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

Percentage Accurate: 75.3% → 90.3%

Time: 17.6s

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: 75.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_3 := 1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, \frac{z}{t\_3}, \frac{x}{t\_3}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_1}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0))))
        (t_3 (+ 1.0 (fma y (/ b t) a))))
   (if (<= t_2 -5e+183)
     (fma (/ y t) (/ z t_3) (/ x t_3))
     (if (<= t_2 2e+305) (/ t_1 (+ (* b (/ y t)) (+ a 1.0))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = 1.0 + fma(y, (b / t), a);
	double tmp;
	if (t_2 <= -5e+183) {
		tmp = fma((y / t), (z / t_3), (x / t_3));
	} else if (t_2 <= 2e+305) {
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_3 = Float64(1.0 + fma(y, Float64(b / t), a))
	tmp = 0.0
	if (t_2 <= -5e+183)
		tmp = fma(Float64(y / t), Float64(z / t_3), Float64(x / t_3));
	elseif (t_2 <= 2e+305)
		tmp = Float64(t_1 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+183], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$3), $MachinePrecision] + N[(x / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+305], N[(t$95$1 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.00000000000000009e183

   1. Initial program 46.8%

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

      1. *-commutative 46.8%

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

      2. associate-/l* 72.1%

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

   4. Applied egg-rr 72.1%

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

   5. Taylor expanded in x around 0 62.9%

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

      1. +-commutative 62.9%

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

      2. times-frac 91.6%

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

      3. fma-define 91.6%

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

      4. +-commutative 91.6%

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

      5. associate-*l/ 91.5%

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

      6. *-commutative 91.5%

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

      7. fma-define 91.5%

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

      8. +-commutative 91.5%

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

      9. associate-*l/ 91.5%

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

      10. *-commutative 91.5%

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

      11. fma-define 91.5%

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

   7. Simplified 91.5%

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

   if -5.00000000000000009e183 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e305

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-/l* 94.3%

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

   4. Applied egg-rr 94.3%

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

   if 1.9999999999999999e305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.5%

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

      1. associate-/l* 23.8%

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

      2. associate-/l* 26.7%

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

   3. Simplified 26.7%

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

   5. Taylor expanded in y around inf 81.4%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, \frac{z}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}, \frac{x}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_1}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_2 (- INFINITY))
     (* (/ y t) (/ z (+ (+ a 1.0) (* y (/ b t)))))
     (if (<= t_2 2e+305) (/ t_1 (+ (* b (/ y t)) (+ a 1.0))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / ((a + 1.0) + (y * (b / t))));
	} else if (t_2 <= 2e+305) {
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / ((a + 1.0) + (y * (b / t))));
	} else if (t_2 <= 2e+305) {
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y / t) * (z / ((a + 1.0) + (y * (b / t))))
	elif t_2 <= 2e+305:
		tmp = t_1 / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))));
	elseif (t_2 <= 2e+305)
		tmp = Float64(t_1 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y / t) * (z / ((a + 1.0) + (y * (b / t))));
	elseif (t_2 <= 2e+305)
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+305], N[(t$95$1 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0

   1. Initial program 9.7%

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

      1. *-commutative 9.7%

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

      2. associate-/l* 52.7%

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

   4. Applied egg-rr 52.7%

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

      1. clear-num 52.7%

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

      2. un-div-inv 52.8%

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

   6. Applied egg-rr 52.8%

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

   7. Taylor expanded in x around 0 37.0%

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

      1. times-frac 80.9%

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

      2. associate-+r+ 80.9%

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

      3. *-commutative 80.9%

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

      4. associate-*r/ 80.9%

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

   9. Simplified 80.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e305

   1. Initial program 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-/l* 94.7%

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

   4. Applied egg-rr 94.7%

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

   if 1.9999999999999999e305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.5%

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

      1. associate-/l* 23.8%

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

      2. associate-/l* 26.7%

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

   3. Simplified 26.7%

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

   5. Taylor expanded in y around inf 81.4%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-203}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-167}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= t -8.2e-203)
     (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))
     (if (<= t 2.7e-167)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= t 5e+21)
         (/ (+ x (* z (/ y t))) (+ (/ (* y b) t) (+ a 1.0)))
         (/ t_1 (+ (+ a 1.0) (* y (/ b t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -8.2e-203) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 2.7e-167) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 5e+21) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (t <= (-8.2d-203)) then
        tmp = t_1 / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= 2.7d-167) then
        tmp = (z + ((x * t) / y)) / b
    else if (t <= 5d+21) then
        tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0d0))
    else
        tmp = t_1 / ((a + 1.0d0) + (y * (b / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -8.2e-203) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 2.7e-167) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 5e+21) {
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	tmp = 0
	if t <= -8.2e-203:
		tmp = t_1 / ((a + 1.0) + (y / (t / b)))
	elif t <= 2.7e-167:
		tmp = (z + ((x * t) / y)) / b
	elif t <= 5e+21:
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0))
	else:
		tmp = t_1 / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -8.2e-203)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= 2.7e-167)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t <= 5e+21)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	else
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (t <= -8.2e-203)
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	elseif (t <= 2.7e-167)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t <= 5e+21)
		tmp = (x + (z * (y / t))) / (((y * b) / t) + (a + 1.0));
	else
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e-203], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-167], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 5e+21], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.19999999999999962e-203

