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

Percentage Accurate: 75.8% → 90.8%

Time: 21.8s

Alternatives: 16

Speedup: 0.4×

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: 75.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right) \cdot \frac{t}{y}}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-235}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{\mathsf{fma}\left(b, \frac{y}{t}, a + 1\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (/ z (* (fma y (/ b t) (+ a 1.0)) (/ t y)))
     (if (<= t_1 -2e-193)
       t_1
       (if (<= t_1 1e-235)
         (/ (fma y (/ z t) x) (fma b (/ y t) (+ a 1.0)))
         (if (<= t_1 2e+292) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z / (fma(y, (b / t), (a + 1.0)) * (t / y));
	} else if (t_1 <= -2e-193) {
		tmp = t_1;
	} else if (t_1 <= 1e-235) {
		tmp = fma(y, (z / t), x) / fma(b, (y / t), (a + 1.0));
	} else if (t_1 <= 2e+292) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z / Float64(fma(y, Float64(b / t), Float64(a + 1.0)) * Float64(t / y)));
	elseif (t_1 <= -2e-193)
		tmp = t_1;
	elseif (t_1 <= 1e-235)
		tmp = Float64(fma(y, Float64(z / t), x) / fma(b, Float64(y / t), Float64(a + 1.0)));
	elseif (t_1 <= 2e+292)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z / N[(N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-193], t$95$1, If[LessEqual[t$95$1, 1e-235], N[(N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision] / N[(b * N[(y / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+292], t$95$1, 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 17.3%

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

      1. *-commutative 17.3%

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

      2. associate-*l/ 58.6%

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

      3. *-commutative 58.6%

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

      4. associate-*l/ 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in x around 0 52.2%

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

      1. times-frac 75.9%

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

      2. associate-+r+ 75.9%

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

      3. associate-/l* 68.9%

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

      4. +-commutative 68.9%

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

      5. associate-/l* 75.9%

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

      6. associate-*r/ 68.6%

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

      7. fma-def 68.6%

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

   7. Simplified 68.6%

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

      1. clear-num 68.9%

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

      2. frac-times 63.0%

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

      3. *-un-lft-identity 63.0%

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

      4. +-commutative 63.0%

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

   9. Applied egg-rr 63.0%

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

       1. *-commutative 63.0%

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

       2. fma-def 63.0%

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

       3. *-commutative 63.0%

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

       4. associate-*l/ 74.9%

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

       5. associate-*r/ 74.9%

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

       6. +-commutative 74.9%

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

       7. fma-def 74.9%

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

   11. Simplified 74.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2.0000000000000001e-193 or 9.9999999999999996e-236 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2e292

   1. Initial program 99.7%

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

   if -2.0000000000000001e-193 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.9999999999999996e-236

   1. Initial program 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-*r/ 74.9%

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

      3. fma-def 74.9%

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

      4. +-commutative 74.9%

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

      5. associate-*l/ 82.8%

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

      6. *-commutative 82.8%

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

      7. fma-def 82.8%

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

   3. Simplified 82.8%

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

   if 2e292 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 4.4%

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

      1. *-commutative 4.4%

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

      2. associate-*l/ 13.8%

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

      3. *-commutative 13.8%

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

      4. associate-*l/ 16.9%

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

   3. Simplified 16.9%

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

   5. Taylor expanded in t around 0 84.9%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right) \cdot \frac{t}{y}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-193}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{-235}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t}, x\right)}{\mathsf{fma}\left(b, \frac{y}{t}, a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right) \cdot \frac{t}{y}}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-235}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (/ z (* (fma y (/ b t) (+ a 1.0)) (/ t y)))
     (if (<= t_1 -1e-161)
       t_1
       (if (<= t_1 1e-235)
         (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (* b (/ y t)))))
         (if (<= t_1 2e+292) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z / (fma(y, (b / t), (a + 1.0)) * (t / y));
	} else if (t_1 <= -1e-161) {
		tmp = t_1;
	} else if (t_1 <= 1e-235) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))));
	} else if (t_1 <= 2e+292) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z / Float64(fma(y, Float64(b / t), Float64(a + 1.0)) * Float64(t / y)));
	elseif (t_1 <= -1e-161)
		tmp = t_1;
	elseif (t_1 <= 1e-235)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(b * Float64(y / t)))));
	elseif (t_1 <= 2e+292)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z / N[(N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-161], t$95$1, If[LessEqual[t$95$1, 1e-235], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+292], t$95$1, 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 17.3%

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

      1. *-commutative 17.3%

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

      2. associate-*l/ 58.6%

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

      3. *-commutative 58.6%

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

      4. associate-*l/ 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in x around 0 52.2%

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

      1. times-frac 75.9%

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

      2. associate-+r+ 75.9%

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

      3. associate-/l* 68.9%

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

      4. +-commutative 68.9%

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

      5. associate-/l* 75.9%

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

      6. associate-*r/ 68.6%

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

      7. fma-def 68.6%

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

   7. Simplified 68.6%

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

      1. clear-num 68.9%

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

      2. frac-times 63.0%

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

      3. *-un-lft-identity 63.0%

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

      4. +-commutative 63.0%

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

   9. Applied egg-rr 63.0%

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

       1. *-commutative 63.0%

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

       2. fma-def 63.0%

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

       3. *-commutative 63.0%

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

       4. associate-*l/ 74.9%

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

       5. associate-*r/ 74.9%

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

       6. +-commutative 74.9%

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

       7. fma-def 74.9%

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

   11. Simplified 74.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.00000000000000003e-161 or 9.9999999999999996e-236 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2e292

