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

Percentage Accurate: 75.7% → 91.2%

Time: 22.1s

Alternatives: 17

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.7% 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1 + \left(a + 1\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(1 + \left(a + t_1\right)\right)}{z}}\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-316}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{t}{y \cdot \frac{b}{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t)) (t_2 (/ (+ x (/ (* y z) t)) (+ t_1 (+ a 1.0)))))
   (if (<= t_2 (- INFINITY))
     (/ y (/ (* t (+ 1.0 (+ a t_1))) z))
     (if (<= t_2 -4e-316)
       t_2
       (if (<= t_2 0.0)
         (/ t (* y (/ b (fma y (/ z t) x))))
         (if (<= t_2 2e+306) t_2 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y / ((t * (1.0 + (a + t_1))) / z);
	} else if (t_2 <= -4e-316) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t / (y * (b / fma(y, (z / t), x)));
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(t_1 + Float64(a + 1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y / Float64(Float64(t * Float64(1.0 + Float64(a + t_1))) / z));
	elseif (t_2 <= -4e-316)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t / Float64(y * Float64(b / fma(y, Float64(z / t), x))));
	elseif (t_2 <= 2e+306)
		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[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y / N[(N[(t * N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-316], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t / N[(y * N[(b / N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], 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

   1. Initial program 24.4%

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

      1. *-commutative 24.4%

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

      2. associate-*l/ 54.0%

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

      3. *-commutative 54.0%

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

      4. associate-*l/ 53.5%

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

   3. Simplified 53.5%

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

      1. associate-*l/ 23.9%

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

      2. *-commutative 23.9%

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

      3. associate-/l* 53.4%

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

   5. Applied egg-rr 53.4%

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

   6. Taylor expanded in x around 0 61.0%

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

      1. associate-/l* 79.6%

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

      2. *-commutative 79.6%

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

   8. Simplified 79.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -3.999999984e-316 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 99.7%

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

   if -3.999999984e-316 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-*l/ 53.6%

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

      3. *-commutative 53.6%

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

      4. associate-*l/ 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in b around inf 59.4%

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

      1. associate-/l* 59.8%

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

      2. *-commutative 59.8%

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

      3. *-lft-identity 59.8%

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

      4. times-frac 78.5%

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

      5. /-rgt-identity 78.5%

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

      6. +-commutative 78.5%

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

      7. associate-*r/ 76.0%

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

      8. fma-udef 76.0%

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

   6. Simplified 76.0%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 10.4%

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

      1. *-commutative 10.4%

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

      2. associate-*l/ 14.9%

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

      3. *-commutative 14.9%

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

      4. associate-*l/ 25.7%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in t around 0 88.9%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -4 \cdot 10^{-316}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{t}{y \cdot \frac{b}{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1 + \left(a + 1\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(1 + \left(a + t_1\right)\right)}{z}}\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t)) (t_2 (/ (+ x (/ (* y z) t)) (+ t_1 (+ a 1.0)))))
   (if (<= t_2 (- INFINITY))
     (/ y (/ (* t (+ 1.0 (+ a t_1))) z))
     (if (<= t_2 -4e-281)
       t_2
       (if (<= t_2 0.0)
         (/ (+ x (/ y (/ t z))) (+ (* y (/ b t)) (+ a 1.0)))
         (if (<= t_2 2e+306) t_2 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y / ((t * (1.0 + (a + t_1))) / z);
	} else if (t_2 <= -4e-281) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y / ((t * (1.0 + (a + t_1))) / z);
	} else if (t_2 <= -4e-281) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y / ((t * (1.0 + (a + t_1))) / z)
	elif t_2 <= -4e-281:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0))
	elif t_2 <= 2e+306:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(t_1 + Float64(a + 1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y / Float64(Float64(t * Float64(1.0 + Float64(a + t_1))) / z));
	elseif (t_2 <= -4e-281)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y / ((t * (1.0 + (a + t_1))) / z);
	elseif (t_2 <= -4e-281)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y / N[(N[(t * N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-281], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], 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

   1. Initial program 24.4%

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

      1. *-commutative 24.4%

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

      2. associate-*l/ 54.0%

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

      3. *-commutative 54.0%

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

      4. associate-*l/ 53.5%

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

   3. Simplified 53.5%

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

      1. associate-*l/ 23.9%

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

      2. *-commutative 23.9%

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

      3. associate-/l* 53.4%

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

   5. Applied egg-rr 53.4%

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

   6. Taylor expanded in x around 0 61.0%

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

      1. associate-/l* 79.6%

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

      2. *-commutative 79.6%

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

   8. Simplified 79.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.0000000000000001e-281 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 99.7%

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

   if -4.0000000000000001e-281 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-*l/ 57.7%