   1. Initial program 82.2%

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

      1. associate-/l* 85.8%

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

      2. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

      1. clear-num 85.7%

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

      2. un-div-inv 86.4%

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

   6. Applied egg-rr 86.4%

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

   if -8.19999999999999962e-203 < t < 2.7000000000000001e-167

   1. Initial program 53.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. 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* 46.9%

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

   4. Applied egg-rr 46.9%

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

   5. Taylor expanded in x around 0 65.2%

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

      1. +-commutative 65.2%

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

      2. times-frac 50.8%

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

      3. fma-define 50.8%

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

      4. +-commutative 50.8%

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

      5. associate-*l/ 47.0%

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

      6. *-commutative 47.0%

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

      7. fma-define 47.0%

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

      8. +-commutative 47.0%

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

      9. associate-*l/ 41.0%

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

      10. *-commutative 41.0%

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

      11. fma-define 41.0%

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

   7. Simplified 41.0%

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

   8. Taylor expanded in b around inf 68.1%

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

      1. *-commutative 68.1%

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

   10. Simplified 68.1%

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

   if 2.7000000000000001e-167 < t < 5e21

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-/l* 89.3%

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

   4. Applied egg-rr 89.3%

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

   if 5e21 < t

   1. Initial program 72.3%

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

      1. associate-/l* 84.6%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-203}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-167}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-167}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= t -5.5e-203)
     (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))
     (if (<= t 3.8e-167)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= t 5e+21)
         (/ (+ x (/ z (/ t y))) (+ (/ (* y b) t) (+ a 1.0)))
         (/ t_1 (+ (+ a 1.0) (* y (/ b t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -5.5e-203) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 3.8e-167) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 5e+21) {
		tmp = (x + (z / (t / y))) / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (t <= (-5.5d-203)) then
        tmp = t_1 / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= 3.8d-167) then
        tmp = (z + ((x * t) / y)) / b
    else if (t <= 5d+21) then
        tmp = (x + (z / (t / y))) / (((y * b) / t) + (a + 1.0d0))
    else
        tmp = t_1 / ((a + 1.0d0) + (y * (b / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -5.5e-203) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 3.8e-167) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 5e+21) {
		tmp = (x + (z / (t / y))) / (((y * b) / t) + (a + 1.0));
	} else {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	tmp = 0
	if t <= -5.5e-203:
		tmp = t_1 / ((a + 1.0) + (y / (t / b)))
	elif t <= 3.8e-167:
		tmp = (z + ((x * t) / y)) / b
	elif t <= 5e+21:
		tmp = (x + (z / (t / y))) / (((y * b) / t) + (a + 1.0))
	else:
		tmp = t_1 / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -5.5e-203)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= 3.8e-167)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t <= 5e+21)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	else
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (t <= -5.5e-203)
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	elseif (t <= 3.8e-167)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t <= 5e+21)
		tmp = (x + (z / (t / y))) / (((y * b) / t) + (a + 1.0));
	else
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e-203], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-167], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 5e+21], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.5000000000000002e-203

   1. Initial program 82.2%

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

      1. associate-/l* 85.8%

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

      2. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

      1. clear-num 85.7%

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

      2. un-div-inv 86.4%

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

   6. Applied egg-rr 86.4%

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

   if -5.5000000000000002e-203 < t < 3.79999999999999967e-167

   1. Initial program 53.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. 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* 46.9%

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

   4. Applied egg-rr 46.9%

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

   5. Taylor expanded in x around 0 65.2%

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

      1. +-commutative 65.2%

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

      2. times-frac 50.8%

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

      3. fma-define 50.8%

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

      4. +-commutative 50.8%

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

      5. associate-*l/ 47.0%

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

      6. *-commutative 47.0%

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

      7. fma-define 47.0%

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

      8. +-commutative 47.0%

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

      9. associate-*l/ 41.0%

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

      10. *-commutative 41.0%

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

      11. fma-define 41.0%

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

   7. Simplified 41.0%

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

   8. Taylor expanded in b around inf 68.1%

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

      1. *-commutative 68.1%

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

   10. Simplified 68.1%

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

   if 3.79999999999999967e-167 < t < 5e21

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-/l* 89.3%

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

   4. Applied egg-rr 89.3%

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

      1. clear-num 89.2%

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

      2. un-div-inv 89.3%

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

   6. Applied egg-rr 89.3%

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

   if 5e21 < t

   1. Initial program 72.3%

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

      1. associate-/l* 84.6%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-167}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-203} \lor \neg \left(t \leq 2.9 \cdot 10^{-147}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.3e-203) (not (<= t 2.9e-147)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.3e-203) || !(t <= 2.9e-147)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.3d-203)) .or. (.not. (t <= 2.9d-147))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.3e-203) || !(t <= 2.9e-147)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.3e-203) or not (t <= 2.9e-147):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.3e-203) || !(t <= 2.9e-147))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.3e-203) || ~((t <= 2.9e-147)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.3e-203], N[Not[LessEqual[t, 2.9e-147]], $MachinePrecision]], 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], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.30000000000000027e-203 or 2.9000000000000001e-147 < t