   1. Initial program 99.7%

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

   if -1.00000000000000003e-161 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.9999999999999996e-236

   1. Initial program 73.5%

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

      1. associate-/l* 76.5%

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

      2. associate-+l+ 76.5%

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

      3. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

      1. associate-/r/ 80.1%

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

   6. Applied egg-rr 83.9%

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

   if 2e292 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 4.4%

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

      1. *-commutative 4.4%

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

      2. associate-*l/ 13.8%

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

      3. *-commutative 13.8%

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

      4. associate-*l/ 16.9%

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

   3. Simplified 16.9%

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

   5. Taylor expanded in t around 0 84.9%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z}{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right) \cdot \frac{t}{y}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-161}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{-235}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + b \cdot \frac{y}{t}}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{a}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-64}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-298}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 95:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (* b (/ y t)))))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 a)))
   (if (<= a -6e+18)
     t_3
     (if (<= a -1.35e-64)
       (/ z b)
       (if (<= a -4.2e-298)
         (+ x (* z (/ y t)))
         (if (<= a 1.15e-225)
           t_1
           (if (<= a 1.02e-103) t_2 (if (<= a 95.0) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (b * (y / t)));
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / a;
	double tmp;
	if (a <= -6e+18) {
		tmp = t_3;
	} else if (a <= -1.35e-64) {
		tmp = z / b;
	} else if (a <= -4.2e-298) {
		tmp = x + (z * (y / t));
	} else if (a <= 1.15e-225) {
		tmp = t_1;
	} else if (a <= 1.02e-103) {
		tmp = t_2;
	} else if (a <= 95.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (1.0d0 + (b * (y / t)))
    t_2 = x + ((y * z) / t)
    t_3 = t_2 / a
    if (a <= (-6d+18)) then
        tmp = t_3
    else if (a <= (-1.35d-64)) then
        tmp = z / b
    else if (a <= (-4.2d-298)) then
        tmp = x + (z * (y / t))
    else if (a <= 1.15d-225) then
        tmp = t_1
    else if (a <= 1.02d-103) then
        tmp = t_2
    else if (a <= 95.0d0) then
        tmp = t_1
    else
        tmp = t_3
    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 / (1.0 + (b * (y / t)));
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / a;
	double tmp;
	if (a <= -6e+18) {
		tmp = t_3;
	} else if (a <= -1.35e-64) {
		tmp = z / b;
	} else if (a <= -4.2e-298) {
		tmp = x + (z * (y / t));
	} else if (a <= 1.15e-225) {
		tmp = t_1;
	} else if (a <= 1.02e-103) {
		tmp = t_2;
	} else if (a <= 95.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (b * (y / t)))
	t_2 = x + ((y * z) / t)
	t_3 = t_2 / a
	tmp = 0
	if a <= -6e+18:
		tmp = t_3
	elif a <= -1.35e-64:
		tmp = z / b
	elif a <= -4.2e-298:
		tmp = x + (z * (y / t))
	elif a <= 1.15e-225:
		tmp = t_1
	elif a <= 1.02e-103:
		tmp = t_2
	elif a <= 95.0:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))))
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / a)
	tmp = 0.0
	if (a <= -6e+18)
		tmp = t_3;
	elseif (a <= -1.35e-64)
		tmp = Float64(z / b);
	elseif (a <= -4.2e-298)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (a <= 1.15e-225)
		tmp = t_1;
	elseif (a <= 1.02e-103)
		tmp = t_2;
	elseif (a <= 95.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (b * (y / t)));
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / a;
	tmp = 0.0;
	if (a <= -6e+18)
		tmp = t_3;
	elseif (a <= -1.35e-64)
		tmp = z / b;
	elseif (a <= -4.2e-298)
		tmp = x + (z * (y / t));
	elseif (a <= 1.15e-225)
		tmp = t_1;
	elseif (a <= 1.02e-103)
		tmp = t_2;
	elseif (a <= 95.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / a), $MachinePrecision]}, If[LessEqual[a, -6e+18], t$95$3, If[LessEqual[a, -1.35e-64], N[(z / b), $MachinePrecision], If[LessEqual[a, -4.2e-298], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-225], t$95$1, If[LessEqual[a, 1.02e-103], t$95$2, If[LessEqual[a, 95.0], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6e18 or 95 < a

   1. Initial program 78.7%

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

      1. *-commutative 78.7%

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

      2. associate-*l/ 79.2%

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

      3. *-commutative 79.2%

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

      4. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in a around inf 67.2%

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

   if -6e18 < a < -1.34999999999999993e-64

   1. Initial program 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*l/ 62.8%

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

      3. *-commutative 62.8%

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

      4. associate-*l/ 62.5%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in t around 0 60.4%

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

   if -1.34999999999999993e-64 < a < -4.2000000000000001e-298

   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/ 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*l/ 79.8%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in b around 0 58.6%

