Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 85.7% → 97.7%

Time: 15.1s

Alternatives: 15

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- x (* y z)) (- t (* a z))))

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (x - (y * z)) / (t - (a * z))
end function

Java

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

Python

def code(x, y, z, t, a):
	return (x - (y * z)) / (t - (a * z))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)))
end

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- x (* y z)) (- t (* a z))))

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (x - (y * z)) / (t - (a * z))
end function

Java

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

Python

def code(x, y, z, t, a):
	return (x - (y * z)) / (t - (a * z))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)))
end

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := x - y \cdot z\\ t_3 := \frac{y \cdot z}{t\_1} - \frac{x}{t\_1}\\ t_4 := t - z \cdot a\\ t_5 := y \cdot \left(\frac{z}{t\_1} + \frac{x}{y \cdot t\_4}\right)\\ t_6 := \frac{t\_2}{t\_4}\\ \mathbf{if}\;t\_6 \leq -1 \cdot 10^{+270}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_6 \leq -2 \cdot 10^{-218}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_6 \leq 0:\\ \;\;\;\;\frac{\frac{t\_2}{\frac{t}{a} - z}}{a}\\ \mathbf{elif}\;t\_6 \leq 10^{+247}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_6 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t))
        (t_2 (- x (* y z)))
        (t_3 (- (/ (* y z) t_1) (/ x t_1)))
        (t_4 (- t (* z a)))
        (t_5 (* y (+ (/ z t_1) (/ x (* y t_4)))))
        (t_6 (/ t_2 t_4)))
   (if (<= t_6 -1e+270)
     t_5
     (if (<= t_6 -2e-218)
       t_3
       (if (<= t_6 0.0)
         (/ (/ t_2 (- (/ t a) z)) a)
         (if (<= t_6 1e+247) t_3 (if (<= t_6 INFINITY) t_5 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = x - (y * z);
	double t_3 = ((y * z) / t_1) - (x / t_1);
	double t_4 = t - (z * a);
	double t_5 = y * ((z / t_1) + (x / (y * t_4)));
	double t_6 = t_2 / t_4;
	double tmp;
	if (t_6 <= -1e+270) {
		tmp = t_5;
	} else if (t_6 <= -2e-218) {
		tmp = t_3;
	} else if (t_6 <= 0.0) {
		tmp = (t_2 / ((t / a) - z)) / a;
	} else if (t_6 <= 1e+247) {
		tmp = t_3;
	} else if (t_6 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = x - (y * z);
	double t_3 = ((y * z) / t_1) - (x / t_1);
	double t_4 = t - (z * a);
	double t_5 = y * ((z / t_1) + (x / (y * t_4)));
	double t_6 = t_2 / t_4;
	double tmp;
	if (t_6 <= -1e+270) {
		tmp = t_5;
	} else if (t_6 <= -2e-218) {
		tmp = t_3;
	} else if (t_6 <= 0.0) {
		tmp = (t_2 / ((t / a) - z)) / a;
	} else if (t_6 <= 1e+247) {
		tmp = t_3;
	} else if (t_6 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = x - (y * z)
	t_3 = ((y * z) / t_1) - (x / t_1)
	t_4 = t - (z * a)
	t_5 = y * ((z / t_1) + (x / (y * t_4)))
	t_6 = t_2 / t_4
	tmp = 0
	if t_6 <= -1e+270:
		tmp = t_5
	elif t_6 <= -2e-218:
		tmp = t_3
	elif t_6 <= 0.0:
		tmp = (t_2 / ((t / a) - z)) / a
	elif t_6 <= 1e+247:
		tmp = t_3
	elif t_6 <= math.inf:
		tmp = t_5
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(x - Float64(y * z))
	t_3 = Float64(Float64(Float64(y * z) / t_1) - Float64(x / t_1))
	t_4 = Float64(t - Float64(z * a))
	t_5 = Float64(y * Float64(Float64(z / t_1) + Float64(x / Float64(y * t_4))))
	t_6 = Float64(t_2 / t_4)
	tmp = 0.0
	if (t_6 <= -1e+270)
		tmp = t_5;
	elseif (t_6 <= -2e-218)
		tmp = t_3;
	elseif (t_6 <= 0.0)
		tmp = Float64(Float64(t_2 / Float64(Float64(t / a) - z)) / a);
	elseif (t_6 <= 1e+247)
		tmp = t_3;
	elseif (t_6 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = x - (y * z);
	t_3 = ((y * z) / t_1) - (x / t_1);
	t_4 = t - (z * a);
	t_5 = y * ((z / t_1) + (x / (y * t_4)));
	t_6 = t_2 / t_4;
	tmp = 0.0;
	if (t_6 <= -1e+270)
		tmp = t_5;
	elseif (t_6 <= -2e-218)
		tmp = t_3;
	elseif (t_6 <= 0.0)
		tmp = (t_2 / ((t / a) - z)) / a;
	elseif (t_6 <= 1e+247)
		tmp = t_3;
	elseif (t_6 <= Inf)
		tmp = t_5;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(N[(z / t$95$1), $MachinePrecision] + N[(x / N[(y * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$2 / t$95$4), $MachinePrecision]}, If[LessEqual[t$95$6, -1e+270], t$95$5, If[LessEqual[t$95$6, -2e-218], t$95$3, If[LessEqual[t$95$6, 0.0], N[(N[(t$95$2 / N[(N[(t / a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$6, 1e+247], t$95$3, If[LessEqual[t$95$6, Infinity], t$95$5, N[(y / a), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1e270 or 9.99999999999999952e246 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 71.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 71.1%

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

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

      3. cancel-sign-sub-inv 99.9%

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

      4. *-commutative 99.9%

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

      5. +-commutative 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-lft-neg-in 99.9%

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

      8. distribute-rgt-neg-in 99.9%

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

      9. fma-undefine 99.9%

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

      10. neg-sub0 99.9%

          \[\leadsto y \cdot \left(\frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      11. fma-undefine 99.9%

          \[\leadsto y \cdot \left(\frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      12. distribute-rgt-neg-in 99.9%

          \[\leadsto y \cdot \left(\frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      13. distribute-lft-neg-in 99.9%

          \[\leadsto y \cdot \left(\frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      14. *-commutative 99.9%

          \[\leadsto y \cdot \left(\frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      15. associate--r+ 99.9%

          \[\leadsto y \cdot \left(\frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      16. neg-sub0 99.9%