   1. Initial program 80.2%

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

      1. associate-/l* 84.9%

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

      2. associate-/l* 86.3%

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

   3. Simplified 86.3%

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

   if -4.30000000000000027e-203 < t < 2.9000000000000001e-147

   1. Initial program 56.2%

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

      1. *-commutative 56.2%

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

      2. associate-/l* 50.0%

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

   4. Applied egg-rr 50.0%

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

   5. Taylor expanded in x around 0 67.2%

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

      1. +-commutative 67.2%

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

      2. times-frac 53.6%

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

      3. fma-define 53.6%

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

      4. +-commutative 53.6%

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

      5. associate-*l/ 50.1%

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

      6. *-commutative 50.1%

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

      7. fma-define 50.1%

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

      8. +-commutative 50.1%

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

      9. associate-*l/ 42.5%

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

      10. *-commutative 42.5%

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

      11. fma-define 42.5%

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

   7. Simplified 42.5%

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

   8. Taylor expanded in b around inf 66.4%

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

      1. *-commutative 66.4%

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

   10. Simplified 66.4%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-203} \lor \neg \left(t \leq 2.9 \cdot 10^{-147}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-145}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= t -7.5e-203)
     (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))
     (if (<= t 2.1e-145)
       (/ (+ z (/ (* x t) y)) b)
       (/ t_1 (+ (+ a 1.0) (* y (/ b t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -7.5e-203) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 2.1e-145) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (t <= (-7.5d-203)) then
        tmp = t_1 / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= 2.1d-145) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_1 / ((a + 1.0d0) + (y * (b / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -7.5e-203) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 2.1e-145) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	tmp = 0
	if t <= -7.5e-203:
		tmp = t_1 / ((a + 1.0) + (y / (t / b)))
	elif t <= 2.1e-145:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_1 / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -7.5e-203)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= 2.1e-145)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (t <= -7.5e-203)
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	elseif (t <= 2.1e-145)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e-203], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-145], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.50000000000000027e-203

   1. Initial program 82.2%

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

      1. associate-/l* 85.8%

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

      2. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

      1. clear-num 85.7%

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

      2. un-div-inv 86.4%

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

   6. Applied egg-rr 86.4%

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

   if -7.50000000000000027e-203 < t < 2.09999999999999991e-145

   1. Initial program 56.2%

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

      1. *-commutative 56.2%

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

      2. associate-/l* 50.0%

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

   4. Applied egg-rr 50.0%

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

   5. Taylor expanded in x around 0 67.2%

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

      1. +-commutative 67.2%

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

      2. times-frac 53.6%

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

      3. fma-define 53.6%

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

      4. +-commutative 53.6%

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

      5. associate-*l/ 50.1%

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

      6. *-commutative 50.1%

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

      7. fma-define 50.1%

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

      8. +-commutative 50.1%

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

      9. associate-*l/ 42.5%

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

      10. *-commutative 42.5%

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

      11. fma-define 42.5%

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

   7. Simplified 42.5%

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

   8. Taylor expanded in b around inf 66.4%

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

      1. *-commutative 66.4%

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

   10. Simplified 66.4%

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

   if 2.09999999999999991e-145 < t

   1. Initial program 77.9%

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

      1. associate-/l* 84.0%

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

      2. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-145}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-137}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-71}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -1.7e-32)
     t_1
     (if (<= t 1.02e-137)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= t 1.6e-71) (/ (* y z) (* t (+ a 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -1.7e-32) {
		tmp = t_1;
	} else if (t <= 1.02e-137) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 1.6e-71) {
		tmp = (y * z) / (t * (a + 1.0));
	} 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) + (y * (b / t)))
    if (t <= (-1.7d-32)) then
        tmp = t_1
    else if (t <= 1.02d-137) then
        tmp = (z + ((x * t) / y)) / b
    else if (t <= 1.6d-71) then
        tmp = (y * z) / (t * (a + 1.0d0))
    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) + (y * (b / t)));
	double tmp;
	if (t <= -1.7e-32) {
		tmp = t_1;
	} else if (t <= 1.02e-137) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 1.6e-71) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -1.7e-32:
		tmp = t_1
	elif t <= 1.02e-137:
		tmp = (z + ((x * t) / y)) / b
	elif t <= 1.6e-71:
		tmp = (y * z) / (t * (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -1.7e-32)
		tmp = t_1;
	elseif (t <= 1.02e-137)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t <= 1.6e-71)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	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) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -1.7e-32)
		tmp = t_1;
	elseif (t <= 1.02e-137)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t <= 1.6e-71)
		tmp = (y * z) / (t * (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e-32], t$95$1, If[LessEqual[t, 1.02e-137], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 1.6e-71], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.69999999999999989e-32 or 1.5999999999999999e-71 < t