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

   6. Taylor expanded in a around 0 58.6%

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

      1. associate-*r/ 62.1%

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

   8. Simplified 62.1%

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

   9. Taylor expanded in y around 0 58.6%

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

       1. associate-/l* 62.0%

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

       2. associate-/r/ 63.9%

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

   11. Simplified 63.9%

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

   if -4.2000000000000001e-298 < a < 1.1499999999999999e-225 or 1.01999999999999998e-103 < a < 95

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*l/ 63.3%

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

      3. *-commutative 63.3%

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

      4. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in a around 0 61.4%

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

      1. associate-*l/ 69.6%

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

      2. *-commutative 69.6%

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

      3. clear-num 69.6%

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

      4. div-inv 69.6%

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

      5. add-cube-cbrt 69.1%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{t}{b}}} \]

      6. *-un-lft-identity 69.1%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{1 \cdot \frac{t}{b}}}} \]

      7. times-frac 69.1%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}}} \]

      8. pow2 69.1%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}} \]

   7. Applied egg-rr 69.1%

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}}} \]
   8. Step-by-step derivation

      1. /-rgt-identity 69.1%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}} \]

      2. associate-*r/ 69.1%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{\frac{t}{b}}}} \]

      3. unpow2 69.1%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{\frac{t}{b}}} \]

      4. rem-3cbrt-lft 69.6%

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

   9. Simplified 69.6%

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

   10. Taylor expanded in x around inf 53.4%

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

       1. *-commutative 53.4%

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

       2. associate-/l* 59.1%

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

       3. associate-/r/ 59.1%

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

   12. Simplified 59.1%

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

   if 1.1499999999999999e-225 < a < 1.01999999999999998e-103

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

      2. associate-*l/ 75.5%

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

      3. *-commutative 75.5%

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

      4. associate-*l/ 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in b around 0 62.5%

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

   6. Taylor expanded in a around 0 62.5%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+18}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-64}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-298}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-225}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 95:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))) 2e+292)
   (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (* b (/ y t)))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))) <= 2e+292) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b * (y / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))) <= 2d+292) then
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (b * (y / t))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))) <= 2e+292) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b * (y / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))) <= 2e+292:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b * (y / t))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))) <= 2e+292)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(b * Float64(y / t)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))) <= 2e+292)
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b * (y / t))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], 2e+292], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2e292

   1. Initial program 86.3%

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

      1. associate-/l* 85.2%

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

      2. associate-+l+ 85.2%

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

      3. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

      1. associate-/r/ 86.9%

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

   6. Applied egg-rr 86.9%

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

      1. associate-/r/ 89.4%

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

   8. Applied egg-rr 89.4%

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

   if 2e292 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 4.4%

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

      1. *-commutative 4.4%

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

      2. associate-*l/ 13.8%

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

      3. *-commutative 13.8%

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

      4. associate-*l/ 16.9%

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

   3. Simplified 16.9%

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

   5. Taylor expanded in t around 0 84.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-64}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-266}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.25e+34)
   (/ x a)
   (if (<= a -1.1e-64)
     (/ z b)
     (if (<= a -3.3e-266)
       x
       (if (<= a 5.2e-169)
         (/ z b)
         (if (<= a 1.5e-138) x (if (<= a 5.5e+16) (/ z b) (/ x a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.25e+34) {
		tmp = x / a;
	} else if (a <= -1.1e-64) {
		tmp = z / b;
	} else if (a <= -3.3e-266) {
		tmp = x;
	} else if (a <= 5.2e-169) {
		tmp = z / b;
	} else if (a <= 1.5e-138) {
		tmp = x;
	} else if (a <= 5.5e+16) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.25d+34)) then
        tmp = x / a
    else if (a <= (-1.1d-64)) then
        tmp = z / b
    else if (a <= (-3.3d-266)) then
        tmp = x
    else if (a <= 5.2d-169) then
        tmp = z / b
    else if (a <= 1.5d-138) then
        tmp = x
    else if (a <= 5.5d+16) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.25e+34) {
		tmp = x / a;
	} else if (a <= -1.1e-64) {
		tmp = z / b;
	} else if (a <= -3.3e-266) {
		tmp = x;
	} else if (a <= 5.2e-169) {
		tmp = z / b;
	} else if (a <= 1.5e-138) {
		tmp = x;
	} else if (a <= 5.5e+16) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.25e+34:
		tmp = x / a
	elif a <= -1.1e-64:
		tmp = z / b
	elif a <= -3.3e-266:
		tmp = x
	elif a <= 5.2e-169:
		tmp = z / b
	elif a <= 1.5e-138:
		tmp = x
	elif a <= 5.5e+16:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.25e+34)
		tmp = Float64(x / a);
	elseif (a <= -1.1e-64)
		tmp = Float64(z / b);
	elseif (a <= -3.3e-266)
		tmp = x;
	elseif (a <= 5.2e-169)
		tmp = Float64(z / b);
	elseif (a <= 1.5e-138)
		tmp = x;
	elseif (a <= 5.5e+16)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.25e+34)
		tmp = x / a;
	elseif (a <= -1.1e-64)
		tmp = z / b;
	elseif (a <= -3.3e-266)
		tmp = x;
	elseif (a <= 5.2e-169)
		tmp = z / b;
	elseif (a <= 1.5e-138)
		tmp = x;
	elseif (a <= 5.5e+16)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.25e+34], N[(x / a), $MachinePrecision], If[LessEqual[a, -1.1e-64], N[(z / b), $MachinePrecision], If[LessEqual[a, -3.3e-266], x, If[LessEqual[a, 5.2e-169], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.5e-138], x, If[LessEqual[a, 5.5e+16], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.25e34 or 5.5e16 < a