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

      17. distribute-rgt-neg-out 99.9%

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

      18. remove-double-neg 99.9%

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

   7. Simplified 99.9%

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

   if -1e270 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -2.0000000000000001e-218 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 9.99999999999999952e246

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.7%

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

   if -2.0000000000000001e-218 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 69.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 69.4%

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

   3. Simplified 69.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 69.4%

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

      1. *-un-lft-identity 69.4%

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

      2. times-frac 99.6%

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

      3. *-commutative 99.6%

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

   7. Applied egg-rr 99.6%

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

      1. associate-*l/ 99.8%

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

      2. *-un-lft-identity 99.8%

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

   9. Applied egg-rr 99.8%

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

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

   1. Initial program 0.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{+270}:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{-218}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{x - y \cdot z}{\frac{t}{a} - z}}{a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+247}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{z}{t\_1}\\ t_3 := x - y \cdot z\\ t_4 := t - z \cdot a\\ t_5 := \frac{t\_3}{t\_4}\\ t_6 := \sqrt[3]{t\_4}\\ \mathbf{if}\;t\_5 \leq -1 \cdot 10^{+270}:\\ \;\;\;\;y \cdot \left(t\_2 + \frac{x}{y \cdot t\_4}\right)\\ \mathbf{elif}\;t\_5 \leq -2 \cdot 10^{-218}:\\ \;\;\;\;\frac{y \cdot z}{t\_1} - \frac{x}{t\_1}\\ \mathbf{elif}\;t\_5 \leq 10^{-296}:\\ \;\;\;\;\frac{\frac{t\_3}{\frac{t}{a} - z}}{a}\\ \mathbf{elif}\;t\_5 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{{t\_6}^{2}}, \frac{x}{t\_6}, y \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t))
        (t_2 (/ z t_1))
        (t_3 (- x (* y z)))
        (t_4 (- t (* z a)))
        (t_5 (/ t_3 t_4))
        (t_6 (cbrt t_4)))
   (if (<= t_5 -1e+270)
     (* y (+ t_2 (/ x (* y t_4))))
     (if (<= t_5 -2e-218)
       (- (/ (* y z) t_1) (/ x t_1))
       (if (<= t_5 1e-296)
         (/ (/ t_3 (- (/ t a) z)) a)
         (if (<= t_5 INFINITY)
           (fma (/ 1.0 (pow t_6 2.0)) (/ x t_6) (* y t_2))
           (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = z / t_1;
	double t_3 = x - (y * z);
	double t_4 = t - (z * a);
	double t_5 = t_3 / t_4;
	double t_6 = cbrt(t_4);
	double tmp;
	if (t_5 <= -1e+270) {
		tmp = y * (t_2 + (x / (y * t_4)));
	} else if (t_5 <= -2e-218) {
		tmp = ((y * z) / t_1) - (x / t_1);
	} else if (t_5 <= 1e-296) {
		tmp = (t_3 / ((t / a) - z)) / a;
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = fma((1.0 / pow(t_6, 2.0)), (x / t_6), (y * t_2));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(z / t_1)
	t_3 = Float64(x - Float64(y * z))
	t_4 = Float64(t - Float64(z * a))
	t_5 = Float64(t_3 / t_4)
	t_6 = cbrt(t_4)
	tmp = 0.0
	if (t_5 <= -1e+270)
		tmp = Float64(y * Float64(t_2 + Float64(x / Float64(y * t_4))));
	elseif (t_5 <= -2e-218)
		tmp = Float64(Float64(Float64(y * z) / t_1) - Float64(x / t_1));
	elseif (t_5 <= 1e-296)
		tmp = Float64(Float64(t_3 / Float64(Float64(t / a) - z)) / a);
	elseif (t_5 <= Inf)
		tmp = fma(Float64(1.0 / (t_6 ^ 2.0)), Float64(x / t_6), Float64(y * t_2));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(z / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 / t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[Power[t$95$4, 1/3], $MachinePrecision]}, If[LessEqual[t$95$5, -1e+270], N[(y * N[(t$95$2 + N[(x / N[(y * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, -2e-218], N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 1e-296], N[(N[(t$95$3 / N[(N[(t / a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$5, Infinity], N[(N[(1.0 / N[Power[t$95$6, 2.0], $MachinePrecision]), $MachinePrecision] * N[(x / t$95$6), $MachinePrecision] + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1e270

   1. Initial program 71.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 71.6%

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

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-neg-frac2 99.8%

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

      3. cancel-sign-sub-inv 99.8%

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

      4. *-commutative 99.8%

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

      5. +-commutative 99.8%

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

      6. *-commutative 99.8%

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

      7. distribute-lft-neg-in 99.8%

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

      8. distribute-rgt-neg-in 99.8%

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

      9. fma-undefine 99.8%

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

      10. neg-sub0 99.8%

          \[\leadsto y \cdot \left(\frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      11. fma-undefine 99.8%

          \[\leadsto y \cdot \left(\frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      12. distribute-rgt-neg-in 99.8%

          \[\leadsto y \cdot \left(\frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      13. distribute-lft-neg-in 99.8%

          \[\leadsto y \cdot \left(\frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      14. *-commutative 99.8%

          \[\leadsto y \cdot \left(\frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      15. associate--r+ 99.8%

          \[\leadsto y \cdot \left(\frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      16. neg-sub0 99.8%

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

      17. distribute-rgt-neg-out 99.8%

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

      18. remove-double-neg 99.8%

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

   7. Simplified 99.8%

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

   if -1e270 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -2.0000000000000001e-218

   1. Initial program 99.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.7%

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

   if -2.0000000000000001e-218 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1e-296

   1. Initial program 70.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 70.1%

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

   3. Simplified 70.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 70.1%

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

      1. *-un-lft-identity 70.1%

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

      2. times-frac 99.6%

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

      3. *-commutative 99.6%

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

   7. Applied egg-rr 99.6%

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

      1. associate-*l/ 99.7%

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

      2. *-un-lft-identity 99.7%

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

   9. Applied egg-rr 99.7%

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

   if 1e-296 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 95.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 95.7%