   1. Initial program 79.8%

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

      1. associate-/l* 86.8%

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

      2. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in x around inf 66.7%

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

   if -1.69999999999999989e-32 < t < 1.02e-137

   1. Initial program 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 60.1%

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

   4. Applied egg-rr 60.1%

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

   5. Taylor expanded in x around 0 77.2%

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

      1. +-commutative 77.2%

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

      2. times-frac 63.4%

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

      3. fma-define 63.4%

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

      4. +-commutative 63.4%

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

      5. associate-*l/ 57.0%

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

      6. *-commutative 57.0%

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

      7. fma-define 57.0%

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

      8. +-commutative 57.0%

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

      9. associate-*l/ 52.4%

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

      10. *-commutative 52.4%

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

      11. fma-define 52.4%

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

   7. Simplified 52.4%

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

   8. Taylor expanded in b around inf 60.7%

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

      1. *-commutative 60.7%

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

   10. Simplified 60.7%

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

   if 1.02e-137 < t < 1.5999999999999999e-71

   1. Initial program 88.0%

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

      1. associate-/l* 76.8%

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

      2. associate-/l* 71.3%

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

   3. Simplified 71.3%

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

      1. associate-*r/ 82.5%

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

      2. clear-num 82.4%

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

   6. Applied egg-rr 82.4%

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

   7. Taylor expanded in y around 0 72.6%

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

   8. Taylor expanded in x around 0 53.6%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-137}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-71}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{a + 1} + \frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-182}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.9e-55)
   (+ (/ x (+ a 1.0)) (* (/ y t) (/ z (+ a 1.0))))
   (if (<= t -6.8e-203)
     (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
     (if (<= t 3.9e-182)
       (/ (+ z (/ (* x t) y)) b)
       (/ (+ x (/ z (/ t y))) (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.9e-55) {
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	} else if (t <= -6.8e-203) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 3.9e-182) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.9d-55)) then
        tmp = (x / (a + 1.0d0)) + ((y / t) * (z / (a + 1.0d0)))
    else if (t <= (-6.8d-203)) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else if (t <= 3.9d-182) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + (z / (t / y))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.9e-55) {
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	} else if (t <= -6.8e-203) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 3.9e-182) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.9e-55:
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)))
	elif t <= -6.8e-203:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	elif t <= 3.9e-182:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + (z / (t / y))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.9e-55)
		tmp = Float64(Float64(x / Float64(a + 1.0)) + Float64(Float64(y / t) * Float64(z / Float64(a + 1.0))));
	elseif (t <= -6.8e-203)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	elseif (t <= 3.9e-182)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.9e-55)
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	elseif (t <= -6.8e-203)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	elseif (t <= 3.9e-182)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + (z / (t / y))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.9e-55], N[(N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.8e-203], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-182], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9e-55

   1. Initial program 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-/l* 90.0%

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in x around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. times-frac 94.8%

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

      3. fma-define 94.8%

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

      4. +-commutative 94.8%

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

      5. associate-*l/ 94.8%

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

      6. *-commutative 94.8%

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

      7. fma-define 94.8%

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

      8. +-commutative 94.8%

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

      9. associate-*l/ 98.4%

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

      10. *-commutative 98.4%

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

      11. fma-define 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in b around 0 70.1%

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

      1. times-frac 80.1%

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

   10. Simplified 80.1%

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

   if -2.9e-55 < t < -6.7999999999999998e-203

   1. Initial program 78.2%

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

      1. associate-/l* 80.9%

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

      2. associate-/l* 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in x around 0 74.8%