   1. Initial program 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-*l/ 78.1%

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

      3. *-commutative 78.1%

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

      4. associate-*l/ 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in x around inf 58.0%

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

   6. Taylor expanded in a around inf 53.4%

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

   if -1.25e34 < a < -1.1e-64 or -3.3000000000000003e-266 < a < 5.20000000000000028e-169 or 1.5e-138 < a < 5.5e16

   1. Initial program 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*l/ 66.3%

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

      3. *-commutative 66.3%

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

      4. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in t around 0 46.4%

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

   if -1.1e-64 < a < -3.3000000000000003e-266 or 5.20000000000000028e-169 < a < 1.5e-138

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      2. associate-*l/ 87.4%

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

      3. *-commutative 87.4%

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

      4. associate-*l/ 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in t around inf 52.3%

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

   6. Taylor expanded in a around 0 52.3%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-64}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-266}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := \frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -6.1 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x t) (* y b))))
        (t_2 (/ x (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -6.1e-30)
     t_2
     (if (<= t -2.7e-103)
       t_1
       (if (<= t -4.4e-161)
         (/ x (+ 1.0 (+ a (/ (* y b) t))))
         (if (<= t 3.9e-16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * t) / (y * b));
	double t_2 = x / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -6.1e-30) {
		tmp = t_2;
	} else if (t <= -2.7e-103) {
		tmp = t_1;
	} else if (t <= -4.4e-161) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (t <= 3.9e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z / b) + ((x * t) / (y * b))
    t_2 = x / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-6.1d-30)) then
        tmp = t_2
    else if (t <= (-2.7d-103)) then
        tmp = t_1
    else if (t <= (-4.4d-161)) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (t <= 3.9d-16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * t) / (y * b));
	double t_2 = x / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -6.1e-30) {
		tmp = t_2;
	} else if (t <= -2.7e-103) {
		tmp = t_1;
	} else if (t <= -4.4e-161) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (t <= 3.9e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * t) / (y * b))
	t_2 = x / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -6.1e-30:
		tmp = t_2
	elif t <= -2.7e-103:
		tmp = t_1
	elif t <= -4.4e-161:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif t <= 3.9e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)))
	t_2 = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -6.1e-30)
		tmp = t_2;
	elseif (t <= -2.7e-103)
		tmp = t_1;
	elseif (t <= -4.4e-161)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (t <= 3.9e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * t) / (y * b));
	t_2 = x / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -6.1e-30)
		tmp = t_2;
	elseif (t <= -2.7e-103)
		tmp = t_1;
	elseif (t <= -4.4e-161)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (t <= 3.9e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.1e-30], t$95$2, If[LessEqual[t, -2.7e-103], t$95$1, If[LessEqual[t, -4.4e-161], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.09999999999999981e-30 or 3.89999999999999977e-16 < t

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l/ 90.8%

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

      3. *-commutative 90.8%

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

      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. Add Preprocessing

   5. Taylor expanded in x around inf 72.8%

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

   if -6.09999999999999981e-30 < t < -2.7000000000000001e-103 or -4.40000000000000004e-161 < t < 3.89999999999999977e-16

