y < 3.80000000000000015e-26

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l/ 89.3%

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

      3. +-rgt-identity 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-*l/ 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around inf 68.0%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-28} \lor \neg \left(y \leq 3.8 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 12: 65.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+19} \lor \neg \left(y \leq 1.2 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3e+19) (not (<= y 1.2e+51)))
   (+ (/ z b) (* t (/ (/ x y) b)))
   (/ x (+ 1.0 (+ a (/ (* y b) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3e+19) || !(y <= 1.2e+51)) {
		tmp = (z / b) + (t * ((x / y) / b));
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3d+19)) .or. (.not. (y <= 1.2d+51))) then
        tmp = (z / b) + (t * ((x / y) / b))
    else
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3e+19) || !(y <= 1.2e+51)) {
		tmp = (z / b) + (t * ((x / y) / b));
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3e+19) or not (y <= 1.2e+51):
		tmp = (z / b) + (t * ((x / y) / b))
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3e+19) || !(y <= 1.2e+51))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / y) / b)));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3e+19) || ~((y <= 1.2e+51)))
		tmp = (z / b) + (t * ((x / y) / b));
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3e+19], N[Not[LessEqual[y, 1.2e+51]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e19 or 1.1999999999999999e51 < y

   1. Initial program 54.5%

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

      1. *-commutative 54.5%

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

      2. associate-*l/ 58.3%

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

      3. +-rgt-identity 58.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 58.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 58.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 58.3%

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

      7. *-commutative 58.3%

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

      8. associate-*l/ 68.1%

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

   3. Simplified 68.1%

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

   4. Taylor expanded in t around 0 48.1%

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

   5. Taylor expanded in x around inf 55.3%

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

      1. *-commutative 55.3%

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

      2. associate-*r/ 57.8%

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

      3. associate-/r* 61.7%

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

   7. Simplified 61.7%

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

   if -3e19 < y < 1.1999999999999999e51

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l/ 88.8%

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

      3. +-rgt-identity 88.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 88.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 88.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 88.8%

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

      7. *-commutative 88.8%

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

      8. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in x around inf 73.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+19} \lor \neg \left(y \leq 1.2 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]

Alternative 13: 56.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-25} \lor \neg \left(y \leq 5.3 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.1e-25) (not (<= y 5.3e-24))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.1e-25) || !(y <= 5.3e-24)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.1d-25)) .or. (.not. (y <= 5.3d-24))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.1e-25) || !(y <= 5.3e-24)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.1e-25) or not (y <= 5.3e-24):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.1e-25) || !(y <= 5.3e-24))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.1e-25) || ~((y <= 5.3e-24)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.1e-25], N[Not[LessEqual[y, 5.3e-24]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000002e-25 or 5.29999999999999969e-24 < y

   1. Initial program 59.0%

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

      1. *-commutative 59.0%

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

      2. associate-*l/ 62.8%

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

      3. +-rgt-identity 62.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 62.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 62.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 62.8%

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

      7. *-commutative 62.8%

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

      8. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in t around 0 51.0%

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

   if -2.10000000000000002e-25 < y < 5.29999999999999969e-24

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l/ 89.3%

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

      3. +-rgt-identity 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 89.3%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-*l/ 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around inf 68.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-25} \lor \neg \left(y \leq 5.3 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 14: 43.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+16} \lor \neg \left(a \leq 2.4 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.8e+16) (not (<= a 2.4e+68))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.8e+16) || !(a <= 2.4e+68)) {
		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 ((a <= (-6.8d+16)) .or. (.not. (a <= 2.4d+68))) 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 ((a <= -6.8e+16) || !(a <= 2.4e+68)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6.8e+16) or not (a <= 2.4e+68):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6.8e+16) || !(a <= 2.4e+68))
		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 ((a <= -6.8e+16) || ~((a <= 2.4e+68)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6.8e+16], N[Not[LessEqual[a, 2.4e+68]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.8e16 or 2.40000000000000008e68 < a

   1. Initial program 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-*l/ 80.2%

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

      3. +-rgt-identity 80.2%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 80.2%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 80.2%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 80.2%

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

      7. *-commutative 80.2%

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

      8. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in t around inf 50.2%

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

   5. Taylor expanded in a around inf 50.2%

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

   if -6.8e16 < a < 2.40000000000000008e68

   1. Initial program 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-*l/ 72.8%

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

      3. +-rgt-identity 72.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

      4. associate-+l+ 72.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

      5. associate-+r+ 72.8%

         \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

      6. +-rgt-identity 72.8%

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

      7. *-commutative 72.8%

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

      8. associate-*l/ 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in t around 0 45.7%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+16} \lor \neg \left(a \leq 2.4 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 15: 25.2% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / a), $MachinePrecision]

Derivation

1. Initial program 75.3%

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

   1. *-commutative 75.3%

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

   2. associate-*l/ 76.1%

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

   3. +-rgt-identity 76.1%

      \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right) + 0}} \]

   4. associate-+l+ 76.1%

      \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{\left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)} + 0} \]

   5. associate-+r+ 76.1%

      \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a + \left(\left(1 + \frac{y \cdot b}{t}\right) + 0\right)}} \]

   6. +-rgt-identity 76.1%

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

   7. *-commutative 76.1%

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

   8. associate-*l/ 76.4%

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

3. Simplified 76.4%

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

4. Taylor expanded in t around inf 42.6%

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

5. Taylor expanded in a around inf 25.2%

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

6. Final simplification 25.2%

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

Developer target: 79.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023301 
(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))))