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

   if -6.7999999999999998e-203 < t < 3.9e-182

   1. Initial program 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-/l* 48.7%

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

   4. Applied egg-rr 48.7%

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

   5. Taylor expanded in x around 0 66.6%

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

      1. +-commutative 66.6%

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

      2. times-frac 52.9%

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

      3. fma-define 52.9%

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

      4. +-commutative 52.9%

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

      5. associate-*l/ 48.8%

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

      6. *-commutative 48.8%

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

      7. fma-define 48.8%

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

      8. +-commutative 48.8%

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

      9. associate-*l/ 42.2%

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

      10. *-commutative 42.2%

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

      11. fma-define 42.2%

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

   7. Simplified 42.2%

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

   8. Taylor expanded in b around inf 69.7%

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

      1. *-commutative 69.7%

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

   10. Simplified 69.7%

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

   if 3.9e-182 < t

   1. Initial program 76.6%

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

      1. associate-/l* 81.3%

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

      2. associate-/l* 83.2%

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

   3. Simplified 83.2%

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

      1. associate-*r/ 77.6%

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

      2. clear-num 77.5%

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

   6. Applied egg-rr 77.5%

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

   7. Taylor expanded in y around 0 67.5%

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

      1. *-un-lft-identity 67.5%

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

      2. clear-num 67.5%

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

      3. *-commutative 67.5%

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

      4. associate-*r/ 73.1%

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

      5. clear-num 73.1%

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

      6. un-div-inv 73.1%

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

   9. Applied egg-rr 73.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{a + 1} + \frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-182}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-137}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.75e+16)
     t_1
     (if (<= t 2.5e-137)
       (/ z b)
       (if (<= t 1.3e-39) (/ (* y z) (* t (+ a 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.75e+16) {
		tmp = t_1;
	} else if (t <= 2.5e-137) {
		tmp = z / b;
	} else if (t <= 1.3e-39) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-1.75d+16)) then
        tmp = t_1
    else if (t <= 2.5d-137) then
        tmp = z / b
    else if (t <= 1.3d-39) then
        tmp = (y * z) / (t * (a + 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.75e+16) {
		tmp = t_1;
	} else if (t <= 2.5e-137) {
		tmp = z / b;
	} else if (t <= 1.3e-39) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.75e+16:
		tmp = t_1
	elif t <= 2.5e-137:
		tmp = z / b
	elif t <= 1.3e-39:
		tmp = (y * z) / (t * (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.75e+16)
		tmp = t_1;
	elseif (t <= 2.5e-137)
		tmp = Float64(z / b);
	elseif (t <= 1.3e-39)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.75e+16)
		tmp = t_1;
	elseif (t <= 2.5e-137)
		tmp = z / b;
	elseif (t <= 1.3e-39)
		tmp = (y * z) / (t * (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+16], t$95$1, If[LessEqual[t, 2.5e-137], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.3e-39], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e16 or 1.3e-39 < t

   1. Initial program 78.4%

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

      1. associate-/l* 86.4%

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

      2. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in y around 0 61.2%

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

   if -1.75e16 < t < 2.5e-137

   1. Initial program 68.0%

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

      1. associate-/l* 64.1%

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

      2. associate-/l* 56.5%

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

   3. Simplified 56.5%

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

   5. Taylor expanded in y around inf 50.2%

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

   if 2.5e-137 < t < 1.3e-39

   1. Initial program 90.7%

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

      1. associate-/l* 82.0%

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

      2. associate-/l* 73.4%

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

   3. Simplified 73.4%

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

      1. associate-*r/ 82.0%

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

      2. clear-num 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in y around 0 69.9%

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

   8. Taylor expanded in x around 0 50.7%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-137}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{if}\;a \leq -1.15:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 1300000000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) a)))
   (if (<= a -1.15)
     t_1
     (if (<= a 1.55e-69)
       (/ x (+ 1.0 (* b (/ y t))))
       (if (<= a 1300000000.0) (/ z b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -1.15) {
		tmp = t_1;
	} else if (a <= 1.55e-69) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 1300000000.0) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / a
    if (a <= (-1.15d0)) then
        tmp = t_1
    else if (a <= 1.55d-69) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if (a <= 1300000000.0d0) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -1.15) {
		tmp = t_1;
	} else if (a <= 1.55e-69) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 1300000000.0) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / a
	tmp = 0
	if a <= -1.15:
		tmp = t_1
	elif a <= 1.55e-69:
		tmp = x / (1.0 + (b * (y / t)))
	elif a <= 1300000000.0:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / a)
	tmp = 0.0
	if (a <= -1.15)
		tmp = t_1;
	elseif (a <= 1.55e-69)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (a <= 1300000000.0)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / a;
	tmp = 0.0;
	if (a <= -1.15)
		tmp = t_1;
	elseif (a <= 1.55e-69)
		tmp = x / (1.0 + (b * (y / t)));
	elseif (a <= 1300000000.0)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -1.15], t$95$1, If[LessEqual[a, 1.55e-69], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1300000000.0], N[(z / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1499999999999999 or 1.3e9 < a

   1. Initial program 75.5%

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

      1. associate-/l* 80.1%

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

      2. associate-/l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in a around inf 67.8%