   1. Initial program 62.8%

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

      1. associate-/l* 54.7%

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

      2. associate-+l+ 54.7%

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

      3. associate-/l* 50.5%

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

   3. Simplified 50.5%

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

      1. associate-/r/ 52.9%

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

   6. Applied egg-rr 52.9%

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

      1. associate-/r/ 58.3%

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

   8. Applied egg-rr 58.3%

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

   9. Taylor expanded in b around inf 40.4%

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

       1. times-frac 33.2%

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

       2. associate-*r/ 33.3%

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

   11. Simplified 33.3%

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

   12. Taylor expanded in t around 0 65.4%

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

   if -2.7000000000000001e-103 < t < -4.40000000000000004e-161

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

      2. associate-*l/ 91.1%

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

      3. *-commutative 91.1%

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

      4. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around inf 56.9%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-16}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-58}:\\ \;\;\;\;\frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \frac{z}{t \cdot a}\\ \mathbf{elif}\;t \leq 10^{-15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -6.2e-18)
     t_1
     (if (<= t -3.2e-58)
       (/ (* x t) (* y b))
       (if (<= t -2.2e-135)
         (* y (/ z (* t a)))
         (if (<= t 1e-15) (/ 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 <= -6.2e-18) {
		tmp = t_1;
	} else if (t <= -3.2e-58) {
		tmp = (x * t) / (y * b);
	} else if (t <= -2.2e-135) {
		tmp = y * (z / (t * a));
	} else if (t <= 1e-15) {
		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 <= (-6.2d-18)) then
        tmp = t_1
    else if (t <= (-3.2d-58)) then
        tmp = (x * t) / (y * b)
    else if (t <= (-2.2d-135)) then
        tmp = y * (z / (t * a))
    else if (t <= 1d-15) 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 <= -6.2e-18) {
		tmp = t_1;
	} else if (t <= -3.2e-58) {
		tmp = (x * t) / (y * b);
	} else if (t <= -2.2e-135) {
		tmp = y * (z / (t * a));
	} else if (t <= 1e-15) {
		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 <= -6.2e-18:
		tmp = t_1
	elif t <= -3.2e-58:
		tmp = (x * t) / (y * b)
	elif t <= -2.2e-135:
		tmp = y * (z / (t * a))
	elif t <= 1e-15:
		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 <= -6.2e-18)
		tmp = t_1;
	elseif (t <= -3.2e-58)
		tmp = Float64(Float64(x * t) / Float64(y * b));
	elseif (t <= -2.2e-135)
		tmp = Float64(y * Float64(z / Float64(t * a)));
	elseif (t <= 1e-15)
		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 <= -6.2e-18)
		tmp = t_1;
	elseif (t <= -3.2e-58)
		tmp = (x * t) / (y * b);
	elseif (t <= -2.2e-135)
		tmp = y * (z / (t * a));
	elseif (t <= 1e-15)
		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, -6.2e-18], t$95$1, If[LessEqual[t, -3.2e-58], N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.2e-135], N[(y * N[(z / N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-15], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.20000000000000014e-18 or 1.0000000000000001e-15 < t

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 90.5%

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

      3. *-commutative 90.5%

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

      4. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t around inf 63.8%

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

   if -6.20000000000000014e-18 < t < -3.2000000000000001e-58

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 64.9%

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

   6. Taylor expanded in b around inf 56.6%

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

   if -3.2000000000000001e-58 < t < -2.2e-135

   1. Initial program 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*l/ 62.9%

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

      3. *-commutative 62.9%

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

      4. associate-*l/ 62.8%

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

   3. Simplified 62.8%

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

   5. Taylor expanded in x around 0 47.4%

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

      1. times-frac 47.0%

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

      2. associate-+r+ 47.0%

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

      3. associate-/l* 47.0%

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

      4. +-commutative 47.0%

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

      5. associate-/l* 47.0%

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

      6. associate-*r/ 46.5%

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

      7. fma-def 46.5%

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

   7. Simplified 46.5%

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

   8. Taylor expanded in a around inf 33.1%

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

      1. expm1-log1p-u 17.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot z}{a \cdot t}\right)\right)} \]

      2. expm1-udef 4.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot z}{a \cdot t}\right)} - 1} \]

      3. *-commutative 4.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y \cdot z}{\color{blue}{t \cdot a}}\right)} - 1 \]

      4. times-frac 4.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{t} \cdot \frac{z}{a}}\right)} - 1 \]

   10. Applied egg-rr 4.1%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{t} \cdot \frac{z}{a}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 17.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{t} \cdot \frac{z}{a}\right)\right)} \]

       2. expm1-log1p 32.7%

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

       3. times-frac 33.1%

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

       4. associate-*r/ 40.4%

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

   12. Simplified 40.4%

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

   if -2.2e-135 < t < 1.0000000000000001e-15

   1. Initial program 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*l/ 54.6%

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

      3. *-commutative 54.6%

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

      4. associate-*l/ 50.2%

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

   3. Simplified 50.2%

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

   5. Taylor expanded in t around 0 56.0%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-58}:\\ \;\;\;\;\frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \frac{z}{t \cdot a}\\ \mathbf{elif}\;t \leq 10^{-15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-13}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -5.5e-18)
     t_1
     (if (<= t -3.2e-62)
       (/ (* x t) (* y b))
       (if (<= t -8.2e-150)
         (* (/ y t) (/ z (+ a 1.0)))
         (if (<= t 1.65e-13) (/ 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 <= -5.5e-18) {
		tmp = t_1;
	} else if (t <= -3.2e-62) {
		tmp = (x * t) / (y * b);
	} else if (t <= -8.2e-150) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 1.65e-13) {
		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 <= (-5.5d-18)) then
        tmp = t_1
    else if (t <= (-3.2d-62)) then
        tmp = (x * t) / (y * b)
    else if (t <= (-8.2d-150)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (t <= 1.65d-13) 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 <= -5.5e-18) {
		tmp = t_1;
	} else if (t <= -3.2e-62) {
		tmp = (x * t) / (y * b);
	} else if (t <= -8.2e-150) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 1.65e-13) {
		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 <= -5.5e-18:
		tmp = t_1
	elif t <= -3.2e-62:
		tmp = (x * t) / (y * b)
	elif t <= -8.2e-150:
		tmp = (y / t) * (z / (a + 1.0))
	elif t <= 1.65e-13:
		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 <= -5.5e-18)
		tmp = t_1;
	elseif (t <= -3.2e-62)
		tmp = Float64(Float64(x * t) / Float64(y * b));
	elseif (t <= -8.2e-150)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (t <= 1.65e-13)
		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 <= -5.5e-18)
		tmp = t_1;
	elseif (t <= -3.2e-62)
		tmp = (x * t) / (y * b);
	elseif (t <= -8.2e-150)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (t <= 1.65e-13)
		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, -5.5e-18], t$95$1, If[LessEqual[t, -3.2e-62], N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.2e-150], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e-13], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.5e-18 or 1.65e-13 < t