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

   3. Simplified 95.7%

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

      1. div-sub 95.8%

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

      2. *-un-lft-identity 95.8%

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

      3. add-cube-cbrt 94.9%

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

      4. times-frac 94.8%

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

      5. fmm-def 94.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\sqrt[3]{t - z \cdot a} \cdot \sqrt[3]{t - z \cdot a}}, \frac{x}{\sqrt[3]{t - z \cdot a}}, -\frac{y \cdot z}{t - z \cdot a}\right)} \]

   6. Applied egg-rr 94.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{{\left(\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}\right)}^{2}}, \frac{x}{\sqrt[3]{\mathsf{fma}\left(a, -z, t\right)}}, -\frac{y \cdot z}{\mathsf{fma}\left(a, -z, t\right)}\right)} \]

   8. Simplified 97.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{{\left(\sqrt[3]{t - z \cdot a}\right)}^{2}}, \frac{x}{\sqrt[3]{t - z \cdot a}}, y \cdot \frac{z}{z \cdot a - t}\right)} \]

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

   1. Initial program 0.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{\frac{y}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{+270}:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{-218}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{-296}:\\ \;\;\;\;\frac{\frac{x - y \cdot z}{\frac{t}{a} - z}}{a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{{\left(\sqrt[3]{t - z \cdot a}\right)}^{2}}, \frac{x}{\sqrt[3]{t - z \cdot a}}, y \cdot \frac{z}{z \cdot a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t - z \cdot a\\ t_3 := y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot t\_2}\right)\\ t_4 := \frac{t\_1}{t\_2}\\ \mathbf{if}\;t\_4 \leq -1 \cdot 10^{+270}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq -2 \cdot 10^{-218}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;\frac{\frac{t\_1}{\frac{t}{a} - z}}{a}\\ \mathbf{elif}\;t\_4 \leq 10^{+247}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y z)))
        (t_2 (- t (* z a)))
        (t_3 (* y (+ (/ z (- (* z a) t)) (/ x (* y t_2)))))
        (t_4 (/ t_1 t_2)))
   (if (<= t_4 -1e+270)
     t_3
     (if (<= t_4 -2e-218)
       t_4
       (if (<= t_4 0.0)
         (/ (/ t_1 (- (/ t a) z)) a)
         (if (<= t_4 1e+247) t_4 (if (<= t_4 INFINITY) t_3 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t - (z * a);
	double t_3 = y * ((z / ((z * a) - t)) + (x / (y * t_2)));
	double t_4 = t_1 / t_2;
	double tmp;
	if (t_4 <= -1e+270) {
		tmp = t_3;
	} else if (t_4 <= -2e-218) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = (t_1 / ((t / a) - z)) / a;
	} else if (t_4 <= 1e+247) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t - (z * a);
	double t_3 = y * ((z / ((z * a) - t)) + (x / (y * t_2)));
	double t_4 = t_1 / t_2;
	double tmp;
	if (t_4 <= -1e+270) {
		tmp = t_3;
	} else if (t_4 <= -2e-218) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = (t_1 / ((t / a) - z)) / a;
	} else if (t_4 <= 1e+247) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * z)
	t_2 = t - (z * a)
	t_3 = y * ((z / ((z * a) - t)) + (x / (y * t_2)))
	t_4 = t_1 / t_2
	tmp = 0
	if t_4 <= -1e+270:
		tmp = t_3
	elif t_4 <= -2e-218:
		tmp = t_4
	elif t_4 <= 0.0:
		tmp = (t_1 / ((t / a) - z)) / a
	elif t_4 <= 1e+247:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t - Float64(z * a))
	t_3 = Float64(y * Float64(Float64(z / Float64(Float64(z * a) - t)) + Float64(x / Float64(y * t_2))))
	t_4 = Float64(t_1 / t_2)
	tmp = 0.0
	if (t_4 <= -1e+270)
		tmp = t_3;
	elseif (t_4 <= -2e-218)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(t_1 / Float64(Float64(t / a) - z)) / a);
	elseif (t_4 <= 1e+247)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * z);
	t_2 = t - (z * a);
	t_3 = y * ((z / ((z * a) - t)) + (x / (y * t_2)));
	t_4 = t_1 / t_2;
	tmp = 0.0;
	if (t_4 <= -1e+270)
		tmp = t_3;
	elseif (t_4 <= -2e-218)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = (t_1 / ((t / a) - z)) / a;
	elseif (t_4 <= 1e+247)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, -1e+270], t$95$3, If[LessEqual[t$95$4, -2e-218], t$95$4, If[LessEqual[t$95$4, 0.0], N[(N[(t$95$1 / N[(N[(t / a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$4, 1e+247], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$3, N[(y / a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1e270 or 9.99999999999999952e246 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 71.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 71.1%

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

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

      3. cancel-sign-sub-inv 99.9%

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

      4. *-commutative 99.9%

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

      5. +-commutative 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-lft-neg-in 99.9%

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

      8. distribute-rgt-neg-in 99.9%

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

      9. fma-undefine 99.9%

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

      10. neg-sub0 99.9%

          \[\leadsto y \cdot \left(\frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      11. fma-undefine 99.9%

          \[\leadsto y \cdot \left(\frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      12. distribute-rgt-neg-in 99.9%

          \[\leadsto y \cdot \left(\frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      13. distribute-lft-neg-in 99.9%

          \[\leadsto y \cdot \left(\frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      14. *-commutative 99.9%

          \[\leadsto y \cdot \left(\frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      15. associate--r+ 99.9%

          \[\leadsto y \cdot \left(\frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right) \]

      16. neg-sub0 99.9%

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

      17. distribute-rgt-neg-out 99.9%

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

      18. remove-double-neg 99.9%

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

   7. Simplified 99.9%

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

   if -1e270 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -2.0000000000000001e-218 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 9.99999999999999952e246

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   if -2.0000000000000001e-218 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 69.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 69.4%

