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

Percentage Accurate: 75.1% → 92.2%

Time: 21.7s

Alternatives: 18

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.1% 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: 92.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}{z}}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-314}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* t (/ (/ x b) y))))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_2 (- INFINITY))
     (/ y (/ (* t (fma y (/ b t) (+ a 1.0))) z))
     (if (<= t_2 -2e-314)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 1e+297)
           t_2
           (if (<= t_2 INFINITY)
             (* (/ y t) (/ z (+ 1.0 (fma y (/ b t) a))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + (t * ((x / b) / y));
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y / ((t * fma(y, (b / t), (a + 1.0))) / z);
	} else if (t_2 <= -2e-314) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+297) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + fma(y, (b / t), a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y / Float64(Float64(t * fma(y, Float64(b / t), Float64(a + 1.0))) / z));
	elseif (t_2 <= -2e-314)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 1e+297)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + fma(y, Float64(b / t), a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y / N[(N[(t * N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-314], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 1e+297], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

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 38.5%

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

      1. *-commutative 38.5%

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

      2. associate-*l/ 48.2%

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

      3. *-commutative 48.2%

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

      4. associate-*l/ 48.2%

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

   3. Simplified 48.2%

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

   5. Taylor expanded in x around 0 71.3%

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

      1. associate-/l* 90.1%

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

      2. associate-+r+ 90.1%

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

      3. +-commutative 90.1%

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

      4. associate-/l* 49.2%

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

      5. +-commutative 49.2%

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

      6. associate-/r/ 90.1%

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

      7. *-commutative 90.1%

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

      8. fma-udef 90.1%

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

      9. +-commutative 90.1%

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

   7. Simplified 90.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.9999999999e-314 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e297

   1. Initial program 99.5%

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

   if -1.9999999999e-314 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0 or +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 31.8%

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

      1. *-commutative 31.8%

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

      2. associate-*l/ 32.0%

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

      3. *-commutative 32.0%

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

      4. associate-*l/ 42.4%

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

   3. Simplified 42.4%

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

   5. Taylor expanded in b around inf 30.3%

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

      1. associate-/l* 30.4%

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

      2. *-commutative 30.4%

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

      3. +-commutative 30.4%

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

      4. associate-*r/ 30.6%

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

      5. fma-udef 30.6%

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

   7. Simplified 30.6%

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

      1. fma-udef 30.6%

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

      2. *-commutative 30.6%

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

   9. Applied egg-rr 30.6%

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

   10. Taylor expanded in t around 0 77.6%

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

       1. associate-*r/ 79.3%

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

       2. associate-/r* 83.4%

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

   12. Simplified 83.4%

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

   if 1e297 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 5.6%

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

      1. *-commutative 5.6%

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

      2. associate-*l/ 27.1%

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

      3. *-commutative 27.1%

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

      4. associate-*l/ 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x around 0 57.2%

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

      1. times-frac 89.0%

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

      2. associate-/l* 89.0%

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

      3. +-commutative 89.0%

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

      4. associate-/r/ 88.8%

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

      5. *-commutative 88.8%

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

      6. fma-def 88.8%

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

   7. Simplified 88.8%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t \cdot \mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-314}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+297}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{y}{t} \cdot \frac{z}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-314}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* t (/ (/ x b) y))))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_3 (* (/ y t) (/ z (+ 1.0 (fma y (/ b t) a))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-314)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 1e+297) t_2 (if (<= t_2 INFINITY) t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + (t * ((x / b) / y));
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_3 = (y / t) * (z / (1.0 + fma(y, (b / t), a)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-314) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+297) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(Float64(y / t) * Float64(z / Float64(1.0 + fma(y, Float64(b / t), a))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-314)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 1e+297)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-314], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 1e+297], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 1e297 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 28.3%

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

      1. *-commutative 28.3%

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

      2. associate-*l/ 41.6%

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

      3. *-commutative 41.6%

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

      4. associate-*l/ 41.6%

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

   3. Simplified 41.6%

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

   5. Taylor expanded in x around 0 66.9%

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

      1. times-frac 80.1%

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

      2. associate-/l* 65.5%

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

      3. +-commutative 65.5%

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

      4. associate-/r/ 80.0%

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

      5. *-commutative 80.0%

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

      6. fma-def 80.0%

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

   7. Simplified 80.0%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.9999999999e-314 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e297

   1. Initial program 99.5%

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

   if -1.9999999999e-314 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0 or +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 31.8%

