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

Percentage Accurate: 75.9% → 87.7%

Time: 16.8s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.9% 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: 87.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}{\frac{z}{t}}}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{t}{b} \cdot \mathsf{fma}\left(\frac{z}{t}, y, x\right)}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(a + 1\right)}{z} + \frac{b}{\frac{z}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (/ y (/ (+ 1.0 (fma y (/ b t) a)) (/ z t)))
     (if (<= t_1 -5e-303)
       t_1
       (if (<= t_1 0.0)
         (/ (* (/ t b) (fma (/ z t) y x)) y)
         (if (<= t_1 2e+295)
           t_1
           (/ y (+ (/ (* t (+ a 1.0)) z) (/ b (/ z y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y / ((1.0 + fma(y, (b / t), a)) / (z / t));
	} else if (t_1 <= -5e-303) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((t / b) * fma((z / t), y, x)) / y;
	} else if (t_1 <= 2e+295) {
		tmp = t_1;
	} else {
		tmp = y / (((t * (a + 1.0)) / z) + (b / (z / y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y / Float64(Float64(1.0 + fma(y, Float64(b / t), a)) / Float64(z / t)));
	elseif (t_1 <= -5e-303)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(t / b) * fma(Float64(z / t), y, x)) / y);
	elseif (t_1 <= 2e+295)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(Float64(Float64(t * Float64(a + 1.0)) / z) + Float64(b / Float64(z / y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y / N[(N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-303], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+295], t$95$1, N[(y / N[(N[(N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(b / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 28.1%

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

      1. *-commutative 28.1%

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

      2. associate-*l/ 62.0%

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

      3. *-commutative 62.0%

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

      4. associate-*l/ 61.8%

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

   3. Simplified 61.8%

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

   5. Taylor expanded in x around 0 60.2%

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

      1. associate-/l* 72.1%

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

      2. *-commutative 72.1%

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

      3. associate-+r+ 72.1%

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

      4. associate-/l* 54.7%

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

      5. +-commutative 54.7%

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

      6. associate-/l* 72.1%

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

      7. associate-*r/ 54.5%

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

      8. +-commutative 54.5%

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

      9. fma-udef 54.5%

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

      10. associate-/l* 54.6%

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

      11. +-commutative 54.6%

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

      12. fma-def 54.6%

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

      13. associate-*r/ 71.9%

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

      14. associate-/l* 54.6%

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

      15. +-commutative 54.6%

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

      16. associate-+r+ 54.6%

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

      17. +-commutative 54.6%

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

      18. associate-/r/ 71.7%

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

      19. *-commutative 71.7%

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

      20. fma-def 71.7%

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

   7. Simplified 71.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.9999999999999998e-303 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2e295

   1. Initial program 99.7%

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

   if -4.9999999999999998e-303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*l/ 51.6%

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

      3. *-commutative 51.6%

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

      4. associate-*l/ 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in b around inf 44.8%