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

      3. *-commutative 57.7%

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

      4. associate-*l/ 70.4%

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

   3. Simplified 70.4%

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

      1. associate-*l/ 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-/l* 70.5%

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

   5. Applied egg-rr 70.5%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 10.4%

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

      1. *-commutative 10.4%

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

      2. associate-*l/ 14.9%

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

      3. *-commutative 14.9%

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

      4. associate-*l/ 25.7%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in t around 0 88.9%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -4 \cdot 10^{-281}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := y \cdot \frac{b}{t}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + t_2\right)}\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-77}:\\ \;\;\;\;\left(x + z \cdot \frac{y}{t}\right) \cdot \frac{1}{a + 1}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{t_2 + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-153}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\frac{t \cdot t_1}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (* y (/ b t))))
   (if (<= t -2.9e+123)
     (/ x (+ a (+ 1.0 (/ b (/ t y)))))
     (if (<= t -4.6e+66)
       (* (/ y t) (/ z (+ 1.0 (+ a t_2))))
       (if (<= t -1.26e-77)
         (* (+ x (* z (/ y t))) (/ 1.0 (+ a 1.0)))
         (if (<= t -5.8e-99)
           (/ z b)
           (if (<= t -2.55e-163)
             (/ x (+ t_2 (+ a 1.0)))
             (if (<= t 4.2e-212)
               (/ z b)
               (if (<= t 1.05e-153)
                 (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
                 (if (<= t 4e-111)
                   (/ (* t t_1) (* y b))
                   (/ t_1 (+ a 1.0))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = y * (b / t);
	double tmp;
	if (t <= -2.9e+123) {
		tmp = x / (a + (1.0 + (b / (t / y))));
	} else if (t <= -4.6e+66) {
		tmp = (y / t) * (z / (1.0 + (a + t_2)));
	} else if (t <= -1.26e-77) {
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0));
	} else if (t <= -5.8e-99) {
		tmp = z / b;
	} else if (t <= -2.55e-163) {
		tmp = x / (t_2 + (a + 1.0));
	} else if (t <= 4.2e-212) {
		tmp = z / b;
	} else if (t <= 1.05e-153) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 4e-111) {
		tmp = (t * t_1) / (y * b);
	} else {
		tmp = t_1 / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = y * (b / t)
    if (t <= (-2.9d+123)) then
        tmp = x / (a + (1.0d0 + (b / (t / y))))
    else if (t <= (-4.6d+66)) then
        tmp = (y / t) * (z / (1.0d0 + (a + t_2)))
    else if (t <= (-1.26d-77)) then
        tmp = (x + (z * (y / t))) * (1.0d0 / (a + 1.0d0))
    else if (t <= (-5.8d-99)) then
        tmp = z / b
    else if (t <= (-2.55d-163)) then
        tmp = x / (t_2 + (a + 1.0d0))
    else if (t <= 4.2d-212) then
        tmp = z / b
    else if (t <= 1.05d-153) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else if (t <= 4d-111) then
        tmp = (t * t_1) / (y * b)
    else
        tmp = t_1 / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = y * (b / t);
	double tmp;
	if (t <= -2.9e+123) {
		tmp = x / (a + (1.0 + (b / (t / y))));
	} else if (t <= -4.6e+66) {
		tmp = (y / t) * (z / (1.0 + (a + t_2)));
	} else if (t <= -1.26e-77) {
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0));
	} else if (t <= -5.8e-99) {
		tmp = z / b;
	} else if (t <= -2.55e-163) {
		tmp = x / (t_2 + (a + 1.0));
	} else if (t <= 4.2e-212) {
		tmp = z / b;
	} else if (t <= 1.05e-153) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 4e-111) {
		tmp = (t * t_1) / (y * b);
	} else {
		tmp = t_1 / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = y * (b / t)
	tmp = 0
	if t <= -2.9e+123:
		tmp = x / (a + (1.0 + (b / (t / y))))
	elif t <= -4.6e+66:
		tmp = (y / t) * (z / (1.0 + (a + t_2)))
	elif t <= -1.26e-77:
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0))
	elif t <= -5.8e-99:
		tmp = z / b
	elif t <= -2.55e-163:
		tmp = x / (t_2 + (a + 1.0))
	elif t <= 4.2e-212:
		tmp = z / b
	elif t <= 1.05e-153:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	elif t <= 4e-111:
		tmp = (t * t_1) / (y * b)
	else:
		tmp = t_1 / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(y * Float64(b / t))
	tmp = 0.0
	if (t <= -2.9e+123)
		tmp = Float64(x / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	elseif (t <= -4.6e+66)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + t_2))));
	elseif (t <= -1.26e-77)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) * Float64(1.0 / Float64(a + 1.0)));
	elseif (t <= -5.8e-99)
		tmp = Float64(z / b);
	elseif (t <= -2.55e-163)
		tmp = Float64(x / Float64(t_2 + Float64(a + 1.0)));
	elseif (t <= 4.2e-212)
		tmp = Float64(z / b);
	elseif (t <= 1.05e-153)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	elseif (t <= 4e-111)
		tmp = Float64(Float64(t * t_1) / Float64(y * b));
	else
		tmp = Float64(t_1 / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = y * (b / t);
	tmp = 0.0;
	if (t <= -2.9e+123)
		tmp = x / (a + (1.0 + (b / (t / y))));
	elseif (t <= -4.6e+66)
		tmp = (y / t) * (z / (1.0 + (a + t_2)));
	elseif (t <= -1.26e-77)
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0));
	elseif (t <= -5.8e-99)
		tmp = z / b;
	elseif (t <= -2.55e-163)
		tmp = x / (t_2 + (a + 1.0));
	elseif (t <= 4.2e-212)
		tmp = z / b;
	elseif (t <= 1.05e-153)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	elseif (t <= 4e-111)
		tmp = (t * t_1) / (y * b);
	else
		tmp = t_1 / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+123], N[(x / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e+66], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.26e-77], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.8e-99], N[(z / b), $MachinePrecision], If[LessEqual[t, -2.55e-163], N[(x / N[(t$95$2 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-212], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.05e-153], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-111], N[(N[(t * t$95$1), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -2.9000000000000001e123

   1. Initial program 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*l/ 84.4%

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

      3. *-commutative 84.4%

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

      4. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

      1. associate-*l/ 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-/l* 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in x around inf 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-+l+ 74.7%

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

      3. +-commutative 74.7%

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

      4. associate-/l* 81.1%

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

   8. Simplified 81.1%

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

   if -2.9000000000000001e123 < t < -4.6e66

   1. Initial program 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around 0 56.0%

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

      1. times-frac 81.8%

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

      2. associate-*l/ 90.7%

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

      3. *-commutative 90.7%

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

   6. Simplified 90.7%

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

   if -4.6e66 < t < -1.2599999999999999e-77

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-*l/ 83.3%

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

      3. *-commutative 83.3%

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

      4. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in b around 0 76.6%

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

      1. div-inv 76.7%

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

      2. associate-/l* 73.4%

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

      3. +-commutative 73.4%

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

      4. associate-/r/ 76.6%

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

      5. fma-def 76.6%

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

      6. +-commutative 76.6%

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

   6. Applied egg-rr 76.6%

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

      1. fma-udef 76.6%

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

   8. Applied egg-rr 76.6%

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

   if -1.2599999999999999e-77 < t < -5.79999999999999971e-99 or -2.54999999999999995e-163 < t < 4.1999999999999999e-212

   1. Initial program 41.6%

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

      1. *-commutative 41.6%

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

      2. associate-*l/ 38.1%

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

      3. *-commutative 38.1%

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

      4. associate-*l/ 34.7%

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

   3. Simplified 34.7%

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

   4. Taylor expanded in t around 0 77.9%

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

   if -5.79999999999999971e-99 < t < -2.54999999999999995e-163

   1. Initial program 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-*l/ 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-*l/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in x around inf 83.8%

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

   if 4.1999999999999999e-212 < t < 1.05000000000000002e-153

   1. Initial program 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*l/ 48.3%

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

      3. *-commutative 48.3%

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

      4. associate-*l/ 42.2%

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

   3. Simplified 42.2%

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

   4. Taylor expanded in x around 0 61.2%

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

   if 1.05000000000000002e-153 < t < 4.00000000000000035e-111

   1. Initial program 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*l/ 71.9%

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

      3. *-commutative 71.9%

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

      4. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in b around inf 99.6%

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

   if 4.00000000000000035e-111 < t

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-*l/ 86.3%

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

      3. *-commutative 86.3%

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

      4. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in b around 0 79.0%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z}{t}}{1 + a}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-77}:\\ \;\;\;\;\left(x + z \cdot \frac{y}{t}\right) \cdot \frac{1}{a + 1}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-153}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-111}:\\ \;\;\;\;\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]