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

      1. *-commutative 31.8%

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

      2. associate-*l/ 32.0%

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

      3. *-commutative 32.0%

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

      4. associate-*l/ 42.4%

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

   3. Simplified 42.4%

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

   5. Taylor expanded in b around inf 30.3%

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

      1. associate-/l* 30.4%

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

      2. *-commutative 30.4%

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

      3. +-commutative 30.4%

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

      4. associate-*r/ 30.6%

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

      5. fma-udef 30.6%

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

   7. Simplified 30.6%

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

      1. fma-udef 30.6%

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

      2. *-commutative 30.6%

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

   9. Applied egg-rr 30.6%

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

   10. Taylor expanded in t around 0 77.6%

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

       1. associate-*r/ 79.3%

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

       2. associate-/r* 83.4%

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

   12. Simplified 83.4%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-314}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+297}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + t_1\right)\right)}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-314} \lor \neg \left(t_2 \leq 0\right) \land t_2 \leq 10^{+297}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t)) (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) t_1))))
   (if (<= t_2 (- INFINITY))
     (/ (* y z) (* t (+ 1.0 (+ a t_1))))
     (if (or (<= t_2 -2e-314) (and (not (<= t_2 0.0)) (<= t_2 1e+297)))
       t_2
       (+ (/ z b) (* t (/ (/ x b) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	} else if ((t_2 <= -2e-314) || (!(t_2 <= 0.0) && (t_2 <= 1e+297))) {
		tmp = t_2;
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	} else if ((t_2 <= -2e-314) || (!(t_2 <= 0.0) && (t_2 <= 1e+297))) {
		tmp = t_2;
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y * z) / (t * (1.0 + (a + t_1)))
	elif (t_2 <= -2e-314) or (not (t_2 <= 0.0) and (t_2 <= 1e+297)):
		tmp = t_2
	else:
		tmp = (z / b) + (t * ((x / b) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + t_1))));
	elseif ((t_2 <= -2e-314) || (!(t_2 <= 0.0) && (t_2 <= 1e+297)))
		tmp = t_2;
	else
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	elseif ((t_2 <= -2e-314) || (~((t_2 <= 0.0)) && (t_2 <= 1e+297)))
		tmp = t_2;
	else
		tmp = (z / b) + (t * ((x / b) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, -2e-314], And[N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision], LessEqual[t$95$2, 1e+297]]], t$95$2, N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 38.5%

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

      1. *-commutative 38.5%

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

      2. associate-*l/ 48.2%

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

      3. *-commutative 48.2%

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

      4. associate-*l/ 48.2%

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

   3. Simplified 48.2%

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

   5. Taylor expanded in x around 0 71.3%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.9999999999e-314 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e297

   1. Initial program 99.5%

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

   if -1.9999999999e-314 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0 or 1e297 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 28.6%

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

      1. *-commutative 28.6%

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

      2. associate-*l/ 31.4%

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

      3. *-commutative 31.4%

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

      4. associate-*l/ 40.5%

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

   3. Simplified 40.5%

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

   5. Taylor expanded in b around inf 27.3%

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

      1. associate-/l* 27.3%

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

      2. *-commutative 27.3%

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

      3. +-commutative 27.3%

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

      4. associate-*r/ 27.5%

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

      5. fma-udef 27.5%

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

   7. Simplified 27.5%

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

      1. fma-udef 27.5%

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

      2. *-commutative 27.5%

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

   9. Applied egg-rr 27.5%

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

   10. Taylor expanded in t around 0 74.9%

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

       1. associate-*r/ 75.0%

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

       2. associate-/r* 78.7%

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

   12. Simplified 78.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-314} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0\right) \land \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+297}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;y \leq -8.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+61}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+78} \lor \neg \left(y \leq 10^{+145}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= y -8.4e-29)
     (/ z b)
     (if (<= y 2.6e-63)
       t_1
       (if (<= y 2.15e+15)
         (/ x (+ 1.0 (/ (* y b) t)))
         (if (<= y 2.3e+61)
           (/ (+ x (* z (/ y t))) a)
           (if (or (<= y 5.2e+78) (not (<= y 1e+145))) (/ 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 (y <= -8.4e-29) {
		tmp = z / b;
	} else if (y <= 2.6e-63) {
		tmp = t_1;
	} else if (y <= 2.15e+15) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= 2.3e+61) {
		tmp = (x + (z * (y / t))) / a;
	} else if ((y <= 5.2e+78) || !(y <= 1e+145)) {
		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 (y <= (-8.4d-29)) then
        tmp = z / b
    else if (y <= 2.6d-63) then
        tmp = t_1
    else if (y <= 2.15d+15) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (y <= 2.3d+61) then
        tmp = (x + (z * (y / t))) / a
    else if ((y <= 5.2d+78) .or. (.not. (y <= 1d+145))) 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 (y <= -8.4e-29) {
		tmp = z / b;
	} else if (y <= 2.6e-63) {
		tmp = t_1;
	} else if (y <= 2.15e+15) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (y <= 2.3e+61) {
		tmp = (x + (z * (y / t))) / a;
	} else if ((y <= 5.2e+78) || !(y <= 1e+145)) {
		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 y <= -8.4e-29:
		tmp = z / b
	elif y <= 2.6e-63:
		tmp = t_1
	elif y <= 2.15e+15:
		tmp = x / (1.0 + ((y * b) / t))
	elif y <= 2.3e+61:
		tmp = (x + (z * (y / t))) / a
	elif (y <= 5.2e+78) or not (y <= 1e+145):
		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 (y <= -8.4e-29)
		tmp = Float64(z / b);
	elseif (y <= 2.6e-63)
		tmp = t_1;
	elseif (y <= 2.15e+15)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (y <= 2.3e+61)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / a);
	elseif ((y <= 5.2e+78) || !(y <= 1e+145))
		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 (y <= -8.4e-29)
		tmp = z / b;
	elseif (y <= 2.6e-63)
		tmp = t_1;
	elseif (y <= 2.15e+15)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (y <= 2.3e+61)
		tmp = (x + (z * (y / t))) / a;
	elseif ((y <= 5.2e+78) || ~((y <= 1e+145)))
		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[y, -8.4e-29], N[(z / b), $MachinePrecision], If[LessEqual[y, 2.6e-63], t$95$1, If[LessEqual[y, 2.15e+15], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+61], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[y, 5.2e+78], N[Not[LessEqual[y, 1e+145]], $MachinePrecision]], N[(z / b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.39999999999999958e-29 or 2.3e61 < y < 5.2e78 or 9.9999999999999999e144 < y