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

      1. times-frac 71.8%

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

      2. +-commutative 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-*l/ 71.9%

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

      5. fma-def 71.9%

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

   7. Simplified 71.9%

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

      1. associate-*r/ 72.1%

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

   9. Applied egg-rr 72.1%

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

   if 2e295 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.0%

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

      1. *-commutative 13.0%

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

      2. associate-*l/ 21.9%

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

      3. *-commutative 21.9%

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

      4. associate-*l/ 30.3%

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

   3. Simplified 30.3%

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

   5. Taylor expanded in x around 0 30.8%

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

      1. associate-/l* 45.7%

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

      2. *-commutative 45.7%

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

      3. associate-+r+ 45.7%

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

      4. associate-/l* 34.2%

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

      5. +-commutative 34.2%

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

      6. associate-/l* 45.7%

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

      7. associate-*r/ 34.2%

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

      8. +-commutative 34.2%

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

      9. fma-udef 34.2%

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

      10. associate-/l* 33.7%

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

      11. +-commutative 33.7%

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

      12. fma-def 33.7%

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

      13. associate-*r/ 39.4%

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

      14. associate-/l* 33.7%

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

      15. +-commutative 33.7%

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

      16. associate-+r+ 33.7%

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

      17. +-commutative 33.7%

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

      18. associate-/r/ 42.4%

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

      19. *-commutative 42.4%

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

      20. fma-def 42.4%

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

   7. Simplified 42.4%

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

   8. Taylor expanded in y around 0 71.2%

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

      1. +-commutative 71.2%

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

      2. associate-/l* 76.9%

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

   10. Simplified 76.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}{\frac{z}{t}}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{\frac{t}{b} \cdot \mathsf{fma}\left(\frac{z}{t}, y, x\right)}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(a + 1\right)}{z} + \frac{b}{\frac{z}{y}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{t}{b} \cdot \mathsf{fma}\left(\frac{z}{t}, y, x\right)}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(a + 1\right)}{z} + \frac{b}{\frac{z}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 -2e+91)
     (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
     (if (<= t_1 -5e-303)
       t_1
       (if (<= t_1 0.0)
         (/ (* (/ t b) (fma (/ z t) y x)) y)
         (if (<= t_1 2e+295)
           t_1
           (/ y (+ (/ (* t (+ a 1.0)) z) (/ b (/ z y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= -5e-303) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((t / b) * fma((z / t), y, x)) / y;
	} else if (t_1 <= 2e+295) {
		tmp = t_1;
	} else {
		tmp = y / (((t * (a + 1.0)) / z) + (b / (z / y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= -2e+91)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t_1 <= -5e-303)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(t / b) * fma(Float64(z / t), y, x)) / y);
	elseif (t_1 <= 2e+295)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(Float64(Float64(t * Float64(a + 1.0)) / z) + Float64(b / Float64(z / y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+91], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-303], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+295], t$95$1, N[(y / N[(N[(N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(b / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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))) < -2.00000000000000016e91

   1. Initial program 75.4%

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

      1. associate-/l* 78.9%

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

      2. associate-+l+ 78.9%

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

      3. associate-/l* 78.8%

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

   3. Simplified 78.8%

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

      1. associate-/r/ 87.0%

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

   6. Applied egg-rr 87.0%

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

   if -2.00000000000000016e91 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.9999999999999998e-303 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2e295

   1. Initial program 99.7%

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

   if -4.9999999999999998e-303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*l/ 51.6%

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

      3. *-commutative 51.6%

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

      4. associate-*l/ 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in b around inf 44.8%

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

      1. times-frac 71.8%

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

      2. +-commutative 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-*l/ 71.9%

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

      5. fma-def 71.9%

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

   7. Simplified 71.9%

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

      1. associate-*r/ 72.1%

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

   9. Applied egg-rr 72.1%

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

   if 2e295 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.0%

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

      1. *-commutative 13.0%

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

      2. associate-*l/ 21.9%

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

      3. *-commutative 21.9%

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

      4. associate-*l/ 30.3%

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

   3. Simplified 30.3%

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

   5. Taylor expanded in x around 0 30.8%

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

      1. associate-/l* 45.7%

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

      2. *-commutative 45.7%

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

      3. associate-+r+ 45.7%

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

      4. associate-/l* 34.2%

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

      5. +-commutative 34.2%

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

      6. associate-/l* 45.7%

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

      7. associate-*r/ 34.2%

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

      8. +-commutative 34.2%

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

      9. fma-udef 34.2%

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

      10. associate-/l* 33.7%

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

      11. +-commutative 33.7%

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

      12. fma-def 33.7%

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

      13. associate-*r/ 39.4%

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

      14. associate-/l* 33.7%

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

      15. +-commutative 33.7%

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

      16. associate-+r+ 33.7%

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

      17. +-commutative 33.7%

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

      18. associate-/r/ 42.4%

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

      19. *-commutative 42.4%

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

      20. fma-def 42.4%

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

   7. Simplified 42.4%

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

   8. Taylor expanded in y around 0 71.2%

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

      1. +-commutative 71.2%

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

      2. associate-/l* 76.9%

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

   10. Simplified 76.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{\frac{t}{b} \cdot \mathsf{fma}\left(\frac{z}{t}, y, x\right)}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(a + 1\right)}{z} + \frac{b}{\frac{z}{y}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(a + 1\right)}{z} + \frac{b}{\frac{z}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 -2e+91)
     (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
     (if (<= t_1 -5e-303)
       t_1
       (if (<= t_1 0.0)
         (* (/ t b) (+ (/ z t) (/ x y)))
         (if (<= t_1 2e+295)
           t_1
           (/ y (+ (/ (* t (+ a 1.0)) z) (/ b (/ z y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= -5e-303) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (t_1 <= 2e+295) {
		tmp = t_1;
	} else {
		tmp = y / (((t * (a + 1.0)) / z) + (b / (z / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0d0))
    if (t_1 <= (-2d+91)) then
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    else if (t_1 <= (-5d-303)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = (t / b) * ((z / t) + (x / y))
    else if (t_1 <= 2d+295) then
        tmp = t_1
    else
        tmp = y / (((t * (a + 1.0d0)) / z) + (b / (z / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= -5e-303) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (t_1 <= 2e+295) {
		tmp = t_1;
	} else {
		tmp = y / (((t * (a + 1.0)) / z) + (b / (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -2e+91:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	elif t_1 <= -5e-303:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (t / b) * ((z / t) + (x / y))
	elif t_1 <= 2e+295:
		tmp = t_1
	else:
		tmp = y / (((t * (a + 1.0)) / z) + (b / (z / y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= -2e+91)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t_1 <= -5e-303)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	elseif (t_1 <= 2e+295)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(Float64(Float64(t * Float64(a + 1.0)) / z) + Float64(b / Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -2e+91)
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	elseif (t_1 <= -5e-303)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (t / b) * ((z / t) + (x / y));
	elseif (t_1 <= 2e+295)
		tmp = t_1;
	else
		tmp = y / (((t * (a + 1.0)) / z) + (b / (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+91], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-303], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+295], t$95$1, N[(y / N[(N[(N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(b / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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))) < -2.00000000000000016e91