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

   3. Simplified 69.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 69.4%

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

      1. *-un-lft-identity 69.4%

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

      2. times-frac 99.6%

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

      3. *-commutative 99.6%

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

   7. Applied egg-rr 99.6%

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

      1. associate-*l/ 99.8%

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

      2. *-un-lft-identity 99.8%

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

   9. Applied egg-rr 99.8%

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

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

   1. Initial program 0.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{+270}:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{-218}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{x - y \cdot z}{\frac{t}{a} - z}}{a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+247}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := \frac{t\_1}{t - z \cdot a}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-218}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{\frac{t\_1}{\frac{t}{a} - z}}{a}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+277}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (/ t_1 (- t (* z a)))))
   (if (<= t_2 -2e-218)
     t_2
     (if (<= t_2 0.0)
       (/ (/ t_1 (- (/ t a) z)) a)
       (if (<= t_2 5e+277)
         t_2
         (if (<= t_2 INFINITY) (* z (/ y (- (* z a) t))) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t_1 / (t - (z * a));
	double tmp;
	if (t_2 <= -2e-218) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (t_1 / ((t / a) - z)) / a;
	} else if (t_2 <= 5e+277) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = z * (y / ((z * a) - t));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t_1 / (t - (z * a));
	double tmp;
	if (t_2 <= -2e-218) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (t_1 / ((t / a) - z)) / a;
	} else if (t_2 <= 5e+277) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = z * (y / ((z * a) - t));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * z)
	t_2 = t_1 / (t - (z * a))
	tmp = 0
	if t_2 <= -2e-218:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (t_1 / ((t / a) - z)) / a
	elif t_2 <= 5e+277:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = z * (y / ((z * a) - t))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t_1 / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_2 <= -2e-218)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(t_1 / Float64(Float64(t / a) - z)) / a);
	elseif (t_2 <= 5e+277)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(z * Float64(y / Float64(Float64(z * a) - t)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * z);
	t_2 = t_1 / (t - (z * a));
	tmp = 0.0;
	if (t_2 <= -2e-218)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (t_1 / ((t / a) - z)) / a;
	elseif (t_2 <= 5e+277)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = z * (y / ((z * a) - t));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-218], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(t$95$1 / N[(N[(t / a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$2, 5e+277], t$95$2, If[LessEqual[t$95$2, Infinity], N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -2.0000000000000001e-218 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 4.99999999999999982e277

   1. Initial program 96.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   if -2.0000000000000001e-218 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 69.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 69.4%

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

   3. Simplified 69.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 69.4%

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

      1. *-un-lft-identity 69.4%

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

      2. times-frac 99.6%

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

      3. *-commutative 99.6%

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

   7. Applied egg-rr 99.6%

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

      1. associate-*l/ 99.8%

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

      2. *-un-lft-identity 99.8%

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

   9. Applied egg-rr 99.8%

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

   if 4.99999999999999982e277 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 66.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 66.2%

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

   3. Simplified 66.2%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 52.7%

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

      1. mul-1-neg 52.7%

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

      2. associate-/l* 86.5%

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

      3. distribute-rgt-neg-in 86.5%

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

      4. distribute-neg-frac2 86.5%

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

      5. cancel-sign-sub-inv 86.5%

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

      6. *-commutative 86.5%

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

      7. +-commutative 86.5%

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

      8. *-commutative 86.5%

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

      9. distribute-lft-neg-in 86.5%

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

      10. distribute-rgt-neg-in 86.5%

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

      11. fma-undefine 86.5%

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

      12. neg-sub0 86.5%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 86.5%

          \[\leadsto y \cdot \frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} \]

      14. distribute-rgt-neg-in 86.5%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} \]

      15. distribute-lft-neg-in 86.5%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} \]

      16. *-commutative 86.5%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} \]

      17. associate--r+ 86.5%

          \[\leadsto y \cdot \frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} \]

      18. neg-sub0 86.5%

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

      19. distribute-rgt-neg-out 86.5%

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

      20. remove-double-neg 86.5%

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

   7. Simplified 86.5%

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

      1. clear-num 86.4%

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

      2. un-div-inv 86.5%

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

      3. fmm-def 86.5%

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

   9. Applied egg-rr 86.5%

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

       1. associate-/r/ 99.9%

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

       2. fmm-undef 99.9%

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

       3. *-commutative 99.9%

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

   11. Simplified 99.9%

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

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

   1. Initial program 0.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{-218}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{x - y \cdot z}{\frac{t}{a} - z}}{a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+277}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+46}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+42)
   (/ y a)
   (if (<= z -1.6e-132)
     (/ (* y z) (- t))
     (if (<= z -7.5e-202)
       (/ x (* z (- a)))
       (if (<= z 1.8e-172)
         (/ x t)
         (if (<= z 1.3e+46) (* (* y z) (/ -1.0 t)) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+42) {
		tmp = y / a;
	} else if (z <= -1.6e-132) {
		tmp = (y * z) / -t;
	} else if (z <= -7.5e-202) {
		tmp = x / (z * -a);
	} else if (z <= 1.8e-172) {
		tmp = x / t;
	} else if (z <= 1.3e+46) {
		tmp = (y * z) * (-1.0 / t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-7.5d+42)) then
        tmp = y / a
    else if (z <= (-1.6d-132)) then
        tmp = (y * z) / -t
    else if (z <= (-7.5d-202)) then
        tmp = x / (z * -a)
    else if (z <= 1.8d-172) then
        tmp = x / t
    else if (z <= 1.3d+46) then
        tmp = (y * z) * ((-1.0d0) / t)
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+42) {
		tmp = y / a;
	} else if (z <= -1.6e-132) {
		tmp = (y * z) / -t;
	} else if (z <= -7.5e-202) {
		tmp = x / (z * -a);
	} else if (z <= 1.8e-172) {
		tmp = x / t;
	} else if (z <= 1.3e+46) {
		tmp = (y * z) * (-1.0 / t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+42:
		tmp = y / a
	elif z <= -1.6e-132:
		tmp = (y * z) / -t
	elif z <= -7.5e-202:
		tmp = x / (z * -a)
	elif z <= 1.8e-172:
		tmp = x / t
	elif z <= 1.3e+46:
		tmp = (y * z) * (-1.0 / t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+42)
		tmp = Float64(y / a);
	elseif (z <= -1.6e-132)
		tmp = Float64(Float64(y * z) / Float64(-t));
	elseif (z <= -7.5e-202)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 1.8e-172)
		tmp = Float64(x / t);
	elseif (z <= 1.3e+46)
		tmp = Float64(Float64(y * z) * Float64(-1.0 / t));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+42)
		tmp = y / a;
	elseif (z <= -1.6e-132)
		tmp = (y * z) / -t;
	elseif (z <= -7.5e-202)
		tmp = x / (z * -a);
	elseif (z <= 1.8e-172)
		tmp = x / t;
	elseif (z <= 1.3e+46)
		tmp = (y * z) * (-1.0 / t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+42], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.6e-132], N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, -7.5e-202], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-172], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.3e+46], N[(N[(y * z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.50000000000000041e42 or 1.30000000000000007e46 < z