   1. Initial program 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-*l/ 55.0%

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

      3. *-commutative 55.0%

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

      4. associate-*l/ 60.0%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in t around 0 63.3%

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

   if -8.39999999999999958e-29 < y < 2.6000000000000001e-63 or 5.2e78 < y < 9.9999999999999999e144

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*l/ 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in t around inf 67.1%

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

   if 2.6000000000000001e-63 < y < 2.15e15

   1. Initial program 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*l/ 93.4%

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

      3. *-commutative 93.4%

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

      4. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in x around inf 67.5%

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

      1. expm1-log1p-u 32.7%

         \[\leadsto \frac{x}{1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a + \frac{b \cdot y}{t}\right)\right)}} \]

      2. expm1-udef 32.7%

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

      3. log1p-udef 32.7%

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

      4. add-exp-log 67.5%

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

      5. associate-/l* 67.3%

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

   7. Applied egg-rr 67.3%

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

      1. associate--l+ 67.1%

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

   9. Simplified 67.1%

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

   10. Taylor expanded in a around 0 60.1%

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

   if 2.15e15 < y < 2.3e61

   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. associate-/l* 81.2%

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

      2. associate-+l+ 81.2%

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

      3. associate-/l* 81.2%

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

   3. Simplified 81.2%

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

      1. associate-/r/ 81.2%

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

   6. Applied egg-rr 81.2%

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

   7. Taylor expanded in a around inf 80.5%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+61}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+78} \lor \neg \left(y \leq 10^{+145}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-21}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-257}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+145}:\\ \;\;\;\;\frac{1}{\frac{1 + \left(a + \frac{b}{\frac{t}{y}}\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.55e-21)
   (+ (/ z b) (* t (/ (/ x b) y)))
   (if (<= y -7.5e-257)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (<= y 9e+145) (/ 1.0 (/ (+ 1.0 (+ a (/ b (/ t y)))) x)) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.55e-21) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (y <= -7.5e-257) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 9e+145) {
		tmp = 1.0 / ((1.0 + (a + (b / (t / y)))) / x);
	} 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 <= (-1.55d-21)) then
        tmp = (z / b) + (t * ((x / b) / y))
    else if (y <= (-7.5d-257)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (y <= 9d+145) then
        tmp = 1.0d0 / ((1.0d0 + (a + (b / (t / y)))) / x)
    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 <= -1.55e-21) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (y <= -7.5e-257) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 9e+145) {
		tmp = 1.0 / ((1.0 + (a + (b / (t / y)))) / x);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.55e-21:
		tmp = (z / b) + (t * ((x / b) / y))
	elif y <= -7.5e-257:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif y <= 9e+145:
		tmp = 1.0 / ((1.0 + (a + (b / (t / y)))) / x)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.55e-21)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	elseif (y <= -7.5e-257)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (y <= 9e+145)
		tmp = Float64(1.0 / Float64(Float64(1.0 + Float64(a + Float64(b / Float64(t / y)))) / x));
	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 <= -1.55e-21)
		tmp = (z / b) + (t * ((x / b) / y));
	elseif (y <= -7.5e-257)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (y <= 9e+145)
		tmp = 1.0 / ((1.0 + (a + (b / (t / y)))) / x);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.55e-21], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-257], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+145], N[(1.0 / N[(N[(1.0 + N[(a + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5499999999999999e-21

   1. Initial program 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-*l/ 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*l/ 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in b around inf 36.8%

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

      1. associate-/l* 34.4%

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

      2. *-commutative 34.4%

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

      3. +-commutative 34.4%

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

      4. associate-*r/ 34.6%

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

      5. fma-udef 34.6%

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

   7. Simplified 34.6%

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

      1. fma-udef 34.6%

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

      2. *-commutative 34.6%

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

   9. Applied egg-rr 34.6%

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

   10. Taylor expanded in t around 0 69.1%

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

       1. associate-*r/ 70.3%

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

       2. associate-/r* 70.2%

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

   12. Simplified 70.2%

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

   if -1.5499999999999999e-21 < y < -7.4999999999999995e-257

   1. Initial program 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l/ 82.0%

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

      3. *-commutative 82.0%

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

      4. associate-*l/ 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in b around 0 75.3%

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

   if -7.4999999999999995e-257 < y < 8.9999999999999996e145

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-*l/ 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around inf 78.5%