Alternative 4: 78.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-166}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 9.1 \cdot 10^{-153}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-108}:\\ \;\;\;\;\frac{t \cdot t_1}{y \cdot b}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-94}:\\ \;\;\;\;\frac{t_1}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= t -1.4e-166)
     (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 (/ y (/ t b)))))
     (if (<= t 8.4e-212)
       (/ z b)
       (if (<= t 9.1e-153)
         (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
         (if (<= t 9e-108)
           (/ (* t t_1) (* y b))
           (if (<= t 4.3e-94)
             (/ t_1 (+ a 1.0))
             (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (t <= -1.4e-166) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	} else if (t <= 8.4e-212) {
		tmp = z / b;
	} else if (t <= 9.1e-153) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 9e-108) {
		tmp = (t * t_1) / (y * b);
	} else if (t <= 4.3e-94) {
		tmp = t_1 / (a + 1.0);
	} else {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    if (t <= (-1.4d-166)) then
        tmp = (x + (z / (t / y))) / (a + (1.0d0 + (y / (t / b))))
    else if (t <= 8.4d-212) then
        tmp = z / b
    else if (t <= 9.1d-153) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else if (t <= 9d-108) then
        tmp = (t * t_1) / (y * b)
    else if (t <= 4.3d-94) then
        tmp = t_1 / (a + 1.0d0)
    else
        tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (t <= -1.4e-166) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	} else if (t <= 8.4e-212) {
		tmp = z / b;
	} else if (t <= 9.1e-153) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 9e-108) {
		tmp = (t * t_1) / (y * b);
	} else if (t <= 4.3e-94) {
		tmp = t_1 / (a + 1.0);
	} else {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if t <= -1.4e-166:
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))))
	elif t <= 8.4e-212:
		tmp = z / b
	elif t <= 9.1e-153:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	elif t <= 9e-108:
		tmp = (t * t_1) / (y * b)
	elif t <= 4.3e-94:
		tmp = t_1 / (a + 1.0)
	else:
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (t <= -1.4e-166)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t <= 8.4e-212)
		tmp = Float64(z / b);
	elseif (t <= 9.1e-153)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	elseif (t <= 9e-108)
		tmp = Float64(Float64(t * t_1) / Float64(y * b));
	elseif (t <= 4.3e-94)
		tmp = Float64(t_1 / Float64(a + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	tmp = 0.0;
	if (t <= -1.4e-166)
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	elseif (t <= 8.4e-212)
		tmp = z / b;
	elseif (t <= 9.1e-153)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	elseif (t <= 9e-108)
		tmp = (t * t_1) / (y * b);
	elseif (t <= 4.3e-94)
		tmp = t_1 / (a + 1.0);
	else
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-166], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e-212], N[(z / b), $MachinePrecision], If[LessEqual[t, 9.1e-153], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-108], N[(N[(t * t$95$1), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-94], N[(t$95$1 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.4e-166

   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* 82.4%

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

      3. associate-*l/ 87.8%

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

      4. *-commutative 87.8%

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

      5. cancel-sign-sub 87.8%

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

      6. *-commutative 87.8%

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

      7. associate-*l/ 82.4%

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

      8. associate-+r- 82.4%

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

      9. associate-*l/ 87.8%

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

      10. *-commutative 87.8%

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

      11. cancel-sign-sub 87.8%

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

      12. *-commutative 87.8%

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

      13. associate-/r/ 87.8%

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

   3. Simplified 87.8%

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

   if -1.4e-166 < t < 8.3999999999999999e-212

   1. Initial program 42.4%

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

      1. *-commutative 42.4%

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

      2. associate-*l/ 38.4%

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

      3. *-commutative 38.4%

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

      4. associate-*l/ 34.7%

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

   3. Simplified 34.7%

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

   4. Taylor expanded in t around 0 75.8%

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

   if 8.3999999999999999e-212 < t < 9.10000000000000045e-153

   1. Initial program 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*l/ 48.3%

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

      3. *-commutative 48.3%

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

      4. associate-*l/ 42.2%

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

   3. Simplified 42.2%

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

   4. Taylor expanded in x around 0 61.2%

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

   if 9.10000000000000045e-153 < t < 8.99999999999999941e-108

   1. Initial program 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*l/ 71.9%

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

      3. *-commutative 71.9%

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

      4. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in b around inf 99.6%

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

   if 8.99999999999999941e-108 < t < 4.2999999999999998e-94

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*l/ 51.0%

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

      3. *-commutative 51.0%

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

      4. associate-*l/ 41.3%

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

   3. Simplified 41.3%

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

   4. Taylor expanded in b around 0 70.8%

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

   if 4.2999999999999998e-94 < t

   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/ 90.6%

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

      3. *-commutative 90.6%

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

      4. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-166}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-212}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 9.1 \cdot 10^{-153}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-108}:\\ \;\;\;\;\frac{t \cdot \left(x + \frac{y \cdot z}{t}\right)}{y \cdot b}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-94}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]

Alternative 5: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{t}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + t_1\right)}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-75}:\\ \;\;\;\;\left(x + z \cdot \frac{y}{t}\right) \cdot \frac{1}{a + 1}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{t_1 + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-110}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ b t))))
   (if (<= t -3e+123)
     (/ x (+ a (+ 1.0 (/ b (/ t y)))))
     (if (<= t -4.6e+66)
       (* (/ y t) (/ z (+ 1.0 (+ a t_1))))
       (if (<= t -9.5e-75)
         (* (+ x (* z (/ y t))) (/ 1.0 (+ a 1.0)))
         (if (<= t -3.2e-104)
           (/ z b)
           (if (<= t -2.2e-163)
             (/ x (+ t_1 (+ a 1.0)))
             (if (<= t 1.35e-110)
               (/ z b)
               (/ (+ x (/ (* y z) t)) (+ a 1.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / t);
	double tmp;
	if (t <= -3e+123) {
		tmp = x / (a + (1.0 + (b / (t / y))));
	} else if (t <= -4.6e+66) {
		tmp = (y / t) * (z / (1.0 + (a + t_1)));
	} else if (t <= -9.5e-75) {
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0));
	} else if (t <= -3.2e-104) {
		tmp = z / b;
	} else if (t <= -2.2e-163) {
		tmp = x / (t_1 + (a + 1.0));
	} else if (t <= 1.35e-110) {
		tmp = z / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b / t)
    if (t <= (-3d+123)) then
        tmp = x / (a + (1.0d0 + (b / (t / y))))
    else if (t <= (-4.6d+66)) then
        tmp = (y / t) * (z / (1.0d0 + (a + t_1)))
    else if (t <= (-9.5d-75)) then
        tmp = (x + (z * (y / t))) * (1.0d0 / (a + 1.0d0))
    else if (t <= (-3.2d-104)) then
        tmp = z / b
    else if (t <= (-2.2d-163)) then
        tmp = x / (t_1 + (a + 1.0d0))
    else if (t <= 1.35d-110) then
        tmp = z / b
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / t);
	double tmp;
	if (t <= -3e+123) {
		tmp = x / (a + (1.0 + (b / (t / y))));
	} else if (t <= -4.6e+66) {
		tmp = (y / t) * (z / (1.0 + (a + t_1)));
	} else if (t <= -9.5e-75) {
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0));
	} else if (t <= -3.2e-104) {
		tmp = z / b;
	} else if (t <= -2.2e-163) {
		tmp = x / (t_1 + (a + 1.0));
	} else if (t <= 1.35e-110) {
		tmp = z / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b / t)
	tmp = 0
	if t <= -3e+123:
		tmp = x / (a + (1.0 + (b / (t / y))))
	elif t <= -4.6e+66:
		tmp = (y / t) * (z / (1.0 + (a + t_1)))
	elif t <= -9.5e-75:
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0))
	elif t <= -3.2e-104:
		tmp = z / b
	elif t <= -2.2e-163:
		tmp = x / (t_1 + (a + 1.0))
	elif t <= 1.35e-110:
		tmp = z / b
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b / t))
	tmp = 0.0
	if (t <= -3e+123)
		tmp = Float64(x / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	elseif (t <= -4.6e+66)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + t_1))));
	elseif (t <= -9.5e-75)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) * Float64(1.0 / Float64(a + 1.0)));
	elseif (t <= -3.2e-104)
		tmp = Float64(z / b);
	elseif (t <= -2.2e-163)
		tmp = Float64(x / Float64(t_1 + Float64(a + 1.0)));
	elseif (t <= 1.35e-110)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b / t);
	tmp = 0.0;
	if (t <= -3e+123)
		tmp = x / (a + (1.0 + (b / (t / y))));
	elseif (t <= -4.6e+66)
		tmp = (y / t) * (z / (1.0 + (a + t_1)));
	elseif (t <= -9.5e-75)
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0));
	elseif (t <= -3.2e-104)
		tmp = z / b;
	elseif (t <= -2.2e-163)
		tmp = x / (t_1 + (a + 1.0));
	elseif (t <= 1.35e-110)
		tmp = z / b;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+123], N[(x / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e+66], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.5e-75], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.2e-104], N[(z / b), $MachinePrecision], If[LessEqual[t, -2.2e-163], N[(x / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-110], N[(z / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.00000000000000008e123