   1. Initial program 75.4%

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

      1. associate-/l* 78.9%

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

      2. associate-+l+ 78.9%

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

      3. associate-/l* 78.8%

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

   3. Simplified 78.8%

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

      1. associate-/r/ 87.0%

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

   6. Applied egg-rr 87.0%

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

   if -2.00000000000000016e91 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.9999999999999998e-303 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2e295

   1. Initial program 99.7%

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

   if -4.9999999999999998e-303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*l/ 51.6%

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

      3. *-commutative 51.6%

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

      4. associate-*l/ 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in b around inf 44.8%

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

      1. times-frac 71.8%

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

      2. +-commutative 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-*l/ 71.9%

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

      5. fma-def 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in z around 0 71.9%

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

   if 2e295 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.0%

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

      1. *-commutative 13.0%

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

      2. associate-*l/ 21.9%

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

      3. *-commutative 21.9%

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

      4. associate-*l/ 30.3%

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

   3. Simplified 30.3%

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

   5. Taylor expanded in x around 0 30.8%

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

      1. associate-/l* 45.7%

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

      2. *-commutative 45.7%

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

      3. associate-+r+ 45.7%

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

      4. associate-/l* 34.2%

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

      5. +-commutative 34.2%

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

      6. associate-/l* 45.7%

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

      7. associate-*r/ 34.2%

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

      8. +-commutative 34.2%

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

      9. fma-udef 34.2%

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

      10. associate-/l* 33.7%

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

      11. +-commutative 33.7%

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

      12. fma-def 33.7%

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

      13. associate-*r/ 39.4%

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

      14. associate-/l* 33.7%

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

      15. +-commutative 33.7%

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

      16. associate-+r+ 33.7%

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

      17. +-commutative 33.7%

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

      18. associate-/r/ 42.4%

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

      19. *-commutative 42.4%

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

      20. fma-def 42.4%

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

   7. Simplified 42.4%

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

   8. Taylor expanded in y around 0 71.2%

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

      1. +-commutative 71.2%

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

      2. associate-/l* 76.9%

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

   10. Simplified 76.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(a + 1\right)}{z} + \frac{b}{\frac{z}{y}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+146}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-41}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(a + 1\right)}{z} + \frac{b}{\frac{z}{y}}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+176}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) (+ a 1.0))))
   (if (<= y -7e+146)
     (* (/ t b) (+ (/ z t) (/ x y)))
     (if (<= y 2.8e-73)
       t_1
       (if (<= y 1.75e-41)
         (/ (* y z) (* t (+ 1.0 (/ (* y b) t))))
         (if (<= y 1.85e+15)
           t_1
           (if (<= y 7.4e+72)
             (/ y (+ (/ (* t (+ a 1.0)) z) (/ b (/ z y))))
             (if (<= y 3.2e+176)
               (/ x (+ 1.0 (+ a (* y (/ b t)))))
               (/ z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (y <= -7e+146) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (y <= 2.8e-73) {
		tmp = t_1;
	} else if (y <= 1.75e-41) {
		tmp = (y * z) / (t * (1.0 + ((y * b) / t)));
	} else if (y <= 1.85e+15) {
		tmp = t_1;
	} else if (y <= 7.4e+72) {
		tmp = y / (((t * (a + 1.0)) / z) + (b / (z / y)));
	} else if (y <= 3.2e+176) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z * (y / t))) / (a + 1.0d0)
    if (y <= (-7d+146)) then
        tmp = (t / b) * ((z / t) + (x / y))
    else if (y <= 2.8d-73) then
        tmp = t_1
    else if (y <= 1.75d-41) then
        tmp = (y * z) / (t * (1.0d0 + ((y * b) / t)))
    else if (y <= 1.85d+15) then
        tmp = t_1
    else if (y <= 7.4d+72) then
        tmp = y / (((t * (a + 1.0d0)) / z) + (b / (z / y)))
    else if (y <= 3.2d+176) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (y <= -7e+146) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (y <= 2.8e-73) {
		tmp = t_1;
	} else if (y <= 1.75e-41) {
		tmp = (y * z) / (t * (1.0 + ((y * b) / t)));
	} else if (y <= 1.85e+15) {
		tmp = t_1;
	} else if (y <= 7.4e+72) {
		tmp = y / (((t * (a + 1.0)) / z) + (b / (z / y)));
	} else if (y <= 3.2e+176) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / (a + 1.0)
	tmp = 0
	if y <= -7e+146:
		tmp = (t / b) * ((z / t) + (x / y))
	elif y <= 2.8e-73:
		tmp = t_1
	elif y <= 1.75e-41:
		tmp = (y * z) / (t * (1.0 + ((y * b) / t)))
	elif y <= 1.85e+15:
		tmp = t_1
	elif y <= 7.4e+72:
		tmp = y / (((t * (a + 1.0)) / z) + (b / (z / y)))
	elif y <= 3.2e+176:
		tmp = x / (1.0 + (a + (y * (b / t))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (y <= -7e+146)
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	elseif (y <= 2.8e-73)
		tmp = t_1;
	elseif (y <= 1.75e-41)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(Float64(y * b) / t))));
	elseif (y <= 1.85e+15)
		tmp = t_1;
	elseif (y <= 7.4e+72)
		tmp = Float64(y / Float64(Float64(Float64(t * Float64(a + 1.0)) / z) + Float64(b / Float64(z / y))));
	elseif (y <= 3.2e+176)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / (a + 1.0);
	tmp = 0.0;
	if (y <= -7e+146)
		tmp = (t / b) * ((z / t) + (x / y));
	elseif (y <= 2.8e-73)
		tmp = t_1;
	elseif (y <= 1.75e-41)
		tmp = (y * z) / (t * (1.0 + ((y * b) / t)));
	elseif (y <= 1.85e+15)
		tmp = t_1;
	elseif (y <= 7.4e+72)
		tmp = y / (((t * (a + 1.0)) / z) + (b / (z / y)));
	elseif (y <= 3.2e+176)
		tmp = x / (1.0 + (a + (y * (b / t))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+146], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-73], t$95$1, If[LessEqual[y, 1.75e-41], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+15], t$95$1, If[LessEqual[y, 7.4e+72], N[(y / N[(N[(N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(b / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+176], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -7.0000000000000002e146