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

      1. clear-num 78.3%

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

      2. inv-pow 78.3%

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

      3. associate-/l* 79.4%

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

   7. Applied egg-rr 79.4%

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

      1. unpow-1 79.4%

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

   9. Simplified 79.4%

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

   if 8.9999999999999996e145 < y

   1. Initial program 39.6%

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

      1. *-commutative 39.6%

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

      2. associate-*l/ 42.3%

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

      3. *-commutative 42.3%

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

      4. associate-*l/ 50.1%

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

   3. Simplified 50.1%

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

   5. Taylor expanded in t around 0 65.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-21}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-257}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+145}:\\ \;\;\;\;\frac{1}{\frac{1 + \left(a + \frac{b}{\frac{t}{y}}\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-192} \lor \neg \left(t \leq 1.7 \cdot 10^{-183}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.9e-192) (not (<= t 1.7e-183)))
   (/ (+ 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 ((t <= -3.9e-192) || !(t <= 1.7e-183)) {
		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 ((t <= (-3.9d-192)) .or. (.not. (t <= 1.7d-183))) 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 ((t <= -3.9e-192) || !(t <= 1.7e-183)) {
		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 (t <= -3.9e-192) or not (t <= 1.7e-183):
		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 ((t <= -3.9e-192) || !(t <= 1.7e-183))
		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 ((t <= -3.9e-192) || ~((t <= 1.7e-183)))
		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[Or[LessEqual[t, -3.9e-192], N[Not[LessEqual[t, 1.7e-183]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9000000000000003e-192 or 1.70000000000000007e-183 < t

   1. Initial program 81.3%

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

      1. associate-/l* 82.0%

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

      2. associate-+l+ 82.0%

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

      3. associate-/l* 84.0%

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

   3. Simplified 84.0%

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

      1. associate-/r/ 84.1%

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

   6. Applied egg-rr 84.1%

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

   if -3.9000000000000003e-192 < t < 1.70000000000000007e-183

   1. Initial program 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l/ 36.0%

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

      3. *-commutative 36.0%

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

      4. associate-*l/ 32.2%

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

   3. Simplified 32.2%

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

   5. Taylor expanded in t around 0 81.6%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-192} \lor \neg \left(t \leq 1.7 \cdot 10^{-183}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-183}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-183}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.45e-183)
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (if (<= t 1.8e-183)
     (/ z b)
     (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.45e-183) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 1.8e-183) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.45d-183)) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= 1.8d-183) then
        tmp = z / b
    else
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.45e-183) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 1.8e-183) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.45e-183:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif t <= 1.8e-183:
		tmp = z / b
	else:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.45e-183)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= 1.8e-183)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.45e-183)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (t <= 1.8e-183)
		tmp = z / b;
	else
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.45e-183], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-183], N[(z / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45e-183

   1. Initial program 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*l/ 84.6%

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

      3. *-commutative 84.6%

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

      4. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   if -1.45e-183 < t < 1.8000000000000001e-183

   1. Initial program 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l/ 36.0%

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

      3. *-commutative 36.0%

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

      4. associate-*l/ 32.2%

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

   3. Simplified 32.2%

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

   5. Taylor expanded in t around 0 81.6%

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

   if 1.8000000000000001e-183 < t

   1. Initial program 80.4%

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

      1. associate-/l* 79.9%

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

      2. associate-+l+ 79.9%

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

      3. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

      1. associate-/r/ 85.0%

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

   6. Applied egg-rr 85.0%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-183}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-183}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(1 + \frac{y}{\frac{t}{b}}\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{-192}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t_1}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-184}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ 1.0 (/ y (/ t b))))))
   (if (<= t -1.55e-192)
     (/ (+ x (/ y (/ t z))) t_1)
     (if (<= t 2.5e-184) (/ z b) (/ (+ x (* z (/ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (1.0 + (y / (t / b)));
	double tmp;
	if (t <= -1.55e-192) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 2.5e-184) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / 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 = a + (1.0d0 + (y / (t / b)))
    if (t <= (-1.55d-192)) then
        tmp = (x + (y / (t / z))) / t_1
    else if (t <= 2.5d-184) then
        tmp = z / b
    else
        tmp = (x + (z * (y / t))) / 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 = a + (1.0 + (y / (t / b)));
	double tmp;
	if (t <= -1.55e-192) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 2.5e-184) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (1.0 + (y / (t / b)))
	tmp = 0
	if t <= -1.55e-192:
		tmp = (x + (y / (t / z))) / t_1
	elif t <= 2.5e-184:
		tmp = z / b
	else:
		tmp = (x + (z * (y / t))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(1.0 + Float64(y / Float64(t / b))))
	tmp = 0.0
	if (t <= -1.55e-192)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	elseif (t <= 2.5e-184)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (1.0 + (y / (t / b)));
	tmp = 0.0;
	if (t <= -1.55e-192)
		tmp = (x + (y / (t / z))) / t_1;
	elseif (t <= 2.5e-184)
		tmp = z / b;
	else
		tmp = (x + (z * (y / t))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e-192], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 2.5e-184], N[(z / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55e-192