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 90.5%

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

      3. *-commutative 90.5%

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

      4. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t around inf 63.8%

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

   if -5.5e-18 < t < -3.20000000000000021e-62

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l/ 93.0%

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

      3. *-commutative 93.0%

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

      4. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 64.4%

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

   6. Taylor expanded in b around inf 50.9%

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

   if -3.20000000000000021e-62 < t < -8.1999999999999997e-150

   1. Initial program 65.6%

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

      1. *-commutative 65.6%

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

      2. associate-*l/ 72.1%

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

      3. *-commutative 72.1%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 58.1%

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

      1. times-frac 64.5%

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

      2. associate-+r+ 64.5%

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

      3. associate-/l* 64.5%

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

      4. +-commutative 64.5%

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

      5. associate-/l* 64.5%

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

      6. associate-*r/ 64.5%

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

      7. fma-def 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in y around 0 38.2%

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

      1. times-frac 44.6%

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

   10. Simplified 44.6%

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

   if -8.1999999999999997e-150 < t < 1.65e-13

   1. Initial program 62.2%

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

      1. *-commutative 62.2%

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

      2. associate-*l/ 52.6%

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

      3. *-commutative 52.6%

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

      4. associate-*l/ 48.0%

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

   3. Simplified 48.0%

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

   5. Taylor expanded in t around 0 57.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-13}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.45e-16)
     t_1
     (if (<= t -9.2e-63)
       (/ x (+ 1.0 (* b (/ y t))))
       (if (<= t -5.5e-183)
         (* (/ y t) (/ z (+ a 1.0)))
         (if (<= t 1.06e-15) (/ z b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.45e-16) {
		tmp = t_1;
	} else if (t <= -9.2e-63) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (t <= -5.5e-183) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 1.06e-15) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-1.45d-16)) then
        tmp = t_1
    else if (t <= (-9.2d-63)) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if (t <= (-5.5d-183)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (t <= 1.06d-15) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.45e-16) {
		tmp = t_1;
	} else if (t <= -9.2e-63) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (t <= -5.5e-183) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 1.06e-15) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.45e-16:
		tmp = t_1
	elif t <= -9.2e-63:
		tmp = x / (1.0 + (b * (y / t)))
	elif t <= -5.5e-183:
		tmp = (y / t) * (z / (a + 1.0))
	elif t <= 1.06e-15:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.45e-16)
		tmp = t_1;
	elseif (t <= -9.2e-63)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (t <= -5.5e-183)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (t <= 1.06e-15)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.45e-16)
		tmp = t_1;
	elseif (t <= -9.2e-63)
		tmp = x / (1.0 + (b * (y / t)));
	elseif (t <= -5.5e-183)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (t <= 1.06e-15)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-16], t$95$1, If[LessEqual[t, -9.2e-63], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-183], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e-15], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.4499999999999999e-16 or 1.06000000000000007e-15 < t

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 90.5%

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

      3. *-commutative 90.5%

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

      4. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t around inf 63.8%

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

   if -1.4499999999999999e-16 < t < -9.2e-63

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l/ 93.0%

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

      3. *-commutative 93.0%

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

      4. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in a around 0 79.3%

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

      1. associate-*l/ 79.1%

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

      2. *-commutative 79.1%

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

      3. clear-num 79.0%

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

      4. div-inv 79.1%

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

      5. add-cube-cbrt 78.9%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{t}{b}}} \]

      6. *-un-lft-identity 78.9%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{1 \cdot \frac{t}{b}}}} \]

      7. times-frac 79.0%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}}} \]

      8. pow2 79.0%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}} \]

   7. Applied egg-rr 79.0%

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}}} \]
   8. Step-by-step derivation

      1. /-rgt-identity 79.0%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{\frac{t}{b}}} \]

      2. associate-*r/ 78.9%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{\frac{t}{b}}}} \]

      3. unpow2 78.9%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{1 + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{\frac{t}{b}}} \]

      4. rem-3cbrt-lft 79.1%

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

   9. Simplified 79.1%

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

   10. Taylor expanded in x around inf 57.5%

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

       1. *-commutative 57.5%

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

       2. associate-/l* 57.4%

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

       3. associate-/r/ 57.2%

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

   12. Simplified 57.2%

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

   if -9.2e-63 < t < -5.4999999999999999e-183

   1. Initial program 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*l/ 61.5%

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

      3. *-commutative 61.5%

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

      4. associate-*l/ 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in x around 0 61.1%

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

      1. times-frac 60.9%

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

      2. associate-+r+ 60.9%

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

      3. associate-/l* 60.8%

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

      4. +-commutative 60.8%

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

      5. associate-/l* 60.9%

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

      6. associate-*r/ 60.5%

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

      7. fma-def 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in y around 0 36.9%