   1. Initial program 37.9%

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

      1. *-commutative 37.9%

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

      2. associate-*l/ 52.3%

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

      3. *-commutative 52.3%

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

      4. associate-*l/ 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in b around inf 23.5%

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

      1. times-frac 34.7%

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

      2. +-commutative 34.7%

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

      3. *-commutative 34.7%

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

      4. associate-*l/ 43.4%

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

      5. fma-def 43.4%

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

   7. Simplified 43.4%

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

   8. Taylor expanded in z around 0 61.1%

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

   if -7.0000000000000002e146 < y < 2.80000000000000012e-73 or 1.75e-41 < y < 1.85e15

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-*l/ 88.3%

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

      3. *-commutative 88.3%

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

      4. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in b around 0 84.5%

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

      1. associate-*l/ 47.0%

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

   7. Applied egg-rr 85.4%

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

   if 2.80000000000000012e-73 < y < 1.75e-41

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-*l/ 87.5%

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

      3. *-commutative 87.5%

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

      4. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in x around 0 87.3%

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

      1. associate-/l* 87.2%

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

      2. *-commutative 87.2%

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

      3. associate-+r+ 87.2%

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

      4. associate-/l* 87.6%

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

      5. +-commutative 87.6%

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

      6. associate-/l* 87.2%

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

      7. associate-*r/ 87.2%

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

      8. +-commutative 87.2%

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

      9. fma-udef 87.2%

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

      10. associate-/l* 75.3%

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

      11. +-commutative 75.3%

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

      12. fma-def 75.3%

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

      13. associate-*r/ 75.3%

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

      14. associate-/l* 75.5%

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

      15. +-commutative 75.5%

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

      16. associate-+r+ 75.5%

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

      17. +-commutative 75.5%

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

      18. associate-/r/ 74.7%

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

      19. *-commutative 74.7%

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

      20. fma-def 74.7%

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

   7. Simplified 74.7%

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

   8. Taylor expanded in a around 0 87.4%

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

   if 1.85e15 < y < 7.40000000000000041e72

   1. Initial program 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-*l/ 61.0%

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

      3. *-commutative 61.0%

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

      4. associate-*l/ 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in x around 0 54.4%

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

      1. associate-/l* 61.1%

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

      2. *-commutative 61.1%

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

      3. associate-+r+ 61.1%

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

      4. associate-/l* 54.5%

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

      5. +-commutative 54.5%

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

      6. associate-/l* 61.1%

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

      7. associate-*r/ 54.3%

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

      8. +-commutative 54.3%

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

      9. fma-udef 54.3%

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

      10. associate-/l* 59.9%

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

      11. +-commutative 59.9%

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

      12. fma-def 59.9%

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

      13. associate-*r/ 54.4%

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

      14. associate-/l* 60.1%

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

      15. +-commutative 60.1%

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

      16. associate-+r+ 60.1%

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

      17. +-commutative 60.1%

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

      18. associate-/r/ 60.7%

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

      19. *-commutative 60.7%

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

      20. fma-def 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in y around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-/l* 86.7%