   1. Initial program 82.3%

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

      1. associate-/l* 84.5%

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

      2. associate-+l+ 84.5%

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

      3. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

   if -1.55e-192 < t < 2.50000000000000001e-184

   1. Initial program 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l/ 36.0%

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

      3. *-commutative 36.0%

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

      4. associate-*l/ 32.2%

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

   3. Simplified 32.2%

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

   5. Taylor expanded in t around 0 81.6%

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

   if 2.50000000000000001e-184 < t

   1. Initial program 80.4%

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

      1. associate-/l* 79.9%

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

      2. associate-+l+ 79.9%

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

      3. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

      1. associate-/r/ 85.0%

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

   6. Applied egg-rr 85.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-192}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-184}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-253}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.3e-22)
   (+ (/ z b) (* t (/ (/ x b) y)))
   (if (<= y -6e-253)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (<= y 2e+145) (/ x (+ (+ a 1.0) (* y (/ b t)))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.3e-22) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (y <= -6e-253) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 2e+145) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.3d-22)) then
        tmp = (z / b) + (t * ((x / b) / y))
    else if (y <= (-6d-253)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (y <= 2d+145) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.3e-22) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (y <= -6e-253) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 2e+145) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.3e-22:
		tmp = (z / b) + (t * ((x / b) / y))
	elif y <= -6e-253:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif y <= 2e+145:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.3e-22)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	elseif (y <= -6e-253)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (y <= 2e+145)
		tmp = Float64(x / Float64(Float64(a + 1.0) + 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)
	tmp = 0.0;
	if (y <= -3.3e-22)
		tmp = (z / b) + (t * ((x / b) / y));
	elseif (y <= -6e-253)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (y <= 2e+145)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.3e-22], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-253], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+145], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.3000000000000001e-22

   1. Initial program 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-*l/ 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*l/ 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in b around inf 36.8%

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

      1. associate-/l* 34.4%

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

      2. *-commutative 34.4%

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

      3. +-commutative 34.4%

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

      4. associate-*r/ 34.6%

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

      5. fma-udef 34.6%

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

   7. Simplified 34.6%

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

      1. fma-udef 34.6%

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

      2. *-commutative 34.6%

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

   9. Applied egg-rr 34.6%

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

   10. Taylor expanded in t around 0 69.1%

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

       1. associate-*r/ 70.3%

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

       2. associate-/r* 70.2%

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

   12. Simplified 70.2%

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

   if -3.3000000000000001e-22 < y < -6.0000000000000004e-253

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*l/ 80.8%

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

      3. *-commutative 80.8%

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

      4. associate-*l/ 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in b around 0 73.7%

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

   if -6.0000000000000004e-253 < y < 2e145

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-*l/ 91.8%

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

      3. *-commutative 91.8%

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

      4. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf 79.1%

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

   if 2e145 < y

   1. Initial program 39.6%

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

      1. *-commutative 39.6%

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

      2. associate-*l/ 42.3%

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

      3. *-commutative 42.3%

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

      4. associate-*l/ 50.1%

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

   3. Simplified 50.1%

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

   5. Taylor expanded in t around 0 65.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-253}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-21}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.6e-21)
   (+ (/ z b) (* t (/ (/ x b) y)))
   (if (<= y -6.5e-253)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (<= y 7e+148) (/ x (+ 1.0 (+ a (* b (/ y t))))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e-21) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (y <= -6.5e-253) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 7e+148) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.6d-21)) then
        tmp = (z / b) + (t * ((x / b) / y))
    else if (y <= (-6.5d-253)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (y <= 7d+148) then
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e-21) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (y <= -6.5e-253) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 7e+148) {
		tmp = x / (1.0 + (a + (b * (y / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.6e-21:
		tmp = (z / b) + (t * ((x / b) / y))
	elif y <= -6.5e-253:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif y <= 7e+148:
		tmp = x / (1.0 + (a + (b * (y / t))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.6e-21)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	elseif (y <= -6.5e-253)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (y <= 7e+148)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.6e-21)
		tmp = (z / b) + (t * ((x / b) / y));
	elseif (y <= -6.5e-253)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (y <= 7e+148)
		tmp = x / (1.0 + (a + (b * (y / t))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.6e-21], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-253], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+148], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6000000000000001e-21

   1. Initial program 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-*l/ 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*l/ 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in b around inf 36.8%

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

      1. associate-/l* 34.4%

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

      2. *-commutative 34.4%

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

      3. +-commutative 34.4%

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

      4. associate-*r/ 34.6%

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

      5. fma-udef 34.6%

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

   7. Simplified 34.6%

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

      1. fma-udef 34.6%

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

      2. *-commutative 34.6%

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

   9. Applied egg-rr 34.6%

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

   10. Taylor expanded in t around 0 69.1%

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

       1. associate-*r/ 70.3%

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

       2. associate-/r* 70.2%

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

   12. Simplified 70.2%

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

   if -1.6000000000000001e-21 < y < -6.4999999999999998e-253

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*l/ 80.8%

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

      3. *-commutative 80.8%

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

      4. associate-*l/ 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in b around 0 73.7%