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

      1. times-frac 41.3%

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

   10. Simplified 41.3%

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

   if -5.4999999999999999e-183 < t < 1.06000000000000007e-15

   1. Initial program 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*l/ 53.7%

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

      3. *-commutative 53.7%

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

      4. associate-*l/ 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in t around 0 58.7%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -6e-17)
     t_1
     (if (<= t -1.1e-66)
       (/ x (+ 1.0 (/ (* y b) t)))
       (if (<= t -9.2e-183)
         (* (/ y t) (/ z (+ a 1.0)))
         (if (<= t 3.2e-14) (/ 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 <= -6e-17) {
		tmp = t_1;
	} else if (t <= -1.1e-66) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= -9.2e-183) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 3.2e-14) {
		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 <= (-6d-17)) then
        tmp = t_1
    else if (t <= (-1.1d-66)) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (t <= (-9.2d-183)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (t <= 3.2d-14) 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 <= -6e-17) {
		tmp = t_1;
	} else if (t <= -1.1e-66) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (t <= -9.2e-183) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 3.2e-14) {
		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 <= -6e-17:
		tmp = t_1
	elif t <= -1.1e-66:
		tmp = x / (1.0 + ((y * b) / t))
	elif t <= -9.2e-183:
		tmp = (y / t) * (z / (a + 1.0))
	elif t <= 3.2e-14:
		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 <= -6e-17)
		tmp = t_1;
	elseif (t <= -1.1e-66)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (t <= -9.2e-183)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (t <= 3.2e-14)
		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 <= -6e-17)
		tmp = t_1;
	elseif (t <= -1.1e-66)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (t <= -9.2e-183)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (t <= 3.2e-14)
		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, -6e-17], t$95$1, If[LessEqual[t, -1.1e-66], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.2e-183], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-14], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.00000000000000012e-17 or 3.2000000000000002e-14 < t

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 90.5%

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

      3. *-commutative 90.5%

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

      4. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t around inf 63.8%

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

   if -6.00000000000000012e-17 < t < -1.1000000000000001e-66

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l/ 93.0%

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

      3. *-commutative 93.0%

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

      4. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 64.4%

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

   6. Taylor expanded in a around 0 57.5%

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

   if -1.1000000000000001e-66 < t < -9.20000000000000064e-183

   1. Initial program 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*l/ 61.5%

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

      3. *-commutative 61.5%

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

      4. associate-*l/ 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in x around 0 61.1%

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

      1. times-frac 60.9%

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

      2. associate-+r+ 60.9%

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

      3. associate-/l* 60.8%

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

      4. +-commutative 60.8%

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

      5. associate-/l* 60.9%

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

      6. associate-*r/ 60.5%

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

      7. fma-def 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in y around 0 36.9%

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

      1. times-frac 41.3%

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

   10. Simplified 41.3%

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

   if -9.20000000000000064e-183 < t < 3.2000000000000002e-14

   1. Initial program 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*l/ 53.7%

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

      3. *-commutative 53.7%

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

      4. associate-*l/ 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in t around 0 58.7%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+20} \lor \neg \left(y \leq 7.5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e+20) (not (<= y 7.5e+18)))
   (+ (/ z b) (* (/ t b) (/ x y)))
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+20) || !(y <= 7.5e+18)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.05d+20)) .or. (.not. (y <= 7.5d+18))) then
        tmp = (z / b) + ((t / b) * (x / y))
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+20) || !(y <= 7.5e+18)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e+20) or not (y <= 7.5e+18):
		tmp = (z / b) + ((t / b) * (x / y))
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e+20) || !(y <= 7.5e+18))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.05e+20) || ~((y <= 7.5e+18)))
		tmp = (z / b) + ((t / b) * (x / y));
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e+20], N[Not[LessEqual[y, 7.5e+18]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e20 or 7.5e18 < y

   1. Initial program 55.0%

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

      1. associate-/l* 61.8%

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

      2. associate-+l+ 61.8%

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

      3. associate-/l* 66.9%

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

   3. Simplified 66.9%

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

      1. associate-/r/ 64.7%

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

   6. Applied egg-rr 64.7%

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

      1. associate-/r/ 63.6%

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

   8. Applied egg-rr 63.6%

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

   9. Taylor expanded in b around inf 30.6%

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

       1. times-frac 37.2%

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

       2. associate-*r/ 38.8%

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

   11. Simplified 38.8%

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

   12. Taylor expanded in t around 0 55.3%

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

       1. +-commutative 55.3%

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

       2. times-frac 61.1%

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

   14. Simplified 61.1%

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

   if -1.05e20 < y < 7.5e18

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l/ 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in t around inf 62.7%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+20} \lor \neg \left(y \leq 7.5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+32} \lor \neg \left(y \leq 1.7 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.7e+32) (not (<= y 1.7e-41)))
   (+ (/ z b) (* (/ t b) (/ x y)))
   (/ x (+ 1.0 (+ a (/ (* y b) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.7e+32) || !(y <= 1.7e-41)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.7d+32)) .or. (.not. (y <= 1.7d-41))) then
        tmp = (z / b) + ((t / b) * (x / y))
    else
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.7e+32) || !(y <= 1.7e-41)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.7e+32) or not (y <= 1.7e-41):
		tmp = (z / b) + ((t / b) * (x / y))
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.7e+32) || !(y <= 1.7e-41))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.7e+32) || ~((y <= 1.7e-41)))
		tmp = (z / b) + ((t / b) * (x / y));
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.7e+32], N[Not[LessEqual[y, 1.7e-41]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.69999999999999989e32 or 1.6999999999999999e-41 < y