   1. Initial program 71.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 71.7%

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

   3. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.2%

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

   if -7.50000000000000041e42 < z < -1.6000000000000001e-132

   1. Initial program 97.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 49.3%

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

      1. mul-1-neg 49.3%

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

      2. associate-/l* 46.3%

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

      3. distribute-rgt-neg-in 46.3%

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

      4. distribute-neg-frac2 46.3%

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

      5. cancel-sign-sub-inv 46.3%

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

      6. *-commutative 46.3%

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

      7. +-commutative 46.3%

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

      8. *-commutative 46.3%

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

      9. distribute-lft-neg-in 46.3%

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

      10. distribute-rgt-neg-in 46.3%

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

      11. fma-undefine 46.3%

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

      12. neg-sub0 46.3%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 46.3%

          \[\leadsto y \cdot \frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} \]

      14. distribute-rgt-neg-in 46.3%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} \]

      15. distribute-lft-neg-in 46.3%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} \]

      16. *-commutative 46.3%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} \]

      17. associate--r+ 46.3%

          \[\leadsto y \cdot \frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} \]

      18. neg-sub0 46.3%

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

      19. distribute-rgt-neg-out 46.3%

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

      20. remove-double-neg 46.3%

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

   7. Simplified 46.3%

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

   8. Taylor expanded in z around 0 42.0%

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

      1. associate-*r/ 42.0%

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

      2. associate-*r* 42.0%

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

      3. neg-mul-1 42.0%

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

      4. *-commutative 42.0%

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

   10. Simplified 42.0%

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

   if -1.6000000000000001e-132 < z < -7.50000000000000005e-202

   1. Initial program 99.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.6%

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

      1. associate-*r/ 81.6%

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

      2. neg-mul-1 81.6%

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

      3. neg-sub0 81.6%

         \[\leadsto \frac{\color{blue}{0 - \left(x - y \cdot z\right)}}{a \cdot z} \]

      4. sub-neg 81.6%

         \[\leadsto \frac{0 - \color{blue}{\left(x + \left(-y \cdot z\right)\right)}}{a \cdot z} \]

      5. distribute-rgt-neg-out 81.6%

         \[\leadsto \frac{0 - \left(x + \color{blue}{y \cdot \left(-z\right)}\right)}{a \cdot z} \]

      6. +-commutative 81.6%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot \left(-z\right) + x\right)}}{a \cdot z} \]

      7. associate--r+ 81.6%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot \left(-z\right)\right) - x}}{a \cdot z} \]

      8. neg-sub0 81.6%

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

      9. distribute-rgt-neg-out 81.6%

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

      10. remove-double-neg 81.6%

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

      11. *-commutative 81.6%

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

   7. Simplified 81.6%

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

   8. Taylor expanded in y around 0 63.9%

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

      1. neg-mul-1 63.9%

         \[\leadsto \frac{\color{blue}{-x}}{z \cdot a} \]

   10. Simplified 63.9%

       \[\leadsto \frac{\color{blue}{-x}}{z \cdot a} \]

   if -7.50000000000000005e-202 < z < 1.80000000000000007e-172

   1. Initial program 99.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 72.7%

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

   if 1.80000000000000007e-172 < z < 1.30000000000000007e46

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 57.2%

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

      1. mul-1-neg 57.2%

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

      2. associate-/l* 50.4%

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

      3. distribute-rgt-neg-in 50.4%

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

      4. distribute-neg-frac2 50.4%

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

      5. cancel-sign-sub-inv 50.4%

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

      6. *-commutative 50.4%

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

      7. +-commutative 50.4%

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

      8. *-commutative 50.4%

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

      9. distribute-lft-neg-in 50.4%

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

      10. distribute-rgt-neg-in 50.4%

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

      11. fma-undefine 50.4%

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

      12. neg-sub0 50.4%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 50.4%

          \[\leadsto y \cdot \frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} \]

      14. distribute-rgt-neg-in 50.4%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} \]

      15. distribute-lft-neg-in 50.4%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} \]

      16. *-commutative 50.4%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} \]

      17. associate--r+ 50.4%

          \[\leadsto y \cdot \frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} \]