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

   10. Simplified 86.7%

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

   if 7.40000000000000041e72 < y < 3.1999999999999998e176

   1. Initial program 57.2%

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

      1. associate-/l* 61.0%

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

      2. associate-+l+ 61.0%

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

      3. associate-/l* 64.9%

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

   3. Simplified 64.9%

      \[\leadsto \color{blue}{\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}} \]
   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. *-commutative 64.7%

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

      2. clear-num 64.7%

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

      3. un-div-inv 64.7%

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

   8. Applied egg-rr 64.7%

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

   9. Taylor expanded in x around inf 57.6%

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

       1. associate-*l/ 61.5%

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

       2. *-commutative 61.5%

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

   11. Simplified 61.5%

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

   if 3.1999999999999998e176 < y

   1. Initial program 41.9%

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

      1. *-commutative 41.9%

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

      2. associate-*l/ 46.1%

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

      3. *-commutative 46.1%

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

      4. associate-*l/ 57.6%

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

   3. Simplified 57.6%

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

   5. Taylor expanded in t around 0 77.1%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+146}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-41}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(a + 1\right)}{z} + \frac{b}{\frac{z}{y}}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+176}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{if}\;a \leq -24000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;a \leq 1.75:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))) (t_2 (/ (+ x (/ (* y z) t)) a)))
   (if (<= a -24000000000.0)
     t_2
     (if (<= a -2.5e-142)
       t_1
       (if (<= a -1.95e-150)
         (* (/ t b) (+ (/ z t) (/ x y)))
         (if (<= a 1.75) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y / t));
	double t_2 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -24000000000.0) {
		tmp = t_2;
	} else if (a <= -2.5e-142) {
		tmp = t_1;
	} else if (a <= -1.95e-150) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (a <= 1.75) {
		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 = x + (z * (y / t))
    t_2 = (x + ((y * z) / t)) / a
    if (a <= (-24000000000.0d0)) then
        tmp = t_2
    else if (a <= (-2.5d-142)) then
        tmp = t_1
    else if (a <= (-1.95d-150)) then
        tmp = (t / b) * ((z / t) + (x / y))
    else if (a <= 1.75d0) 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 = x + (z * (y / t));
	double t_2 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -24000000000.0) {
		tmp = t_2;
	} else if (a <= -2.5e-142) {
		tmp = t_1;
	} else if (a <= -1.95e-150) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (a <= 1.75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y / t))
	t_2 = (x + ((y * z) / t)) / a
	tmp = 0
	if a <= -24000000000.0:
		tmp = t_2
	elif a <= -2.5e-142:
		tmp = t_1
	elif a <= -1.95e-150:
		tmp = (t / b) * ((z / t) + (x / y))
	elif a <= 1.75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / a)
	tmp = 0.0
	if (a <= -24000000000.0)
		tmp = t_2;
	elseif (a <= -2.5e-142)
		tmp = t_1;
	elseif (a <= -1.95e-150)
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	elseif (a <= 1.75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y / t));
	t_2 = (x + ((y * z) / t)) / a;
	tmp = 0.0;
	if (a <= -24000000000.0)
		tmp = t_2;
	elseif (a <= -2.5e-142)
		tmp = t_1;
	elseif (a <= -1.95e-150)
		tmp = (t / b) * ((z / t) + (x / y));
	elseif (a <= 1.75)
		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[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -24000000000.0], t$95$2, If[LessEqual[a, -2.5e-142], t$95$1, If[LessEqual[a, -1.95e-150], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4e10 or 1.75 < a

   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/ 73.1%

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

      3. *-commutative 73.1%

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

      4. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in a around inf 62.0%

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

   if -2.4e10 < a < -2.5000000000000001e-142 or -1.9500000000000001e-150 < a < 1.75

   1. Initial program 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-*l/ 76.9%

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

      3. *-commutative 76.9%

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

      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 58.1%

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

   6. Taylor expanded in a around 0 57.5%

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

      1. associate-*l/ 60.9%

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

   8. Applied egg-rr 60.9%

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

   if -2.5000000000000001e-142 < a < -1.9500000000000001e-150

   1. Initial program 81.2%

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

      1. *-commutative 81.2%

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

      2. associate-*l/ 81.2%

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

      3. *-commutative 81.2%

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

      4. associate-*l/ 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in b around inf 80.6%