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

   if -6.4999999999999998e-253 < y < 6.9999999999999998e148

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-*l/ 91.8%

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

      3. *-commutative 91.8%

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

      4. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf 79.1%

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

      1. *-un-lft-identity 79.1%

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

      2. times-frac 80.1%

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

   7. Applied egg-rr 80.1%

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

   if 6.9999999999999998e148 < y

   1. Initial program 39.6%

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

      1. *-commutative 39.6%

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

      2. associate-*l/ 42.3%

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

      3. *-commutative 42.3%

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

      4. associate-*l/ 50.1%

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

   3. Simplified 50.1%

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

   5. Taylor expanded in t around 0 65.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-21}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 24:\\ \;\;\;\;t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= y -2.05e-22)
     (/ z b)
     (if (<= y 5.5e-62)
       t_1
       (if (<= y 24.0) (* t (/ (/ x b) y)) (if (<= y 3.5e+19) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -2.05e-22) {
		tmp = z / b;
	} else if (y <= 5.5e-62) {
		tmp = t_1;
	} else if (y <= 24.0) {
		tmp = t * ((x / b) / y);
	} else if (y <= 3.5e+19) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (y <= (-2.05d-22)) then
        tmp = z / b
    else if (y <= 5.5d-62) then
        tmp = t_1
    else if (y <= 24.0d0) then
        tmp = t * ((x / b) / y)
    else if (y <= 3.5d+19) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -2.05e-22) {
		tmp = z / b;
	} else if (y <= 5.5e-62) {
		tmp = t_1;
	} else if (y <= 24.0) {
		tmp = t * ((x / b) / y);
	} else if (y <= 3.5e+19) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if y <= -2.05e-22:
		tmp = z / b
	elif y <= 5.5e-62:
		tmp = t_1
	elif y <= 24.0:
		tmp = t * ((x / b) / y)
	elif y <= 3.5e+19:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (y <= -2.05e-22)
		tmp = Float64(z / b);
	elseif (y <= 5.5e-62)
		tmp = t_1;
	elseif (y <= 24.0)
		tmp = Float64(t * Float64(Float64(x / b) / y));
	elseif (y <= 3.5e+19)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (y <= -2.05e-22)
		tmp = z / b;
	elseif (y <= 5.5e-62)
		tmp = t_1;
	elseif (y <= 24.0)
		tmp = t * ((x / b) / y);
	elseif (y <= 3.5e+19)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.05e-22], N[(z / b), $MachinePrecision], If[LessEqual[y, 5.5e-62], t$95$1, If[LessEqual[y, 24.0], N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+19], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e-22 or 3.5e19 < y

   1. Initial program 53.5%

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

      1. *-commutative 53.5%

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

      2. associate-*l/ 56.5%

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

      3. *-commutative 56.5%

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

      4. associate-*l/ 61.7%

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

   3. Simplified 61.7%

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

   5. Taylor expanded in t around 0 59.7%

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

   if -2.05e-22 < y < 5.50000000000000022e-62 or 24 < y < 3.5e19

   1. Initial program 96.3%

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

      1. *-commutative 96.3%

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

      2. associate-*l/ 89.8%

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

      3. *-commutative 89.8%

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

      4. associate-*l/ 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in t around inf 68.4%

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

   if 5.50000000000000022e-62 < y < 24

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l/ 90.3%

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

      3. *-commutative 90.3%

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

      4. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in x around inf 60.7%

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

      1. expm1-log1p-u 19.4%

         \[\leadsto \frac{x}{1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a + \frac{b \cdot y}{t}\right)\right)}} \]

      2. expm1-udef 19.4%

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

      3. log1p-udef 19.4%

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

      4. add-exp-log 60.7%

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

      5. associate-/l* 60.4%

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

   7. Applied egg-rr 60.4%

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

      1. associate--l+ 60.1%

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

   9. Simplified 60.1%

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

   10. Taylor expanded in b around inf 48.8%

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

       1. associate-*r/ 50.0%

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

       2. associate-/r* 50.0%

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

   12. Simplified 50.0%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 24:\\ \;\;\;\;t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{1 + \frac{b}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.95e-28)
   (/ z b)
   (if (<= y 1.3e-63)
     (/ x (+ a 1.0))
     (if (<= y 2.3e+135) (/ x (+ 1.0 (/ b (/ t y)))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.95e-28) {
		tmp = z / b;
	} else if (y <= 1.3e-63) {
		tmp = x / (a + 1.0);
	} else if (y <= 2.3e+135) {
		tmp = x / (1.0 + (b / (t / y)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.95d-28)) then
        tmp = z / b
    else if (y <= 1.3d-63) then
        tmp = x / (a + 1.0d0)
    else if (y <= 2.3d+135) then
        tmp = x / (1.0d0 + (b / (t / y)))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.95e-28) {
		tmp = z / b;
	} else if (y <= 1.3e-63) {
		tmp = x / (a + 1.0);
	} else if (y <= 2.3e+135) {
		tmp = x / (1.0 + (b / (t / y)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.95e-28:
		tmp = z / b
	elif y <= 1.3e-63:
		tmp = x / (a + 1.0)
	elif y <= 2.3e+135:
		tmp = x / (1.0 + (b / (t / y)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.95e-28)
		tmp = Float64(z / b);
	elseif (y <= 1.3e-63)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 2.3e+135)
		tmp = Float64(x / Float64(1.0 + Float64(b / Float64(t / y))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.95e-28)
		tmp = z / b;
	elseif (y <= 1.3e-63)
		tmp = x / (a + 1.0);
	elseif (y <= 2.3e+135)
		tmp = x / (1.0 + (b / (t / y)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.95e-28], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.3e-63], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+135], N[(x / N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.94999999999999999e-28 or 2.3000000000000001e135 < y

   1. Initial program 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-*l/ 54.7%

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

      3. *-commutative 54.7%

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

      4. associate-*l/ 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in t around 0 63.0%