      18. neg-sub0 50.4%

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

      19. distribute-rgt-neg-out 50.4%

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

      20. remove-double-neg 50.4%

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

   7. Simplified 50.4%

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

      1. associate-*r/ 57.2%

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

      2. clear-num 57.2%

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

      3. fmm-def 57.2%

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

      4. *-commutative 57.2%

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

   9. Applied egg-rr 57.2%

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

       1. associate-/r/ 57.3%

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

       2. fmm-undef 57.3%

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

       3. *-commutative 57.3%

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

   11. Simplified 57.3%

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

   12. Taylor expanded in a around 0 45.2%

       \[\leadsto \color{blue}{\frac{-1}{t}} \cdot \left(z \cdot y\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+46}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+164}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+22} \lor \neg \left(t \leq 2.9 \cdot 10^{+125}\right):\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e+164)
   (* y (/ z (- t)))
   (if (<= t -7.2e-87)
     (/ x t)
     (if (<= t 1.25e-66)
       (/ y a)
       (if (or (<= t 2.9e+22) (not (<= t 2.9e+125)))
         (/ x t)
         (* z (/ (- y) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e+164) {
		tmp = y * (z / -t);
	} else if (t <= -7.2e-87) {
		tmp = x / t;
	} else if (t <= 1.25e-66) {
		tmp = y / a;
	} else if ((t <= 2.9e+22) || !(t <= 2.9e+125)) {
		tmp = x / t;
	} else {
		tmp = z * (-y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (t <= (-9.5d+164)) then
        tmp = y * (z / -t)
    else if (t <= (-7.2d-87)) then
        tmp = x / t
    else if (t <= 1.25d-66) then
        tmp = y / a
    else if ((t <= 2.9d+22) .or. (.not. (t <= 2.9d+125))) then
        tmp = x / t
    else
        tmp = z * (-y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e+164) {
		tmp = y * (z / -t);
	} else if (t <= -7.2e-87) {
		tmp = x / t;
	} else if (t <= 1.25e-66) {
		tmp = y / a;
	} else if ((t <= 2.9e+22) || !(t <= 2.9e+125)) {
		tmp = x / t;
	} else {
		tmp = z * (-y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e+164:
		tmp = y * (z / -t)
	elif t <= -7.2e-87:
		tmp = x / t
	elif t <= 1.25e-66:
		tmp = y / a
	elif (t <= 2.9e+22) or not (t <= 2.9e+125):
		tmp = x / t
	else:
		tmp = z * (-y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e+164)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (t <= -7.2e-87)
		tmp = Float64(x / t);
	elseif (t <= 1.25e-66)
		tmp = Float64(y / a);
	elseif ((t <= 2.9e+22) || !(t <= 2.9e+125))
		tmp = Float64(x / t);
	else
		tmp = Float64(z * Float64(Float64(-y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e+164)
		tmp = y * (z / -t);
	elseif (t <= -7.2e-87)
		tmp = x / t;
	elseif (t <= 1.25e-66)
		tmp = y / a;
	elseif ((t <= 2.9e+22) || ~((t <= 2.9e+125)))
		tmp = x / t;
	else
		tmp = z * (-y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e+164], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e-87], N[(x / t), $MachinePrecision], If[LessEqual[t, 1.25e-66], N[(y / a), $MachinePrecision], If[Or[LessEqual[t, 2.9e+22], N[Not[LessEqual[t, 2.9e+125]], $MachinePrecision]], N[(x / t), $MachinePrecision], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.49999999999999976e164

   1. Initial program 86.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.1%

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

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. associate-/l* 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

      4. distribute-neg-frac2 64.0%

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

      5. cancel-sign-sub-inv 64.0%

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

      6. *-commutative 64.0%

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

      7. +-commutative 64.0%

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

      8. *-commutative 64.0%

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

      9. distribute-lft-neg-in 64.0%

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

      10. distribute-rgt-neg-in 64.0%

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

      11. fma-undefine 64.0%

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

      12. neg-sub0 64.0%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 64.0%

          \[\leadsto y \cdot \frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} \]

      14. distribute-rgt-neg-in 64.0%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} \]

      15. distribute-lft-neg-in 64.0%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} \]

      16. *-commutative 64.0%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} \]

      17. associate--r+ 64.0%

          \[\leadsto y \cdot \frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} \]

      18. neg-sub0 64.0%

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

      19. distribute-rgt-neg-out 64.0%

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

      20. remove-double-neg 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in z around 0 58.3%

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

      1. associate-*r/ 58.3%

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

      2. neg-mul-1 58.3%

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

   10. Simplified 58.3%

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

   if -9.49999999999999976e164 < t < -7.19999999999999986e-87 or 1.2499999999999999e-66 < t < 2.9e22 or 2.89999999999999993e125 < t

   1. Initial program 92.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 55.5%

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

   if -7.19999999999999986e-87 < t < 1.2499999999999999e-66

   1. Initial program 85.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 85.8%

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

   3. Simplified 85.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 59.5%

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

   if 2.9e22 < t < 2.89999999999999993e125

   1. Initial program 84.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 84.1%

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

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 71.9%

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

   6. Taylor expanded in a around 0 55.7%

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

      1. *-commutative 55.7%

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

   8. Simplified 55.7%

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

   9. Taylor expanded in x around 0 39.9%

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

       1. mul-1-neg 39.9%

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

       2. *-commutative 39.9%

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

       3. associate-/l* 51.7%

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

       4. distribute-rgt-neg-in 51.7%

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

       5. mul-1-neg 51.7%

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

       6. associate-*r/ 51.7%

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

       7. neg-mul-1 51.7%

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

   11. Simplified 51.7%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+164}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+22} \lor \neg \left(t \leq 2.9 \cdot 10^{+125}\right):\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{-t}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) (- t))))
   (if (<= z -1e+40)
     (/ y a)
     (if (<= z -7.2e-135)
       t_1
       (if (<= z -7.5e-202)
         (/ x (* z (- a)))
         (if (<= z 2.5e-169) (/ x t) (if (<= z 3.2e+47) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / -t;
	double tmp;
	if (z <= -1e+40) {
		tmp = y / a;
	} else if (z <= -7.2e-135) {
		tmp = t_1;
	} else if (z <= -7.5e-202) {
		tmp = x / (z * -a);
	} else if (z <= 2.5e-169) {
		tmp = x / t;
	} else if (z <= 3.2e+47) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (y * z) / -t
    if (z <= (-1d+40)) then
        tmp = y / a
    else if (z <= (-7.2d-135)) then
        tmp = t_1
    else if (z <= (-7.5d-202)) then
        tmp = x / (z * -a)
    else if (z <= 2.5d-169) then
        tmp = x / t
    else if (z <= 3.2d+47) then
        tmp = t_1
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / -t;
	double tmp;
	if (z <= -1e+40) {
		tmp = y / a;
	} else if (z <= -7.2e-135) {
		tmp = t_1;
	} else if (z <= -7.5e-202) {
		tmp = x / (z * -a);
	} else if (z <= 2.5e-169) {
		tmp = x / t;
	} else if (z <= 3.2e+47) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / -t
	tmp = 0
	if z <= -1e+40:
		tmp = y / a
	elif z <= -7.2e-135:
		tmp = t_1
	elif z <= -7.5e-202:
		tmp = x / (z * -a)
	elif z <= 2.5e-169:
		tmp = x / t
	elif z <= 3.2e+47:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / Float64(-t))
	tmp = 0.0
	if (z <= -1e+40)
		tmp = Float64(y / a);
	elseif (z <= -7.2e-135)
		tmp = t_1;
	elseif (z <= -7.5e-202)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 2.5e-169)
		tmp = Float64(x / t);
	elseif (z <= 3.2e+47)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / -t;
	tmp = 0.0;
	if (z <= -1e+40)
		tmp = y / a;
	elseif (z <= -7.2e-135)
		tmp = t_1;
	elseif (z <= -7.5e-202)
		tmp = x / (z * -a);
	elseif (z <= 2.5e-169)
		tmp = x / t;
	elseif (z <= 3.2e+47)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision]}, If[LessEqual[z, -1e+40], N[(y / a), $MachinePrecision], If[LessEqual[z, -7.2e-135], t$95$1, If[LessEqual[z, -7.5e-202], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-169], N[(x / t), $MachinePrecision], If[LessEqual[z, 3.2e+47], t$95$1, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.00000000000000003e40 or 3.2e47 < z