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

   if -1.1499999999999999 < a < 1.55e-69

   1. Initial program 77.4%

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

      1. associate-/l* 76.6%

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

      2. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in x around inf 51.6%

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

   6. Taylor expanded in b around inf 54.8%

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

      1. distribute-rgt-in 54.9%

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

      2. lft-mult-inverse 54.9%

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

      3. +-commutative 54.9%

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

   8. Simplified 54.9%

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

   9. Taylor expanded in y around inf 53.9%

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

   if 1.55e-69 < a < 1.3e9

   1. Initial program 58.0%

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

      1. associate-/l* 58.0%

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

      2. associate-/l* 65.0%

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

   3. Simplified 65.0%

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

   5. Taylor expanded in y around inf 65.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 1300000000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{if}\;a \leq -2.85:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) a)))
   (if (<= a -2.85)
     t_1
     (if (<= a 7.2e-127)
       (/ x (+ 1.0 (* b (/ y t))))
       (if (<= a 5.5e+15) (/ (+ z (/ (* x t) y)) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -2.85) {
		tmp = t_1;
	} else if (a <= 7.2e-127) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 5.5e+15) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / a
    if (a <= (-2.85d0)) then
        tmp = t_1
    else if (a <= 7.2d-127) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if (a <= 5.5d+15) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -2.85) {
		tmp = t_1;
	} else if (a <= 7.2e-127) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 5.5e+15) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / a
	tmp = 0
	if a <= -2.85:
		tmp = t_1
	elif a <= 7.2e-127:
		tmp = x / (1.0 + (b * (y / t)))
	elif a <= 5.5e+15:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / a)
	tmp = 0.0
	if (a <= -2.85)
		tmp = t_1;
	elseif (a <= 7.2e-127)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (a <= 5.5e+15)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / a;
	tmp = 0.0;
	if (a <= -2.85)
		tmp = t_1;
	elseif (a <= 7.2e-127)
		tmp = x / (1.0 + (b * (y / t)));
	elseif (a <= 5.5e+15)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -2.85], t$95$1, If[LessEqual[a, 7.2e-127], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e+15], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.85000000000000009 or 5.5e15 < a

   1. Initial program 75.5%

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

      1. associate-/l* 80.1%

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

      2. associate-/l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in a around inf 67.8%

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

   if -2.85000000000000009 < a < 7.1999999999999999e-127

   1. Initial program 76.0%

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

      1. associate-/l* 75.1%

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

      2. associate-/l* 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in x around inf 52.0%

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

   6. Taylor expanded in b around inf 55.6%

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

      1. distribute-rgt-in 55.7%

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

      2. lft-mult-inverse 55.8%

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

      3. +-commutative 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in y around inf 54.6%

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

   if 7.1999999999999999e-127 < a < 5.5e15

   1. Initial program 73.0%

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

      1. *-commutative 73.0%

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

      2. associate-/l* 76.3%

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

   4. Applied egg-rr 76.3%

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

   5. Taylor expanded in x around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. times-frac 76.6%

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

      3. fma-define 76.6%

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

      4. +-commutative 76.6%

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

      5. associate-*l/ 77.0%

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

      6. *-commutative 77.0%

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

      7. fma-define 77.0%

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

      8. +-commutative 77.0%

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

      9. associate-*l/ 80.1%

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

      10. *-commutative 80.1%

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

      11. fma-define 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in b around inf 66.8%

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

      1. *-commutative 66.8%

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

   10. Simplified 66.8%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-76}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+66}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8.4e+24)
   (/ x a)
   (if (<= a -3.1e-76)
     (/ z b)
     (if (<= a -4e-159) x (if (<= a 1.8e+66) (/ z b) (/ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8.4e+24) {
		tmp = x / a;
	} else if (a <= -3.1e-76) {
		tmp = z / b;
	} else if (a <= -4e-159) {
		tmp = x;
	} else if (a <= 1.8e+66) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-8.4d+24)) then
        tmp = x / a
    else if (a <= (-3.1d-76)) then
        tmp = z / b
    else if (a <= (-4d-159)) then
        tmp = x
    else if (a <= 1.8d+66) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8.4e+24) {
		tmp = x / a;
	} else if (a <= -3.1e-76) {
		tmp = z / b;
	} else if (a <= -4e-159) {
		tmp = x;
	} else if (a <= 1.8e+66) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8.4e+24:
		tmp = x / a
	elif a <= -3.1e-76:
		tmp = z / b
	elif a <= -4e-159:
		tmp = x
	elif a <= 1.8e+66:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8.4e+24)
		tmp = Float64(x / a);
	elseif (a <= -3.1e-76)
		tmp = Float64(z / b);
	elseif (a <= -4e-159)
		tmp = x;
	elseif (a <= 1.8e+66)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -8.4e+24)
		tmp = x / a;
	elseif (a <= -3.1e-76)
		tmp = z / b;
	elseif (a <= -4e-159)
		tmp = x;
	elseif (a <= 1.8e+66)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8.4e+24], N[(x / a), $MachinePrecision], If[LessEqual[a, -3.1e-76], N[(z / b), $MachinePrecision], If[LessEqual[a, -4e-159], x, If[LessEqual[a, 1.8e+66], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.4000000000000005e24 or 1.8e66 < a

   1. Initial program 77.1%

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

      1. associate-/l* 81.2%

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

      2. associate-/l* 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in x around inf 54.6%

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

   6. Taylor expanded in a around inf 53.0%

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

   if -8.4000000000000005e24 < a < -3.0999999999999997e-76 or -3.99999999999999995e-159 < a < 1.8e66

   1. Initial program 73.8%

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

      1. associate-/l* 73.7%

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

      2. associate-/l* 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around inf 39.5%