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

   if -1.94999999999999999e-28 < y < 1.3000000000000001e-63

   1. Initial program 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-*l/ 89.1%

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

      3. *-commutative 89.1%

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

      4. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in t around inf 68.6%

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

   if 1.3000000000000001e-63 < y < 2.3000000000000001e135

   1. Initial program 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-*l/ 84.3%

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

      3. *-commutative 84.3%

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

      4. associate-*l/ 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around inf 54.6%

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

   6. Taylor expanded in a around 0 43.3%

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

      1. associate-/l* 45.5%

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

   8. Simplified 45.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-28}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{1 + \frac{b}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-27} \lor \neg \left(y \leq 4.6 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.4e-27) (not (<= y 4.6e-62)))
   (+ (/ z b) (* t (/ (/ x b) y)))
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4e-27) || !(y <= 4.6e-62)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.4d-27)) .or. (.not. (y <= 4.6d-62))) then
        tmp = (z / b) + (t * ((x / b) / y))
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4e-27) || !(y <= 4.6e-62)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.4e-27) or not (y <= 4.6e-62):
		tmp = (z / b) + (t * ((x / b) / y))
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.4e-27) || !(y <= 4.6e-62))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.4e-27) || ~((y <= 4.6e-62)))
		tmp = (z / b) + (t * ((x / b) / y));
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.4e-27], N[Not[LessEqual[y, 4.6e-62]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e-27 or 4.60000000000000001e-62 < y

   1. Initial program 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-*l/ 60.6%

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

      3. *-commutative 60.6%

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

      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 36.2%

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

      1. associate-/l* 35.0%

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

      2. *-commutative 35.0%

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

      3. +-commutative 35.0%

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

      4. associate-*r/ 35.1%

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

      5. fma-udef 35.1%

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

   7. Simplified 35.1%

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

      1. fma-udef 35.1%

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

      2. *-commutative 35.1%

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

   9. Applied egg-rr 35.1%

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

   10. Taylor expanded in t around 0 64.9%

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

       1. associate-*r/ 65.6%

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

       2. associate-/r* 64.8%

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

   12. Simplified 64.8%

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

   if -1.4e-27 < y < 4.60000000000000001e-62

   1. Initial program 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-*l/ 89.2%

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

      3. *-commutative 89.2%

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

      4. associate-*l/ 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around inf 68.9%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-27} \lor \neg \left(y \leq 4.6 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.6e-7)
   (+ (/ z b) (* t (/ (/ x b) y)))
   (if (<= y 7e+148) (/ x (+ 1.0 (+ a (/ (* y b) t)))) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.6e-7) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (y <= 7e+148) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.6d-7)) then
        tmp = (z / b) + (t * ((x / b) / y))
    else if (y <= 7d+148) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.6e-7) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else if (y <= 7e+148) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.6e-7:
		tmp = (z / b) + (t * ((x / b) / y))
	elif y <= 7e+148:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.6e-7)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	elseif (y <= 7e+148)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.6e-7)
		tmp = (z / b) + (t * ((x / b) / y));
	elseif (y <= 7e+148)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.6e-7], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+148], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000038e-7

   1. Initial program 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*l/ 56.0%

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

      3. *-commutative 56.0%

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

      4. associate-*l/ 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in b around inf 35.2%

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

      1. associate-/l* 32.7%

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

      2. *-commutative 32.7%

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

      3. +-commutative 32.7%

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

      4. associate-*r/ 32.8%

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

      5. fma-udef 32.8%

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

   7. Simplified 32.8%

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

      1. fma-udef 32.8%

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

      2. *-commutative 32.8%

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

   9. Applied egg-rr 32.8%

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

   10. Taylor expanded in t around 0 69.7%

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

       1. associate-*r/ 71.0%

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

       2. associate-/r* 70.9%

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

   12. Simplified 70.9%

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

   if -5.60000000000000038e-7 < y < 6.9999999999999998e148

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*l/ 88.7%

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

      3. *-commutative 88.7%

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

      4. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around inf 74.1%

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

   if 6.9999999999999998e148 < y

   1. Initial program 39.6%

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

      1. *-commutative 39.6%

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

      2. associate-*l/ 42.3%

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

      3. *-commutative 42.3%

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

      4. associate-*l/ 50.1%

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

   3. Simplified 50.1%

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

   5. Taylor expanded in t around 0 65.0%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-73}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3e-73)
   (/ z b)
   (if (<= y -1.06e-294) (/ x a) (if (<= y 5e-62) x (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3e-73) {
		tmp = z / b;
	} else if (y <= -1.06e-294) {
		tmp = x / a;
	} else if (y <= 5e-62) {
		tmp = x;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3d-73)) then
        tmp = z / b
    else if (y <= (-1.06d-294)) then
        tmp = x / a
    else if (y <= 5d-62) then
        tmp = x
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3e-73) {
		tmp = z / b;
	} else if (y <= -1.06e-294) {
		tmp = x / a;
	} else if (y <= 5e-62) {
		tmp = x;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3e-73:
		tmp = z / b
	elif y <= -1.06e-294:
		tmp = x / a
	elif y <= 5e-62:
		tmp = x
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3e-73)
		tmp = Float64(z / b);
	elseif (y <= -1.06e-294)
		tmp = Float64(x / a);
	elseif (y <= 5e-62)
		tmp = x;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3e-73)
		tmp = z / b;
	elseif (y <= -1.06e-294)
		tmp = x / a;
	elseif (y <= 5e-62)
		tmp = x;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3e-73], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.06e-294], N[(x / a), $MachinePrecision], If[LessEqual[y, 5e-62], x, N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e-73 or 5.0000000000000002e-62 < y