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

      1. times-frac 99.5%

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

      2. +-commutative 99.5%

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

      3. *-commutative 99.5%

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

      4. associate-*l/ 100.0%

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

      5. fma-def 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 100.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -24000000000:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-142}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-150}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;a \leq 1.75:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-167}:\\ \;\;\;\;\frac{\frac{y}{\frac{a + 1}{z}}}{t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-144}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (* y (/ b t)))))))
   (if (<= t -8.2e-20)
     t_1
     (if (<= t -2.8e-167)
       (/ (/ y (/ (+ a 1.0) z)) t)
       (if (<= t 1.15e-144) (/ z b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -8.2e-20) {
		tmp = t_1;
	} else if (t <= -2.8e-167) {
		tmp = (y / ((a + 1.0) / z)) / t;
	} else if (t <= 1.15e-144) {
		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 / (1.0d0 + (a + (y * (b / t))))
    if (t <= (-8.2d-20)) then
        tmp = t_1
    else if (t <= (-2.8d-167)) then
        tmp = (y / ((a + 1.0d0) / z)) / t
    else if (t <= 1.15d-144) 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 / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -8.2e-20) {
		tmp = t_1;
	} else if (t <= -2.8e-167) {
		tmp = (y / ((a + 1.0) / z)) / t;
	} else if (t <= 1.15e-144) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + (y * (b / t))))
	tmp = 0
	if t <= -8.2e-20:
		tmp = t_1
	elif t <= -2.8e-167:
		tmp = (y / ((a + 1.0) / z)) / t
	elif t <= 1.15e-144:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t <= -8.2e-20)
		tmp = t_1;
	elseif (t <= -2.8e-167)
		tmp = Float64(Float64(y / Float64(Float64(a + 1.0) / z)) / t);
	elseif (t <= 1.15e-144)
		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 / (1.0 + (a + (y * (b / t))));
	tmp = 0.0;
	if (t <= -8.2e-20)
		tmp = t_1;
	elseif (t <= -2.8e-167)
		tmp = (y / ((a + 1.0) / z)) / t;
	elseif (t <= 1.15e-144)
		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[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e-20], t$95$1, If[LessEqual[t, -2.8e-167], N[(N[(y / N[(N[(a + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.15e-144], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.2000000000000002e-20 or 1.15e-144 < t

   1. Initial program 80.1%

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

      1. associate-/l* 83.7%

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

      2. associate-+l+ 83.7%

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

      3. associate-/l* 88.2%

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

   3. Simplified 88.2%

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

      1. associate-/r/ 89.0%

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

   6. Applied egg-rr 89.0%

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

      1. *-commutative 89.0%

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

      2. clear-num 88.8%

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

      3. un-div-inv 88.8%

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

   8. Applied egg-rr 88.8%

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

   9. Taylor expanded in x around inf 63.5%

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

       1. associate-*l/ 64.8%

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

       2. *-commutative 64.8%

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

   11. Simplified 64.8%

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

   if -8.2000000000000002e-20 < t < -2.79999999999999986e-167

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l/ 77.5%

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

      3. *-commutative 77.5%

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

      4. associate-*l/ 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in b around 0 69.4%

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

      1. div-inv 69.5%

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

      2. *-commutative 69.5%

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

   7. Applied egg-rr 69.5%

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

   8. Taylor expanded in x around 0 56.6%

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

      1. *-commutative 56.6%

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

      2. associate-/r* 56.5%

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

      3. associate-/l* 60.0%

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

   10. Simplified 60.0%

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

   if -2.79999999999999986e-167 < t < 1.15e-144

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

      2. associate-*l/ 50.7%

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

      3. *-commutative 50.7%

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

      4. associate-*l/ 47.2%

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

   3. Simplified 47.2%

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

   5. Taylor expanded in t around 0 65.3%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-167}:\\ \;\;\;\;\frac{\frac{y}{\frac{a + 1}{z}}}{t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-144}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{+182}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 5.1e+182)
   (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.1e+182) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 5.1d+182) then
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.1e+182) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 5.1e+182:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 5.1e+182)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 5.1e+182)
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 5.1e+182], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.10000000000000009e182

   1. Initial program 80.7%

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

      1. associate-/l* 78.7%

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

      2. associate-+l+ 78.7%

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

      3. associate-/l* 80.2%

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

   3. Simplified 80.2%

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

      1. associate-/r/ 82.3%

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

   6. Applied egg-rr 82.3%

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

   if 5.10000000000000009e182 < y

   1. Initial program 41.9%

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

      1. *-commutative 41.9%

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

      2. associate-*l/ 46.1%

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

      3. *-commutative 46.1%

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

      4. associate-*l/ 57.6%

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

   3. Simplified 57.6%

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

   5. Taylor expanded in t around 0 77.1%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{+182}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.4 \cdot 10^{+179}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 6.4e+179)
   (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 (/ y (/ t b)))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.4e+179) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 6.4d+179) then
        tmp = (x + (z / (t / y))) / (a + (1.0d0 + (y / (t / b))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.4e+179) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6.4e+179:
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6.4e+179)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 6.4e+179)
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6.4e+179], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.4000000000000003e179