   1. Initial program 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*l/ 84.4%

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

      3. *-commutative 84.4%

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

      4. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

      1. associate-*l/ 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-/l* 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in x around inf 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-+l+ 74.7%

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

      3. +-commutative 74.7%

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

      4. associate-/l* 81.1%

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

   8. Simplified 81.1%

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

   if -3.00000000000000008e123 < t < -4.6e66

   1. Initial program 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around 0 56.0%

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

      1. times-frac 81.8%

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

      2. associate-*l/ 90.7%

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

      3. *-commutative 90.7%

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

   6. Simplified 90.7%

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

   if -4.6e66 < t < -9.4999999999999991e-75

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-*l/ 83.3%

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

      3. *-commutative 83.3%

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

      4. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in b around 0 76.6%

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

      1. div-inv 76.7%

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

      2. associate-/l* 73.4%

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

      3. +-commutative 73.4%

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

      4. associate-/r/ 76.6%

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

      5. fma-def 76.6%

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

      6. +-commutative 76.6%

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

   6. Applied egg-rr 76.6%

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

      1. fma-udef 76.6%

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

   8. Applied egg-rr 76.6%

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

   if -9.4999999999999991e-75 < t < -3.19999999999999989e-104 or -2.20000000000000011e-163 < t < 1.3499999999999999e-110

   1. Initial program 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-*l/ 43.0%

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

      3. *-commutative 43.0%

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

      4. associate-*l/ 39.4%

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

   3. Simplified 39.4%

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

   4. Taylor expanded in t around 0 68.4%

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

   if -3.19999999999999989e-104 < t < -2.20000000000000011e-163

   1. Initial program 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-*l/ 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-*l/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in x around inf 83.8%

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

   if 1.3499999999999999e-110 < t

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-*l/ 86.3%

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

      3. *-commutative 86.3%

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

      4. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in b around 0 79.0%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-75}:\\ \;\;\;\;\left(x + z \cdot \frac{y}{t}\right) \cdot \frac{1}{a + 1}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-110}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]

Alternative 6: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+183}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-100}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ a 1.0))))
   (if (<= t -2.6e+183)
     (/ x (+ a (+ 1.0 (/ b (/ t y)))))
     (if (<= t -3.2e-76)
       t_1
       (if (<= t -1.4e-100)
         (/ z b)
         (if (<= t -2.55e-163)
           (/ x (+ (* y (/ b t)) (+ a 1.0)))
           (if (<= t 9.6e-108) (/ z b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (a + 1.0);
	double tmp;
	if (t <= -2.6e+183) {
		tmp = x / (a + (1.0 + (b / (t / y))));
	} else if (t <= -3.2e-76) {
		tmp = t_1;
	} else if (t <= -1.4e-100) {
		tmp = z / b;
	} else if (t <= -2.55e-163) {
		tmp = x / ((y * (b / t)) + (a + 1.0));
	} else if (t <= 9.6e-108) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / (a + 1.0d0)
    if (t <= (-2.6d+183)) then
        tmp = x / (a + (1.0d0 + (b / (t / y))))
    else if (t <= (-3.2d-76)) then
        tmp = t_1
    else if (t <= (-1.4d-100)) then
        tmp = z / b
    else if (t <= (-2.55d-163)) then
        tmp = x / ((y * (b / t)) + (a + 1.0d0))
    else if (t <= 9.6d-108) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (a + 1.0);
	double tmp;
	if (t <= -2.6e+183) {
		tmp = x / (a + (1.0 + (b / (t / y))));
	} else if (t <= -3.2e-76) {
		tmp = t_1;
	} else if (t <= -1.4e-100) {
		tmp = z / b;
	} else if (t <= -2.55e-163) {
		tmp = x / ((y * (b / t)) + (a + 1.0));
	} else if (t <= 9.6e-108) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (a + 1.0)
	tmp = 0
	if t <= -2.6e+183:
		tmp = x / (a + (1.0 + (b / (t / y))))
	elif t <= -3.2e-76:
		tmp = t_1
	elif t <= -1.4e-100:
		tmp = z / b
	elif t <= -2.55e-163:
		tmp = x / ((y * (b / t)) + (a + 1.0))
	elif t <= 9.6e-108:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.6e+183)
		tmp = Float64(x / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	elseif (t <= -3.2e-76)
		tmp = t_1;
	elseif (t <= -1.4e-100)
		tmp = Float64(z / b);
	elseif (t <= -2.55e-163)
		tmp = Float64(x / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	elseif (t <= 9.6e-108)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.6e+183)
		tmp = x / (a + (1.0 + (b / (t / y))));
	elseif (t <= -3.2e-76)
		tmp = t_1;
	elseif (t <= -1.4e-100)
		tmp = z / b;
	elseif (t <= -2.55e-163)
		tmp = x / ((y * (b / t)) + (a + 1.0));
	elseif (t <= 9.6e-108)
		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[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+183], N[(x / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.2e-76], t$95$1, If[LessEqual[t, -1.4e-100], N[(z / b), $MachinePrecision], If[LessEqual[t, -2.55e-163], N[(x / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e-108], N[(z / b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.5999999999999999e183

   1. Initial program 65.8%

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

      1. *-commutative 65.8%

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

      2. associate-*l/ 75.8%

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

      3. *-commutative 75.8%

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

      4. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

      1. associate-*l/ 75.5%

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

      2. *-commutative 75.5%

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

      3. associate-/l* 94.9%

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

   5. Applied egg-rr 94.9%

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

   6. Taylor expanded in x around inf 67.0%

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

      1. +-commutative 67.0%

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

      2. associate-+l+ 67.0%

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

      3. +-commutative 67.0%

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

      4. associate-/l* 76.9%

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

   8. Simplified 76.9%

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

   if -2.5999999999999999e183 < t < -3.1999999999999998e-76 or 9.60000000000000068e-108 < t