   1. Initial program 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-*l/ 60.7%

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

      3. *-commutative 60.7%

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

      4. associate-*l/ 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in t around 0 54.7%

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

   if -3e-73 < y < -1.0600000000000001e-294

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*l/ 89.4%

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

      3. *-commutative 89.4%

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

      4. associate-*l/ 83.2%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in x around inf 71.9%

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

   6. Taylor expanded in a around inf 42.3%

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

   if -1.0600000000000001e-294 < y < 5.0000000000000002e-62

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 94.2%

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

      3. *-commutative 94.2%

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

      4. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf 90.4%

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

      1. expm1-log1p-u 66.3%

         \[\leadsto \frac{x}{1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a + \frac{b \cdot y}{t}\right)\right)}} \]

      2. expm1-udef 66.3%

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

      3. log1p-udef 66.3%

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

      4. add-exp-log 90.4%

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

      5. associate-/l* 90.4%

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

   7. Applied egg-rr 90.4%

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

      1. associate--l+ 90.4%

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

   9. Simplified 90.4%

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

   10. Taylor expanded in b around 0 78.9%

       \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   11. Step-by-step derivation

       1. +-commutative 78.9%

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

   12. Simplified 78.9%

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

   13. Taylor expanded in a around 0 48.4%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-73}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{-23} \lor \neg \left(y \leq 5.5 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.26e-23) (not (<= y 5.5e-62))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.26e-23) || !(y <= 5.5e-62)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.26d-23)) .or. (.not. (y <= 5.5d-62))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.26e-23) || !(y <= 5.5e-62)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.26e-23) or not (y <= 5.5e-62):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.26e-23) || !(y <= 5.5e-62))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.26e-23) || ~((y <= 5.5e-62)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.26e-23], N[Not[LessEqual[y, 5.5e-62]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25999999999999996e-23 or 5.50000000000000022e-62 < y

   1. Initial program 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-*l/ 60.6%

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

      3. *-commutative 60.6%

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

      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 t around 0 56.2%

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

   if -1.25999999999999996e-23 < y < 5.50000000000000022e-62

   1. Initial program 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-*l/ 89.2%

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

      3. *-commutative 89.2%

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

      4. associate-*l/ 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around inf 68.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{-23} \lor \neg \left(y \leq 5.5 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 41.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 7.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.0) (not (<= a 7.5e-6))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 7.5e-6)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.0d0)) .or. (.not. (a <= 7.5d-6))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 7.5e-6)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.0) or not (a <= 7.5e-6):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.0) || !(a <= 7.5e-6))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.0) || ~((a <= 7.5e-6)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.0], N[Not[LessEqual[a, 7.5e-6]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 7.50000000000000019e-6 < a

   1. Initial program 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-*l/ 72.6%

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

      3. *-commutative 72.6%

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

      4. associate-*l/ 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in x around inf 54.5%

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

   6. Taylor expanded in a around inf 44.9%

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

   if -1 < a < 7.50000000000000019e-6

   1. Initial program 73.9%

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

      1. *-commutative 73.9%

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

      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/ 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in x around inf 53.2%

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

      1. expm1-log1p-u 43.7%

         \[\leadsto \frac{x}{1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a + \frac{b \cdot y}{t}\right)\right)}} \]

      2. expm1-udef 43.7%

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

      3. log1p-udef 43.7%

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

      4. add-exp-log 53.2%

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

      5. associate-/l* 53.9%

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

   7. Applied egg-rr 53.9%

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

      1. associate--l+ 53.9%

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

   9. Simplified 53.9%

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

   10. Taylor expanded in b around 0 37.3%

       \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   11. Step-by-step derivation

       1. +-commutative 37.3%

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

   12. Simplified 37.3%

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

   13. Taylor expanded in a around 0 36.8%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 7.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 20.1% 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 74.0%

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

   1. *-commutative 74.0%

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

   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/ 73.4%

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

3. Simplified 73.4%

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

5. Taylor expanded in x around inf 53.8%

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

   1. expm1-log1p-u 34.7%

      \[\leadsto \frac{x}{1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a + \frac{b \cdot y}{t}\right)\right)}} \]

   2. expm1-udef 34.7%

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

   3. log1p-udef 34.7%

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

   4. add-exp-log 53.8%

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

   5. associate-/l* 54.9%

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

7. Applied egg-rr 54.9%

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

   1. associate--l+ 54.9%

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

9. Simplified 54.9%

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

10. Taylor expanded in b around 0 41.5%

    \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
11. Step-by-step derivation

    1. +-commutative 41.5%

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

12. Simplified 41.5%

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

13. Taylor expanded in a around 0 21.2%

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

14. Final simplification 21.2%

    \[\leadsto x \]
15. Add Preprocessing

Developer target: 79.2% 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 2024020 
(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))))