   1. Initial program 71.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 71.7%

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

   3. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.2%

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

   if -1.00000000000000003e40 < z < -7.19999999999999955e-135 or 2.5000000000000001e-169 < z < 3.2e47

   1. Initial program 98.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 98.6%

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

   3. Simplified 98.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 53.7%

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

      1. mul-1-neg 53.7%

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

      2. associate-/l* 48.6%

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

      3. distribute-rgt-neg-in 48.6%

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

      4. distribute-neg-frac2 48.6%

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

      5. cancel-sign-sub-inv 48.6%

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

      6. *-commutative 48.6%

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

      7. +-commutative 48.6%

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

      8. *-commutative 48.6%

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

      9. distribute-lft-neg-in 48.6%

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

      10. distribute-rgt-neg-in 48.6%

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

      11. fma-undefine 48.6%

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

      12. neg-sub0 48.6%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 48.6%

          \[\leadsto y \cdot \frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} \]

      14. distribute-rgt-neg-in 48.6%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} \]

      15. distribute-lft-neg-in 48.6%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} \]

      16. *-commutative 48.6%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} \]

      17. associate--r+ 48.6%

          \[\leadsto y \cdot \frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} \]

      18. neg-sub0 48.6%

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

      19. distribute-rgt-neg-out 48.6%

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

      20. remove-double-neg 48.6%

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

   7. Simplified 48.6%

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

   8. Taylor expanded in z around 0 43.8%

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

      1. associate-*r/ 43.8%

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

      2. associate-*r* 43.8%

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

      3. neg-mul-1 43.8%

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

      4. *-commutative 43.8%

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

   10. Simplified 43.8%

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

   if -7.19999999999999955e-135 < z < -7.50000000000000005e-202

   1. Initial program 99.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.6%

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

      1. associate-*r/ 81.6%

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

      2. neg-mul-1 81.6%

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

      3. neg-sub0 81.6%

         \[\leadsto \frac{\color{blue}{0 - \left(x - y \cdot z\right)}}{a \cdot z} \]

      4. sub-neg 81.6%

         \[\leadsto \frac{0 - \color{blue}{\left(x + \left(-y \cdot z\right)\right)}}{a \cdot z} \]

      5. distribute-rgt-neg-out 81.6%

         \[\leadsto \frac{0 - \left(x + \color{blue}{y \cdot \left(-z\right)}\right)}{a \cdot z} \]

      6. +-commutative 81.6%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot \left(-z\right) + x\right)}}{a \cdot z} \]

      7. associate--r+ 81.6%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot \left(-z\right)\right) - x}}{a \cdot z} \]

      8. neg-sub0 81.6%

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

      9. distribute-rgt-neg-out 81.6%

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

      10. remove-double-neg 81.6%

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

      11. *-commutative 81.6%

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

   7. Simplified 81.6%

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

   8. Taylor expanded in y around 0 63.9%

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

      1. neg-mul-1 63.9%

         \[\leadsto \frac{\color{blue}{-x}}{z \cdot a} \]

   10. Simplified 63.9%

       \[\leadsto \frac{\color{blue}{-x}}{z \cdot a} \]

   if -7.50000000000000005e-202 < z < 2.5000000000000001e-169

   1. Initial program 99.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 72.7%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-135}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t)))
   (if (<= z -4.6e+41)
     (/ y a)
     (if (<= z -5.6e-132)
       t_1
       (if (<= z -2.15e-204)
         (/ x (- t (* z a)))
         (if (<= z 2.9e+47) t_1 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double tmp;
	if (z <= -4.6e+41) {
		tmp = y / a;
	} else if (z <= -5.6e-132) {
		tmp = t_1;
	} else if (z <= -2.15e-204) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.9e+47) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / t
    if (z <= (-4.6d+41)) then
        tmp = y / a
    else if (z <= (-5.6d-132)) then
        tmp = t_1
    else if (z <= (-2.15d-204)) then
        tmp = x / (t - (z * a))
    else if (z <= 2.9d+47) then
        tmp = t_1
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double tmp;
	if (z <= -4.6e+41) {
		tmp = y / a;
	} else if (z <= -5.6e-132) {
		tmp = t_1;
	} else if (z <= -2.15e-204) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.9e+47) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	tmp = 0
	if z <= -4.6e+41:
		tmp = y / a
	elif z <= -5.6e-132:
		tmp = t_1
	elif z <= -2.15e-204:
		tmp = x / (t - (z * a))
	elif z <= 2.9e+47:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (z <= -4.6e+41)
		tmp = Float64(y / a);
	elseif (z <= -5.6e-132)
		tmp = t_1;
	elseif (z <= -2.15e-204)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 2.9e+47)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / t;
	tmp = 0.0;
	if (z <= -4.6e+41)
		tmp = y / a;
	elseif (z <= -5.6e-132)
		tmp = t_1;
	elseif (z <= -2.15e-204)
		tmp = x / (t - (z * a));
	elseif (z <= 2.9e+47)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -4.6e+41], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.6e-132], t$95$1, If[LessEqual[z, -2.15e-204], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+47], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5999999999999997e41 or 2.8999999999999998e47 < z