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-*l/ 86.4%

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

      3. *-commutative 86.4%

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

      4. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in b around 0 77.1%

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

   if -3.1999999999999998e-76 < t < -1.39999999999999998e-100 or -2.54999999999999995e-163 < t < 9.60000000000000068e-108

   1. Initial program 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-*l/ 43.0%

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

      3. *-commutative 43.0%

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

      4. associate-*l/ 39.4%

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

   3. Simplified 39.4%

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

   4. Taylor expanded in t around 0 68.4%

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

   if -1.39999999999999998e-100 < t < -2.54999999999999995e-163

   1. Initial program 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-*l/ 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-*l/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in x around inf 83.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+183}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-100}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]

Alternative 7: 71.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+198}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{1}{\frac{\frac{t}{y}}{b}}\right)}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7e+198)
   (* (/ y t) (/ z (+ 1.0 (+ a (/ 1.0 (/ (/ t y) b))))))
   (if (<= z 2.3e+96)
     (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))
     (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7e+198) {
		tmp = (y / t) * (z / (1.0 + (a + (1.0 / ((t / y) / b)))));
	} else if (z <= 2.3e+96) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-7d+198)) then
        tmp = (y / t) * (z / (1.0d0 + (a + (1.0d0 / ((t / y) / b)))))
    else if (z <= 2.3d+96) then
        tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0d0))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7e+198) {
		tmp = (y / t) * (z / (1.0 + (a + (1.0 / ((t / y) / b)))));
	} else if (z <= 2.3e+96) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7e+198:
		tmp = (y / t) * (z / (1.0 + (a + (1.0 / ((t / y) / b)))))
	elif z <= 2.3e+96:
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7e+198)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(1.0 / Float64(Float64(t / y) / b))))));
	elseif (z <= 2.3e+96)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7e+198)
		tmp = (y / t) * (z / (1.0 + (a + (1.0 / ((t / y) / b)))));
	elseif (z <= 2.3e+96)
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7e+198], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(1.0 / N[(N[(t / y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+96], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000026e198

   1. Initial program 48.4%

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

      1. *-commutative 48.4%

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

      2. associate-*l/ 23.1%

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

      3. *-commutative 23.1%

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

      4. associate-*l/ 29.3%

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

   3. Simplified 29.3%

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

   4. Taylor expanded in x around 0 40.6%

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

      1. times-frac 53.7%

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

      2. associate-*l/ 53.7%

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

      3. *-commutative 53.7%

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

   6. Simplified 53.7%

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

      1. *-commutative 53.7%

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

      2. associate-/r/ 60.1%

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

      3. clear-num 60.2%

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

   8. Applied egg-rr 60.2%

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

   if -7.00000000000000026e198 < z < 2.30000000000000015e96

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*l/ 82.9%

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

      3. *-commutative 82.9%

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

      4. associate-*l/ 85.4%

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

   3. Simplified 85.4%

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

   if 2.30000000000000015e96 < z

   1. Initial program 43.9%

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

      1. *-commutative 43.9%

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

      2. associate-*l/ 42.0%

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

      3. *-commutative 42.0%

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

      4. associate-*l/ 44.0%

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

   3. Simplified 44.0%

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

   4. Taylor expanded in t around 0 62.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+198}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{1}{\frac{\frac{t}{y}}{b}}\right)}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 8: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + 1}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-75}:\\ \;\;\;\;\frac{1}{t} \cdot \frac{y \cdot z}{a + 1}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-104}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -2.9e+123)
     t_1
     (if (<= t -4.6e+66)
       (* (/ z t) (/ y (+ a 1.0)))
       (if (<= t -4.2e-32)
         t_1
         (if (<= t -7e-75)
           (* (/ 1.0 t) (/ (* y z) (+ a 1.0)))
           (if (<= t 5.5e-104) (/ z b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.9e+123) {
		tmp = t_1;
	} else if (t <= -4.6e+66) {
		tmp = (z / t) * (y / (a + 1.0));
	} else if (t <= -4.2e-32) {
		tmp = t_1;
	} else if (t <= -7e-75) {
		tmp = (1.0 / t) * ((y * z) / (a + 1.0));
	} else if (t <= 5.5e-104) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-2.9d+123)) then
        tmp = t_1
    else if (t <= (-4.6d+66)) then
        tmp = (z / t) * (y / (a + 1.0d0))
    else if (t <= (-4.2d-32)) then
        tmp = t_1
    else if (t <= (-7d-75)) then
        tmp = (1.0d0 / t) * ((y * z) / (a + 1.0d0))
    else if (t <= 5.5d-104) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.9e+123) {
		tmp = t_1;
	} else if (t <= -4.6e+66) {
		tmp = (z / t) * (y / (a + 1.0));
	} else if (t <= -4.2e-32) {
		tmp = t_1;
	} else if (t <= -7e-75) {
		tmp = (1.0 / t) * ((y * z) / (a + 1.0));
	} else if (t <= 5.5e-104) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -2.9e+123:
		tmp = t_1
	elif t <= -4.6e+66:
		tmp = (z / t) * (y / (a + 1.0))
	elif t <= -4.2e-32:
		tmp = t_1
	elif t <= -7e-75:
		tmp = (1.0 / t) * ((y * z) / (a + 1.0))
	elif t <= 5.5e-104:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.9e+123)
		tmp = t_1;
	elseif (t <= -4.6e+66)
		tmp = Float64(Float64(z / t) * Float64(y / Float64(a + 1.0)));
	elseif (t <= -4.2e-32)
		tmp = t_1;
	elseif (t <= -7e-75)
		tmp = Float64(Float64(1.0 / t) * Float64(Float64(y * z) / Float64(a + 1.0)));
	elseif (t <= 5.5e-104)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.9e+123)
		tmp = t_1;
	elseif (t <= -4.6e+66)
		tmp = (z / t) * (y / (a + 1.0));
	elseif (t <= -4.2e-32)
		tmp = t_1;
	elseif (t <= -7e-75)
		tmp = (1.0 / t) * ((y * z) / (a + 1.0));
	elseif (t <= 5.5e-104)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+123], t$95$1, If[LessEqual[t, -4.6e+66], N[(N[(z / t), $MachinePrecision] * N[(y / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e-32], t$95$1, If[LessEqual[t, -7e-75], N[(N[(1.0 / t), $MachinePrecision] * N[(N[(y * z), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-104], N[(z / b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9000000000000001e123 or -4.6e66 < t < -4.1999999999999998e-32 or 5.4999999999999998e-104 < t