   1. Initial program 80.7%

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

      1. associate-/l* 78.7%

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

      2. associate-+l+ 78.7%

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

      3. associate-/l* 80.2%

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

   3. Simplified 80.2%

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

      1. associate-/r/ 82.3%

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

   6. Applied egg-rr 82.3%

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

      1. *-commutative 82.3%

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

      2. clear-num 82.2%

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

      3. un-div-inv 82.6%

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

   8. Applied egg-rr 82.6%

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

   if 6.4000000000000003e179 < y

   1. Initial program 41.9%

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

      1. *-commutative 41.9%

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

      2. associate-*l/ 46.1%

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

      3. *-commutative 46.1%

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

      4. associate-*l/ 57.6%

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

   3. Simplified 57.6%

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

   5. Taylor expanded in t around 0 77.1%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.4 \cdot 10^{+179}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-167} \lor \neg \left(t \leq 5 \cdot 10^{-144}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.5e-167) (not (<= t 5e-144)))
   (/ (+ x (* z (/ y t))) (+ a 1.0))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.5e-167) || !(t <= 5e-144)) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.5d-167)) .or. (.not. (t <= 5d-144))) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.5e-167) || !(t <= 5e-144)) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.5e-167) or not (t <= 5e-144):
		tmp = (x + (z * (y / t))) / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.5e-167) || !(t <= 5e-144))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.5e-167) || ~((t <= 5e-144)))
		tmp = (x + (z * (y / t))) / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.5e-167], N[Not[LessEqual[t, 5e-144]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4999999999999999e-167 or 4.9999999999999998e-144 < t

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 82.8%

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

      3. *-commutative 82.8%

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

      4. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in b around 0 69.0%

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

      1. associate-*l/ 36.5%

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

   7. Applied egg-rr 73.1%

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

   if -1.4999999999999999e-167 < t < 4.9999999999999998e-144

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

      2. associate-*l/ 50.7%

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

      3. *-commutative 50.7%

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

      4. associate-*l/ 47.2%

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

   3. Simplified 47.2%

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

   5. Taylor expanded in t around 0 65.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-167} \lor \neg \left(t \leq 5 \cdot 10^{-144}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-168}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-142}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -2.4e-18)
     t_1
     (if (<= t -9.6e-168)
       (* (/ y t) (/ z (+ a 1.0)))
       (if (<= t 1.05e-142) (/ z b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.4e-18) {
		tmp = t_1;
	} else if (t <= -9.6e-168) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 1.05e-142) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-2.4d-18)) then
        tmp = t_1
    else if (t <= (-9.6d-168)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (t <= 1.05d-142) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -2.4e-18) {
		tmp = t_1;
	} else if (t <= -9.6e-168) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 1.05e-142) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -2.4e-18:
		tmp = t_1
	elif t <= -9.6e-168:
		tmp = (y / t) * (z / (a + 1.0))
	elif t <= 1.05e-142:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.4e-18)
		tmp = t_1;
	elseif (t <= -9.6e-168)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (t <= 1.05e-142)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -2.4e-18)
		tmp = t_1;
	elseif (t <= -9.6e-168)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (t <= 1.05e-142)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e-18], t$95$1, If[LessEqual[t, -9.6e-168], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-142], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.39999999999999994e-18 or 1.05e-142 < t

   1. Initial program 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-*l/ 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around inf 58.3%

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

   if -2.39999999999999994e-18 < t < -9.5999999999999997e-168

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l/ 77.5%

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

      3. *-commutative 77.5%

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

      4. associate-*l/ 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in b around 0 69.4%

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

   6. Taylor expanded in x around 0 56.6%

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

      1. times-frac 56.6%

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

   8. Simplified 56.6%

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

   if -9.5999999999999997e-168 < t < 1.05e-142

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

      2. associate-*l/ 50.7%

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

      3. *-commutative 50.7%

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

      4. associate-*l/ 47.2%

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

   3. Simplified 47.2%

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

   5. Taylor expanded in t around 0 65.3%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-168}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-142}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -24000000000 \lor \neg \left(a \leq 1.35\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -24000000000.0) (not (<= a 1.35)))
   (/ (+ x (/ (* y z) t)) a)
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -24000000000.0) || !(a <= 1.35)) {
		tmp = (x + ((y * z) / t)) / a;
	} else {
		tmp = x + (z * (y / 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 ((a <= (-24000000000.0d0)) .or. (.not. (a <= 1.35d0))) then
        tmp = (x + ((y * z) / t)) / a
    else
        tmp = x + (z * (y / 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 ((a <= -24000000000.0) || !(a <= 1.35)) {
		tmp = (x + ((y * z) / t)) / a;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -24000000000.0) or not (a <= 1.35):
		tmp = (x + ((y * z) / t)) / a
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -24000000000.0) || !(a <= 1.35))
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -24000000000.0) || ~((a <= 1.35)))
		tmp = (x + ((y * z) / t)) / a;
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -24000000000.0], N[Not[LessEqual[a, 1.35]], $MachinePrecision]], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4e10 or 1.3500000000000001 < a