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

   if -3.0999999999999997e-76 < a < -3.99999999999999995e-159

   1. Initial program 75.5%

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

      1. associate-/l* 75.8%

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

      2. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in x around inf 75.9%

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

   6. Taylor expanded in a around 0 66.2%

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

   7. Taylor expanded in b around 0 61.1%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-76}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+66}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-58} \lor \neg \left(t \leq 2.15 \cdot 10^{-182}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5e-58) (not (<= t 2.15e-182)))
   (/ (+ x (* z (/ y t))) (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e-58) || !(t <= 2.15e-182)) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5d-58)) .or. (.not. (t <= 2.15d-182))) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e-58) || !(t <= 2.15e-182)) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5e-58) or not (t <= 2.15e-182):
		tmp = (x + (z * (y / t))) / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5e-58) || !(t <= 2.15e-182))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5e-58) || ~((t <= 2.15e-182)))
		tmp = (x + (z * (y / t))) / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5e-58], N[Not[LessEqual[t, 2.15e-182]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.99999999999999977e-58 or 2.15e-182 < t

   1. Initial program 79.7%

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

      1. associate-/l* 84.1%

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

      2. associate-/l* 86.7%

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

   3. Simplified 86.7%

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

      1. associate-*r/ 81.8%

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

      2. clear-num 81.7%

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

   6. Applied egg-rr 81.7%

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

   7. Taylor expanded in y around 0 69.2%

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

      1. clear-num 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*r/ 75.1%

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

      4. *-commutative 75.1%

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

   9. Applied egg-rr 75.1%

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

   if -4.99999999999999977e-58 < t < 2.15e-182

   1. Initial program 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 59.5%

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

   4. Applied egg-rr 59.5%

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

   5. Taylor expanded in x around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. times-frac 62.0%

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

      3. fma-define 62.0%

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

      4. +-commutative 62.0%

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

      5. associate-*l/ 54.6%

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

      6. *-commutative 54.6%

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

      7. fma-define 54.6%

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

      8. +-commutative 54.6%

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

      9. associate-*l/ 50.6%

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

      10. *-commutative 50.6%

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

      11. fma-define 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in b around inf 62.6%

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

      1. *-commutative 62.6%

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

   10. Simplified 62.6%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-58} \lor \neg \left(t \leq 2.15 \cdot 10^{-182}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-58} \lor \neg \left(t \leq 3.4 \cdot 10^{-182}\right):\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.25e-58) (not (<= t 3.4e-182)))
   (/ (+ x (/ z (/ t y))) (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.25e-58) || !(t <= 3.4e-182)) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.25d-58)) .or. (.not. (t <= 3.4d-182))) then
        tmp = (x + (z / (t / y))) / (a + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.25e-58) || !(t <= 3.4e-182)) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.25e-58) or not (t <= 3.4e-182):
		tmp = (x + (z / (t / y))) / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.25e-58) || !(t <= 3.4e-182))
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.25e-58) || ~((t <= 3.4e-182)))
		tmp = (x + (z / (t / y))) / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.25e-58], N[Not[LessEqual[t, 3.4e-182]], $MachinePrecision]], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999994e-58 or 3.39999999999999989e-182 < t

   1. Initial program 79.7%

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

      1. associate-/l* 84.1%

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

      2. associate-/l* 86.7%

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

   3. Simplified 86.7%

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

      1. associate-*r/ 81.8%

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

      2. clear-num 81.7%

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

   6. Applied egg-rr 81.7%

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

   7. Taylor expanded in y around 0 69.2%

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

      1. *-un-lft-identity 69.2%

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

      2. clear-num 69.2%

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

      3. *-commutative 69.2%

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

      4. associate-*r/ 75.1%

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

      5. clear-num 75.1%

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

      6. un-div-inv 75.1%

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

   9. Applied egg-rr 75.1%

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

   if -1.24999999999999994e-58 < t < 3.39999999999999989e-182

   1. Initial program 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 59.5%

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

   4. Applied egg-rr 59.5%

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

   5. Taylor expanded in x around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. times-frac 62.0%

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

      3. fma-define 62.0%

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

      4. +-commutative 62.0%

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

      5. associate-*l/ 54.6%

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

      6. *-commutative 54.6%

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

      7. fma-define 54.6%

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

      8. +-commutative 54.6%

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

      9. associate-*l/ 50.6%

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

      10. *-commutative 50.6%

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

      11. fma-define 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in b around inf 62.6%

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

      1. *-commutative 62.6%

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

   10. Simplified 62.6%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-58} \lor \neg \left(t \leq 3.4 \cdot 10^{-182}\right):\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a + 1} + \frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-180}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.5e-57)
   (+ (/ x (+ a 1.0)) (* (/ y t) (/ z (+ a 1.0))))
   (if (<= t 2.35e-180)
     (/ (+ z (/ (* x t) y)) b)
     (/ (+ x (/ z (/ t y))) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.5e-57) {
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	} else if (t <= 2.35e-180) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-8.5d-57)) then
        tmp = (x / (a + 1.0d0)) + ((y / t) * (z / (a + 1.0d0)))
    else if (t <= 2.35d-180) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + (z / (t / y))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.5e-57) {
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	} else if (t <= 2.35e-180) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8.5e-57:
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)))
	elif t <= 2.35e-180:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + (z / (t / y))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.5e-57)
		tmp = Float64(Float64(x / Float64(a + 1.0)) + Float64(Float64(y / t) * Float64(z / Float64(a + 1.0))));
	elseif (t <= 2.35e-180)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -8.5e-57)
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	elseif (t <= 2.35e-180)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + (z / (t / y))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.5e-57], N[(N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.35e-180], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.49999999999999955e-57