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l/ 85.0%

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

      3. *-commutative 85.0%

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

      4. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around inf 64.1%

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

   if -2.9000000000000001e123 < t < -4.6e66

   1. Initial program 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in b around 0 39.5%

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

   5. Taylor expanded in x around 0 39.1%

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

      1. *-commutative 39.1%

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

      2. +-commutative 39.1%

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

      3. times-frac 48.1%

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

      4. +-commutative 48.1%

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

   7. Applied egg-rr 48.1%

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

   if -4.1999999999999998e-32 < t < -6.9999999999999997e-75

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 90.1%

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

      3. *-commutative 90.1%

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

      4. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in b around 0 80.9%

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

   5. Taylor expanded in x around 0 71.8%

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

      1. *-un-lft-identity 71.8%

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

      2. +-commutative 71.8%

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

      3. times-frac 71.9%

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

      4. +-commutative 71.9%

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

   7. Applied egg-rr 71.9%

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

   if -6.9999999999999997e-75 < t < 5.4999999999999998e-104

   1. Initial program 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-*l/ 48.3%

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

      3. *-commutative 48.3%

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

      4. associate-*l/ 45.2%

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

   3. Simplified 45.2%

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

   4. Taylor expanded in t around 0 64.3%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + 1}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-75}:\\ \;\;\;\;\frac{1}{t} \cdot \frac{y \cdot z}{a + 1}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-104}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 9: 64.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-76}:\\ \;\;\;\;\left(x + z \cdot \frac{y}{t}\right) \cdot \frac{1}{a + 1}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-104}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.2e-76)
   (* (+ x (* z (/ y t))) (/ 1.0 (+ a 1.0)))
   (if (<= t -8.5e-104)
     (/ z b)
     (if (<= t -2.55e-163)
       (/ x (+ (* y (/ b t)) (+ a 1.0)))
       (if (<= t 9.5e-106) (/ z b) (/ (+ x (/ (* y z) t)) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e-76) {
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0));
	} else if (t <= -8.5e-104) {
		tmp = z / b;
	} else if (t <= -2.55e-163) {
		tmp = x / ((y * (b / t)) + (a + 1.0));
	} else if (t <= 9.5e-106) {
		tmp = z / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.2d-76)) then
        tmp = (x + (z * (y / t))) * (1.0d0 / (a + 1.0d0))
    else if (t <= (-8.5d-104)) then
        tmp = z / b
    else if (t <= (-2.55d-163)) then
        tmp = x / ((y * (b / t)) + (a + 1.0d0))
    else if (t <= 9.5d-106) then
        tmp = z / b
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e-76) {
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0));
	} else if (t <= -8.5e-104) {
		tmp = z / b;
	} else if (t <= -2.55e-163) {
		tmp = x / ((y * (b / t)) + (a + 1.0));
	} else if (t <= 9.5e-106) {
		tmp = z / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.2e-76:
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0))
	elif t <= -8.5e-104:
		tmp = z / b
	elif t <= -2.55e-163:
		tmp = x / ((y * (b / t)) + (a + 1.0))
	elif t <= 9.5e-106:
		tmp = z / b
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.2e-76)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) * Float64(1.0 / Float64(a + 1.0)));
	elseif (t <= -8.5e-104)
		tmp = Float64(z / b);
	elseif (t <= -2.55e-163)
		tmp = Float64(x / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	elseif (t <= 9.5e-106)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.2e-76)
		tmp = (x + (z * (y / t))) * (1.0 / (a + 1.0));
	elseif (t <= -8.5e-104)
		tmp = z / b;
	elseif (t <= -2.55e-163)
		tmp = x / ((y * (b / t)) + (a + 1.0));
	elseif (t <= 9.5e-106)
		tmp = z / b;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.2e-76], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e-104], N[(z / b), $MachinePrecision], If[LessEqual[t, -2.55e-163], N[(x / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-106], N[(z / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.19999999999999999e-76

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*l/ 83.6%

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

      3. *-commutative 83.6%

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

      4. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in b around 0 68.6%

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

      1. div-inv 68.6%

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

      2. associate-/l* 71.9%

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

      3. +-commutative 71.9%

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

      4. associate-/r/ 73.2%

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

      5. fma-def 73.2%

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

      6. +-commutative 73.2%

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

   6. Applied egg-rr 73.2%

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

      1. fma-udef 73.2%

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

   8. Applied egg-rr 73.2%

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

   if -2.19999999999999999e-76 < t < -8.50000000000000007e-104 or -2.54999999999999995e-163 < t < 9.4999999999999994e-106

   1. Initial program 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-*l/ 43.0%

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

      3. *-commutative 43.0%

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

      4. associate-*l/ 39.4%

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

   3. Simplified 39.4%

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

   4. Taylor expanded in t around 0 68.4%

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

   if -8.50000000000000007e-104 < t < -2.54999999999999995e-163

   1. Initial program 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-*l/ 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-*l/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in x around inf 83.8%

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

   if 9.4999999999999994e-106 < t

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-*l/ 86.3%

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

      3. *-commutative 86.3%

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

      4. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in b around 0 79.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-76}:\\ \;\;\;\;\left(x + z \cdot \frac{y}{t}\right) \cdot \frac{1}{a + 1}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-104}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]

Alternative 10: 53.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{+66}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + 1}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-73}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 10^{-104}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -3.3e+123)
     t_1
     (if (<= t -2.65e+66)
       (* (/ z t) (/ y (+ a 1.0)))
       (if (<= t -9.2e-33)
         t_1
         (if (<= t -2.15e-73)
           (/ (* y z) (* t (+ a 1.0)))
           (if (<= t 1e-104) (/ z b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -3.3e+123) {
		tmp = t_1;
	} else if (t <= -2.65e+66) {
		tmp = (z / t) * (y / (a + 1.0));
	} else if (t <= -9.2e-33) {
		tmp = t_1;
	} else if (t <= -2.15e-73) {
		tmp = (y * z) / (t * (a + 1.0));
	} else if (t <= 1e-104) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-3.3d+123)) then
        tmp = t_1
    else if (t <= (-2.65d+66)) then
        tmp = (z / t) * (y / (a + 1.0d0))
    else if (t <= (-9.2d-33)) then
        tmp = t_1
    else if (t <= (-2.15d-73)) then
        tmp = (y * z) / (t * (a + 1.0d0))
    else if (t <= 1d-104) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -3.3e+123) {
		tmp = t_1;
	} else if (t <= -2.65e+66) {
		tmp = (z / t) * (y / (a + 1.0));
	} else if (t <= -9.2e-33) {
		tmp = t_1;
	} else if (t <= -2.15e-73) {
		tmp = (y * z) / (t * (a + 1.0));
	} else if (t <= 1e-104) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -3.3e+123:
		tmp = t_1
	elif t <= -2.65e+66:
		tmp = (z / t) * (y / (a + 1.0))
	elif t <= -9.2e-33:
		tmp = t_1
	elif t <= -2.15e-73:
		tmp = (y * z) / (t * (a + 1.0))
	elif t <= 1e-104:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -3.3e+123)
		tmp = t_1;
	elseif (t <= -2.65e+66)
		tmp = Float64(Float64(z / t) * Float64(y / Float64(a + 1.0)));
	elseif (t <= -9.2e-33)
		tmp = t_1;
	elseif (t <= -2.15e-73)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	elseif (t <= 1e-104)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -3.3e+123)
		tmp = t_1;
	elseif (t <= -2.65e+66)
		tmp = (z / t) * (y / (a + 1.0));
	elseif (t <= -9.2e-33)
		tmp = t_1;
	elseif (t <= -2.15e-73)
		tmp = (y * z) / (t * (a + 1.0));
	elseif (t <= 1e-104)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+123], t$95$1, If[LessEqual[t, -2.65e+66], N[(N[(z / t), $MachinePrecision] * N[(y / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.2e-33], t$95$1, If[LessEqual[t, -2.15e-73], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-104], N[(z / b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.30000000000000003e123 or -2.6499999999999998e66 < t < -9.19999999999999942e-33 or 9.99999999999999927e-105 < t