   1. Initial program 57.4%

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

      1. associate-/l* 63.0%

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

      2. associate-+l+ 63.0%

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

      3. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

      1. associate-/r/ 65.7%

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

   6. Applied egg-rr 65.7%

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

      1. associate-/r/ 64.6%

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

   8. Applied egg-rr 64.6%

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

   9. Taylor expanded in b around inf 30.1%

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

       1. times-frac 36.3%

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

       2. associate-*r/ 37.8%

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

   11. Simplified 37.8%

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

   12. Taylor expanded in t around 0 54.0%

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

       1. +-commutative 54.0%

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

       2. times-frac 59.4%

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

   14. Simplified 59.4%

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

   if -1.69999999999999989e32 < y < 1.6999999999999999e-41

   1. Initial program 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*l/ 88.2%

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

      3. *-commutative 88.2%

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

      4. associate-*l/ 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in x around inf 72.0%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+32} \lor \neg \left(y \leq 1.7 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+137} \lor \neg \left(y \leq 1.18 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.4e+137) (not (<= y 1.18e+26)))
   (+ (/ z b) (* (/ t b) (/ x y)))
   (/ (+ 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 ((y <= -4.4e+137) || !(y <= 1.18e+26)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} 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 ((y <= (-4.4d+137)) .or. (.not. (y <= 1.18d+26))) then
        tmp = (z / b) + ((t / b) * (x / y))
    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 ((y <= -4.4e+137) || !(y <= 1.18e+26)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.4e+137) or not (y <= 1.18e+26):
		tmp = (z / b) + ((t / b) * (x / y))
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.4e+137) || !(y <= 1.18e+26))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	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 ((y <= -4.4e+137) || ~((y <= 1.18e+26)))
		tmp = (z / b) + ((t / b) * (x / y));
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.4e+137], N[Not[LessEqual[y, 1.18e+26]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.40000000000000031e137 or 1.18e26 < y

   1. Initial program 48.8%

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

      1. associate-/l* 54.7%

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

      2. associate-+l+ 54.7%

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

      3. associate-/l* 59.3%

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

   3. Simplified 59.3%

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

      1. associate-/r/ 56.8%

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

   6. Applied egg-rr 56.8%

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

      1. associate-/r/ 55.3%

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

   8. Applied egg-rr 55.3%

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

   9. Taylor expanded in b around inf 28.7%

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

       1. times-frac 36.1%

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

       2. associate-*r/ 38.3%

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

   11. Simplified 38.3%

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

   12. Taylor expanded in t around 0 61.3%

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

       1. +-commutative 61.3%

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

       2. times-frac 66.9%

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

   14. Simplified 66.9%

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

   if -4.40000000000000031e137 < y < 1.18e26

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*l/ 86.6%

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

      3. *-commutative 86.6%

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

      4. associate-*l/ 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in b around 0 73.7%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+137} \lor \neg \left(y \leq 1.18 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-31} \lor \neg \left(t \leq 6.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.5e-31) (not (<= t 6.2e-15))) (/ 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 <= -5.5e-31) || !(t <= 6.2e-15)) {
		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 <= (-5.5d-31)) .or. (.not. (t <= 6.2d-15))) 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 <= -5.5e-31) || !(t <= 6.2e-15)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.5e-31) or not (t <= 6.2e-15):
		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 <= -5.5e-31) || !(t <= 6.2e-15))
		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 <= -5.5e-31) || ~((t <= 6.2e-15)))
		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, -5.5e-31], N[Not[LessEqual[t, 6.2e-15]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.49999999999999958e-31 or 6.1999999999999998e-15 < t

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l/ 90.8%

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

      3. *-commutative 90.8%

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

      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. Add Preprocessing

   5. Taylor expanded in t around inf 62.3%

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

   if -5.49999999999999958e-31 < t < 6.1999999999999998e-15

   1. Initial program 64.8%

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

      1. *-commutative 64.8%

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

      2. associate-*l/ 57.9%

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

      3. *-commutative 57.9%

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

      4. associate-*l/ 54.3%

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

   3. Simplified 54.3%

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

   5. Taylor expanded in t around 0 52.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-31} \lor \neg \left(t \leq 6.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if a < -1 or 1 < a

   1. Initial program 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-*l/ 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-*l/ 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in x around inf 57.2%

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

   6. Taylor expanded in a around inf 51.0%

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

   if -1 < a < 1

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-*l/ 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-*l/ 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in t around inf 37.0%

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

   6. Taylor expanded in a around 0 36.1%

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

4. Final simplification 43.7%

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

Alternative 16: 19.9% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.1%

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

   1. *-commutative 76.1%

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

   2. associate-*l/ 76.3%

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

   3. *-commutative 76.3%

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

   4. associate-*l/ 76.9%

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

3. Simplified 76.9%

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

5. Taylor expanded in t around inf 44.7%

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

6. Taylor expanded in a around 0 19.5%

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

7. Final simplification 19.5%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024031 
(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))))