   1. Initial program 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-/l* 90.0%

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in x around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. times-frac 94.8%

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

      3. fma-define 94.8%

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

      4. +-commutative 94.8%

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

      5. associate-*l/ 94.8%

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

      6. *-commutative 94.8%

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

      7. fma-define 94.8%

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

      8. +-commutative 94.8%

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

      9. associate-*l/ 98.4%

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

      10. *-commutative 98.4%

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

      11. fma-define 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in b around 0 70.1%

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

      1. times-frac 80.1%

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

   10. Simplified 80.1%

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

   if -8.49999999999999955e-57 < t < 2.34999999999999988e-180

   1. Initial program 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 59.5%

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

   4. Applied egg-rr 59.5%

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

   5. Taylor expanded in x around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. times-frac 62.0%

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

      3. fma-define 62.0%

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

      4. +-commutative 62.0%

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

      5. associate-*l/ 54.6%

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

      6. *-commutative 54.6%

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

      7. fma-define 54.6%

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

      8. +-commutative 54.6%

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

      9. associate-*l/ 50.6%

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

      10. *-commutative 50.6%

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

      11. fma-define 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in b around inf 62.6%

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

      1. *-commutative 62.6%

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

   10. Simplified 62.6%

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

   if 2.34999999999999988e-180 < t

   1. Initial program 76.6%

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

      1. associate-/l* 81.3%

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

      2. associate-/l* 83.2%

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

   3. Simplified 83.2%

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

      1. associate-*r/ 77.6%

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

      2. clear-num 77.5%

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

   6. Applied egg-rr 77.5%

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

   7. Taylor expanded in y around 0 67.5%

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

      1. *-un-lft-identity 67.5%

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

      2. clear-num 67.5%

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

      3. *-commutative 67.5%

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

      4. associate-*r/ 73.1%

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

      5. clear-num 73.1%

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

      6. un-div-inv 73.1%

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

   9. Applied egg-rr 73.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a + 1} + \frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-180}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+16} \lor \neg \left(t \leq 2.6 \cdot 10^{-166}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3e+16) (not (<= t 2.6e-166))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e+16) || !(t <= 2.6e-166)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3d+16)) .or. (.not. (t <= 2.6d-166))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e+16) || !(t <= 2.6e-166)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3e+16) or not (t <= 2.6e-166):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3e+16) || !(t <= 2.6e-166))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3e+16) || ~((t <= 2.6e-166)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3e+16], N[Not[LessEqual[t, 2.6e-166]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e16 or 2.59999999999999989e-166 < t

   1. Initial program 80.2%

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

      1. associate-/l* 85.1%

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

      2. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in y around 0 55.9%

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

   if -3e16 < t < 2.59999999999999989e-166

   1. Initial program 67.3%

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

      1. associate-/l* 64.2%

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

      2. associate-/l* 57.2%

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

   3. Simplified 57.2%

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

   5. Taylor expanded in y around inf 51.5%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+16} \lor \neg \left(t \leq 2.6 \cdot 10^{-166}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 40.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+15} \lor \neg \left(a \leq 10^{+60}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.5e+15) (not (<= a 1e+60))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.5e+15) || !(a <= 1e+60)) {
		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 <= (-2.5d+15)) .or. (.not. (a <= 1d+60))) 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 <= -2.5e+15) || !(a <= 1e+60)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.5e+15) or not (a <= 1e+60):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.5e+15) || !(a <= 1e+60))
		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 <= -2.5e+15) || ~((a <= 1e+60)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.5e+15], N[Not[LessEqual[a, 1e+60]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -2.5e15 or 9.9999999999999995e59 < a

   1. Initial program 75.3%

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

      1. associate-/l* 80.1%

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

      2. associate-/l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in x around inf 53.4%

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

   6. Taylor expanded in a around inf 51.9%

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

   if -2.5e15 < a < 9.9999999999999995e59

   1. Initial program 75.5%

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

      1. associate-/l* 74.9%

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

      2. associate-/l* 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in x around inf 47.7%

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

   6. Taylor expanded in a around 0 46.2%

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

   7. Taylor expanded in b around 0 32.4%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+15} \lor \neg \left(a \leq 10^{+60}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 20.0% 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 75.4%

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

   1. associate-/l* 77.3%

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

   2. associate-/l* 76.6%

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

3. Simplified 76.6%

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

5. Taylor expanded in x around inf 50.4%

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

6. Taylor expanded in a around 0 27.7%

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

7. Taylor expanded in b around 0 18.8%

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

8. Final simplification 18.8%

   \[\leadsto x \]
9. Add Preprocessing

Developer target: 79.7% 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 2024078 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (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))))