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l/ 85.0%

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

      3. *-commutative 85.0%

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

      4. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around inf 64.1%

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

   if -3.30000000000000003e123 < t < -2.6499999999999998e66

   1. Initial program 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in b around 0 39.5%

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

   5. Taylor expanded in x around 0 39.1%

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

      1. *-commutative 39.1%

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

      2. +-commutative 39.1%

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

      3. times-frac 48.1%

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

      4. +-commutative 48.1%

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

   7. Applied egg-rr 48.1%

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

   if -9.19999999999999942e-33 < t < -2.1499999999999999e-73

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 90.1%

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

      3. *-commutative 90.1%

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

      4. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in b around 0 80.9%

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

   5. Taylor expanded in x around 0 71.8%

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

   if -2.1499999999999999e-73 < t < 9.99999999999999927e-105

   1. Initial program 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-*l/ 48.3%

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

      3. *-commutative 48.3%

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

      4. associate-*l/ 45.2%

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

   3. Simplified 45.2%

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

   4. Taylor expanded in t around 0 64.3%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{+66}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + 1}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-73}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 10^{-104}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 11: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+42}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.25e+42)
   (/ z b)
   (if (<= y 1.36e+72) (/ x (+ 1.0 (+ a (/ (* y b) t)))) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.25e+42) {
		tmp = z / b;
	} else if (y <= 1.36e+72) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.25d+42)) then
        tmp = z / b
    else if (y <= 1.36d+72) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.25e+42) {
		tmp = z / b;
	} else if (y <= 1.36e+72) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.25e+42:
		tmp = z / b
	elif y <= 1.36e+72:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.25e+42)
		tmp = Float64(z / b);
	elseif (y <= 1.36e+72)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.25e+42)
		tmp = z / b;
	elseif (y <= 1.36e+72)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.25e+42], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.36e+72], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25000000000000006e42 or 1.3599999999999999e72 < y

   1. Initial program 46.5%

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

      1. *-commutative 46.5%

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

      2. associate-*l/ 51.6%

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

      3. *-commutative 51.6%

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

      4. associate-*l/ 61.6%

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

   3. Simplified 61.6%

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

   4. Taylor expanded in t around 0 60.8%

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

   if -2.25000000000000006e42 < y < 1.3599999999999999e72

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 84.3%

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

      3. *-commutative 84.3%

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

      4. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around inf 65.5%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+42}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12: 60.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+200}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3e+200)
   (/ z b)
   (if (<= y 3.7e+75) (/ x (+ a (+ 1.0 (/ b (/ t y))))) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3e+200) {
		tmp = z / b;
	} else if (y <= 3.7e+75) {
		tmp = x / (a + (1.0 + (b / (t / y))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3d+200)) then
        tmp = z / b
    else if (y <= 3.7d+75) then
        tmp = x / (a + (1.0d0 + (b / (t / y))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3e+200) {
		tmp = z / b;
	} else if (y <= 3.7e+75) {
		tmp = x / (a + (1.0 + (b / (t / y))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3e+200:
		tmp = z / b
	elif y <= 3.7e+75:
		tmp = x / (a + (1.0 + (b / (t / y))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3e+200)
		tmp = Float64(z / b);
	elseif (y <= 3.7e+75)
		tmp = Float64(x / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3e+200)
		tmp = z / b;
	elseif (y <= 3.7e+75)
		tmp = x / (a + (1.0 + (b / (t / y))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3e+200], N[(z / b), $MachinePrecision], If[LessEqual[y, 3.7e+75], N[(x / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999991e200 or 3.70000000000000011e75 < y

   1. Initial program 39.0%

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

      1. *-commutative 39.0%

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

      2. associate-*l/ 43.2%

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

      3. *-commutative 43.2%

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

      4. associate-*l/ 53.9%

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

   3. Simplified 53.9%

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

   4. Taylor expanded in t around 0 67.4%

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

   if -2.99999999999999991e200 < y < 3.70000000000000011e75

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*l/ 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

      1. associate-*l/ 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-/l* 82.6%

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

   5. Applied egg-rr 82.6%

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

   6. Taylor expanded in x around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. associate-+l+ 62.0%

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

      3. +-commutative 62.0%

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

      4. associate-/l* 63.0%

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

   8. Simplified 63.0%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+200}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13: 53.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123} \lor \neg \left(t \leq -4.2 \cdot 10^{+66} \lor \neg \left(t \leq -3.3 \cdot 10^{-13}\right) \land t \leq 5.4 \cdot 10^{-111}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.9e+123)
         (not
          (or (<= t -4.2e+66) (and (not (<= t -3.3e-13)) (<= t 5.4e-111)))))
   (/ x (+ a 1.0))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.9e+123) || !((t <= -4.2e+66) || (!(t <= -3.3e-13) && (t <= 5.4e-111)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.9d+123)) .or. (.not. (t <= (-4.2d+66)) .or. (.not. (t <= (-3.3d-13))) .and. (t <= 5.4d-111))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.9e+123) || !((t <= -4.2e+66) || (!(t <= -3.3e-13) && (t <= 5.4e-111)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.9e+123) or not ((t <= -4.2e+66) or (not (t <= -3.3e-13) and (t <= 5.4e-111))):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.9e+123) || !((t <= -4.2e+66) || (!(t <= -3.3e-13) && (t <= 5.4e-111))))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.9e+123) || ~(((t <= -4.2e+66) || (~((t <= -3.3e-13)) && (t <= 5.4e-111)))))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.9e+123], N[Not[Or[LessEqual[t, -4.2e+66], And[N[Not[LessEqual[t, -3.3e-13]], $MachinePrecision], LessEqual[t, 5.4e-111]]]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9000000000000001e123 or -4.20000000000000011e66 < t < -3.3000000000000001e-13 or 5.39999999999999977e-111 < t

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*l/ 85.4%

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

      3. *-commutative 85.4%

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

      4. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in t around inf 64.6%

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

   if -2.9000000000000001e123 < t < -4.20000000000000011e66 or -3.3000000000000001e-13 < t < 5.39999999999999977e-111