   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/ 73.1%

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

      3. *-commutative 73.1%

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

      4. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in a around inf 62.0%

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

   if -2.4e10 < a < 1.3500000000000001

   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/ 77.1%

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

      3. *-commutative 77.1%

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

      4. associate-*l/ 79.9%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in b around 0 56.1%

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

   6. Taylor expanded in a around 0 55.5%

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

      1. associate-*l/ 58.8%

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

   8. Applied egg-rr 58.8%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -24000000000 \lor \neg \left(a \leq 1.35\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-131}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 85000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.5e+22)
   (/ x a)
   (if (<= a -3.4e-131) (/ z b) (if (<= a 85000000.0) x (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.5e+22) {
		tmp = x / a;
	} else if (a <= -3.4e-131) {
		tmp = z / b;
	} else if (a <= 85000000.0) {
		tmp = x;
	} 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 <= (-1.5d+22)) then
        tmp = x / a
    else if (a <= (-3.4d-131)) then
        tmp = z / b
    else if (a <= 85000000.0d0) then
        tmp = x
    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 <= -1.5e+22) {
		tmp = x / a;
	} else if (a <= -3.4e-131) {
		tmp = z / b;
	} else if (a <= 85000000.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.5e+22:
		tmp = x / a
	elif a <= -3.4e-131:
		tmp = z / b
	elif a <= 85000000.0:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.5e+22)
		tmp = Float64(x / a);
	elseif (a <= -3.4e-131)
		tmp = Float64(z / b);
	elseif (a <= 85000000.0)
		tmp = x;
	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 <= -1.5e+22)
		tmp = x / a;
	elseif (a <= -3.4e-131)
		tmp = z / b;
	elseif (a <= 85000000.0)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.5e+22], N[(x / a), $MachinePrecision], If[LessEqual[a, -3.4e-131], N[(z / b), $MachinePrecision], If[LessEqual[a, 85000000.0], x, N[(x / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5e22 or 8.5e7 < a

   1. Initial program 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-*l/ 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*l/ 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in t around inf 50.4%

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

   6. Taylor expanded in a around inf 50.2%

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

   if -1.5e22 < a < -3.39999999999999995e-131

   1. Initial program 68.8%

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

      1. *-commutative 68.8%

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

      2. associate-*l/ 71.7%

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

      3. *-commutative 71.7%

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

      4. associate-*l/ 71.6%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in t around 0 44.5%

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

   if -3.39999999999999995e-131 < a < 8.5e7

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. associate-*l/ 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in t around inf 46.2%

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

   6. Taylor expanded in a around 0 45.5%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-131}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 85000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-88} \lor \neg \left(t \leq 3.6 \cdot 10^{-144}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.6e-88) (not (<= t 3.6e-144))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e-88) || !(t <= 3.6e-144)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.6d-88)) .or. (.not. (t <= 3.6d-144))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e-88) || !(t <= 3.6e-144)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.6e-88) or not (t <= 3.6e-144):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.6e-88) || !(t <= 3.6e-144))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.6e-88) || ~((t <= 3.6e-144)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.6e-88], N[Not[LessEqual[t, 3.6e-144]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.60000000000000014e-88 or 3.6e-144 < t

   1. Initial program 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-*l/ 84.8%

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

      3. *-commutative 84.8%

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

      4. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t around inf 56.7%

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

   if -2.60000000000000014e-88 < t < 3.6e-144

   1. Initial program 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-*l/ 53.1%

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

      3. *-commutative 53.1%

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

      4. associate-*l/ 50.4%

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

   3. Simplified 50.4%

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

   5. Taylor expanded in t around 0 57.8%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-88} \lor \neg \left(t \leq 3.6 \cdot 10^{-144}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1850 \lor \neg \left(a \leq 85000000\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1850.0) (not (<= a 85000000.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1850.0) || !(a <= 85000000.0)) {
		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 <= (-1850.0d0)) .or. (.not. (a <= 85000000.0d0))) 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 <= -1850.0) || !(a <= 85000000.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1850.0) or not (a <= 85000000.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1850.0) || !(a <= 85000000.0))
		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 <= -1850.0) || ~((a <= 85000000.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1850.0], N[Not[LessEqual[a, 85000000.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1850 or 8.5e7 < a

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-*l/ 72.7%

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

      3. *-commutative 72.7%

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

      4. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in t around inf 49.7%

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

   6. Taylor expanded in a around inf 49.3%

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

   if -1850 < a < 8.5e7

   1. Initial program 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*l/ 77.4%

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

      3. *-commutative 77.4%

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

      4. associate-*l/ 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in t around inf 43.0%

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

   6. Taylor expanded in a around 0 42.4%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1850 \lor \neg \left(a \leq 85000000\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 20.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

   1. *-commutative 76.9%

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

   2. associate-*l/ 75.1%

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

   3. *-commutative 75.1%

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

   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 46.2%

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

6. Taylor expanded in a around 0 24.0%

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

7. Final simplification 24.0%

   \[\leadsto x \]
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 2024027 
(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))))