   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/ 55.6%

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

      3. *-commutative 55.6%

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

      4. associate-*l/ 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in t around 0 59.0%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123} \lor \neg \left(t \leq -4.2 \cdot 10^{+66} \lor \neg \left(t \leq -3.3 \cdot 10^{-13}\right) \land t \leq 5.4 \cdot 10^{-111}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14: 53.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-14} \lor \neg \left(t \leq 7 \cdot 10^{-109}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -2.9e+123)
     t_1
     (if (<= t -4.6e+66)
       (* (/ y t) (/ z a))
       (if (or (<= t -1.75e-14) (not (<= t 7e-109))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.9e+123) {
		tmp = t_1;
	} else if (t <= -4.6e+66) {
		tmp = (y / t) * (z / a);
	} else if ((t <= -1.75e-14) || !(t <= 7e-109)) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-2.9d+123)) then
        tmp = t_1
    else if (t <= (-4.6d+66)) then
        tmp = (y / t) * (z / a)
    else if ((t <= (-1.75d-14)) .or. (.not. (t <= 7d-109))) then
        tmp = t_1
    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 = x / (a + 1.0);
	double tmp;
	if (t <= -2.9e+123) {
		tmp = t_1;
	} else if (t <= -4.6e+66) {
		tmp = (y / t) * (z / a);
	} else if ((t <= -1.75e-14) || !(t <= 7e-109)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -2.9e+123:
		tmp = t_1
	elif t <= -4.6e+66:
		tmp = (y / t) * (z / a)
	elif (t <= -1.75e-14) or not (t <= 7e-109):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.9e+123)
		tmp = t_1;
	elseif (t <= -4.6e+66)
		tmp = Float64(Float64(y / t) * Float64(z / a));
	elseif ((t <= -1.75e-14) || !(t <= 7e-109))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.9e+123)
		tmp = t_1;
	elseif (t <= -4.6e+66)
		tmp = (y / t) * (z / a);
	elseif ((t <= -1.75e-14) || ~((t <= 7e-109)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+123], t$95$1, If[LessEqual[t, -4.6e+66], N[(N[(y / t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.75e-14], N[Not[LessEqual[t, 7e-109]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9000000000000001e123 or -4.6e66 < t < -1.7500000000000001e-14 or 7e-109 < t

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*l/ 85.4%

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

      3. *-commutative 85.4%

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

      4. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in t around inf 64.6%

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

   if -2.9000000000000001e123 < t < -4.6e66

   1. Initial program 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around 0 56.0%

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

      1. times-frac 81.8%

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

      2. associate-*l/ 90.7%

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

      3. *-commutative 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in a around inf 47.8%

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

   if -1.7500000000000001e-14 < t < 7e-109

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-*l/ 52.8%

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

      3. *-commutative 52.8%

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

      4. associate-*l/ 50.1%

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

   3. Simplified 50.1%

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

   4. Taylor expanded in t around 0 60.3%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-14} \lor \neg \left(t \leq 7 \cdot 10^{-109}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 15: 54.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + 1}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-12} \lor \neg \left(t \leq 9 \cdot 10^{-105}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -3e+123)
     t_1
     (if (<= t -3.15e+61)
       (* (/ z t) (/ y (+ a 1.0)))
       (if (or (<= t -4.5e-12) (not (<= t 9e-105))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -3e+123) {
		tmp = t_1;
	} else if (t <= -3.15e+61) {
		tmp = (z / t) * (y / (a + 1.0));
	} else if ((t <= -4.5e-12) || !(t <= 9e-105)) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-3d+123)) then
        tmp = t_1
    else if (t <= (-3.15d+61)) then
        tmp = (z / t) * (y / (a + 1.0d0))
    else if ((t <= (-4.5d-12)) .or. (.not. (t <= 9d-105))) then
        tmp = t_1
    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 = x / (a + 1.0);
	double tmp;
	if (t <= -3e+123) {
		tmp = t_1;
	} else if (t <= -3.15e+61) {
		tmp = (z / t) * (y / (a + 1.0));
	} else if ((t <= -4.5e-12) || !(t <= 9e-105)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -3e+123:
		tmp = t_1
	elif t <= -3.15e+61:
		tmp = (z / t) * (y / (a + 1.0))
	elif (t <= -4.5e-12) or not (t <= 9e-105):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -3e+123)
		tmp = t_1;
	elseif (t <= -3.15e+61)
		tmp = Float64(Float64(z / t) * Float64(y / Float64(a + 1.0)));
	elseif ((t <= -4.5e-12) || !(t <= 9e-105))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -3e+123)
		tmp = t_1;
	elseif (t <= -3.15e+61)
		tmp = (z / t) * (y / (a + 1.0));
	elseif ((t <= -4.5e-12) || ~((t <= 9e-105)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+123], t$95$1, If[LessEqual[t, -3.15e+61], N[(N[(z / t), $MachinePrecision] * N[(y / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -4.5e-12], N[Not[LessEqual[t, 9e-105]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.00000000000000008e123 or -3.14999999999999988e61 < t < -4.49999999999999981e-12 or 8.9999999999999995e-105 < t

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*l/ 85.4%

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

      3. *-commutative 85.4%

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

      4. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in t around inf 64.6%

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

   if -3.00000000000000008e123 < t < -3.14999999999999988e61

   1. Initial program 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in b around 0 39.5%

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

   5. Taylor expanded in x around 0 39.1%

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

      1. *-commutative 39.1%

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

      2. +-commutative 39.1%

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

      3. times-frac 48.1%

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

      4. +-commutative 48.1%

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

   7. Applied egg-rr 48.1%

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

   if -4.49999999999999981e-12 < t < 8.9999999999999995e-105

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-*l/ 52.8%

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

      3. *-commutative 52.8%

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

      4. associate-*l/ 50.1%

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

   3. Simplified 50.1%

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

   4. Taylor expanded in t around 0 60.3%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{+61}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + 1}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-12} \lor \neg \left(t \leq 9 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 16: 40.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.9e+123) (/ x a) (if (<= t 2.7e-95) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.9e+123) {
		tmp = x / a;
	} else if (t <= 2.7e-95) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.9d+123)) then
        tmp = x / a
    else if (t <= 2.7d-95) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.9e+123) {
		tmp = x / a;
	} else if (t <= 2.7e-95) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.9e+123:
		tmp = x / a
	elif t <= 2.7e-95:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.9e+123)
		tmp = Float64(x / a);
	elseif (t <= 2.7e-95)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.9e+123)
		tmp = x / a;
	elseif (t <= 2.7e-95)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.9e+123], N[(x / a), $MachinePrecision], If[LessEqual[t, 2.7e-95], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9000000000000001e123 or 2.7e-95 < t

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-*l/ 88.3%

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

      3. *-commutative 88.3%

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

      4. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t around inf 65.5%

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

   5. Taylor expanded in a around inf 39.5%

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

   if -2.9000000000000001e123 < t < 2.7e-95

   1. Initial program 62.5%

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

      1. *-commutative 62.5%

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

      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. *-commutative 58.3%

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

      4. associate-*l/ 56.3%

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

   3. Simplified 56.3%

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

   4. Taylor expanded in t around 0 53.8%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 17: 25.3% 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 73.4%

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

   1. *-commutative 73.4%

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

   2. associate-*l/ 71.9%

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

   3. *-commutative 71.9%

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

   4. associate-*l/ 74.5%

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

3. Simplified 74.5%

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

4. Taylor expanded in t around inf 41.8%

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

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: 78.8% 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 2023279 
(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))))