   1. Initial program 71.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 71.7%

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

   3. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.2%

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

   if -4.5999999999999997e41 < z < -5.60000000000000005e-132 or -2.1500000000000001e-204 < z < 2.8999999999999998e47

   1. Initial program 99.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 76.1%

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

   if -5.60000000000000005e-132 < z < -2.1500000000000001e-204

   1. Initial program 99.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 81.6%

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

      1. *-commutative 81.6%

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

   7. Simplified 81.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+47}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+34}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-134}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+34)
   (/ y a)
   (if (<= z 4.3e-134)
     (/ x t)
     (if (<= z 9e-54)
       (* y (/ z (- t)))
       (if (<= z 1.12e+46) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+34) {
		tmp = y / a;
	} else if (z <= 4.3e-134) {
		tmp = x / t;
	} else if (z <= 9e-54) {
		tmp = y * (z / -t);
	} else if (z <= 1.12e+46) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-1.3d+34)) then
        tmp = y / a
    else if (z <= 4.3d-134) then
        tmp = x / t
    else if (z <= 9d-54) then
        tmp = y * (z / -t)
    else if (z <= 1.12d+46) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+34) {
		tmp = y / a;
	} else if (z <= 4.3e-134) {
		tmp = x / t;
	} else if (z <= 9e-54) {
		tmp = y * (z / -t);
	} else if (z <= 1.12e+46) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+34:
		tmp = y / a
	elif z <= 4.3e-134:
		tmp = x / t
	elif z <= 9e-54:
		tmp = y * (z / -t)
	elif z <= 1.12e+46:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+34)
		tmp = Float64(y / a);
	elseif (z <= 4.3e-134)
		tmp = Float64(x / t);
	elseif (z <= 9e-54)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= 1.12e+46)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+34)
		tmp = y / a;
	elseif (z <= 4.3e-134)
		tmp = x / t;
	elseif (z <= 9e-54)
		tmp = y * (z / -t);
	elseif (z <= 1.12e+46)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+34], N[(y / a), $MachinePrecision], If[LessEqual[z, 4.3e-134], N[(x / t), $MachinePrecision], If[LessEqual[z, 9e-54], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+46], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.29999999999999999e34 or 1.12e46 < z

   1. Initial program 72.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 72.2%

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

   3. Simplified 72.2%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 61.0%

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

   if -1.29999999999999999e34 < z < 4.29999999999999987e-134 or 8.9999999999999997e-54 < z < 1.12e46

   1. Initial program 99.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.0%

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 52.5%

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

   if 4.29999999999999987e-134 < z < 8.9999999999999997e-54

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. associate-/l* 64.2%

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

      3. distribute-rgt-neg-in 64.2%

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

      4. distribute-neg-frac2 64.2%

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

      5. cancel-sign-sub-inv 64.2%

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

      6. *-commutative 64.2%

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

      7. +-commutative 64.2%

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

      8. *-commutative 64.2%

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

      9. distribute-lft-neg-in 64.2%

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

      10. distribute-rgt-neg-in 64.2%

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

      11. fma-undefine 64.2%

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

      12. neg-sub0 64.2%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      13. fma-undefine 64.2%

          \[\leadsto y \cdot \frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} \]

      14. distribute-rgt-neg-in 64.2%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} \]

      15. distribute-lft-neg-in 64.2%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} \]

      16. *-commutative 64.2%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} \]

      17. associate--r+ 64.2%

          \[\leadsto y \cdot \frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} \]

      18. neg-sub0 64.2%

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

      19. distribute-rgt-neg-out 64.2%

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

      20. remove-double-neg 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in z around 0 52.4%

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

      1. associate-*r/ 52.4%

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

      2. neg-mul-1 52.4%

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

   10. Simplified 52.4%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+34}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-134}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-73}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t)))
   (if (<= t -3.7e-83)
     t_1
     (if (<= t 1.4e-73)
       (/ (- y (/ x z)) a)
       (if (<= t 4.5e-21) (/ x (- t (* z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double tmp;
	if (t <= -3.7e-83) {
		tmp = t_1;
	} else if (t <= 1.4e-73) {
		tmp = (y - (x / z)) / a;
	} else if (t <= 4.5e-21) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / t
    if (t <= (-3.7d-83)) then
        tmp = t_1
    else if (t <= 1.4d-73) then
        tmp = (y - (x / z)) / a
    else if (t <= 4.5d-21) then
        tmp = x / (t - (z * a))
    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 t_1 = (x - (y * z)) / t;
	double tmp;
	if (t <= -3.7e-83) {
		tmp = t_1;
	} else if (t <= 1.4e-73) {
		tmp = (y - (x / z)) / a;
	} else if (t <= 4.5e-21) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	tmp = 0
	if t <= -3.7e-83:
		tmp = t_1
	elif t <= 1.4e-73:
		tmp = (y - (x / z)) / a
	elif t <= 4.5e-21:
		tmp = x / (t - (z * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (t <= -3.7e-83)
		tmp = t_1;
	elseif (t <= 1.4e-73)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (t <= 4.5e-21)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / t;
	tmp = 0.0;
	if (t <= -3.7e-83)
		tmp = t_1;
	elseif (t <= 1.4e-73)
		tmp = (y - (x / z)) / a;
	elseif (t <= 4.5e-21)
		tmp = x / (t - (z * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -3.7e-83], t$95$1, If[LessEqual[t, 1.4e-73], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 4.5e-21], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.69999999999999995e-83 or 4.49999999999999968e-21 < t

   1. Initial program 88.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.8%

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

   if -3.69999999999999995e-83 < t < 1.40000000000000006e-73

   1. Initial program 86.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.0%

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

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 81.6%

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

   6. Taylor expanded in t around 0 76.6%

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

      1. associate-*r/ 76.6%

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

      2. distribute-lft-out-- 76.6%

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

      3. sub-neg 76.6%

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

      4. neg-mul-1 76.6%

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

      5. remove-double-neg 76.6%

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

      6. +-commutative 76.6%

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

      7. mul-1-neg 76.6%

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

      8. unsub-neg 76.6%

         \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   8. Simplified 76.6%

      \[\leadsto \color{blue}{\frac{y - \frac{x}{z}}{a}} \]

   if 1.40000000000000006e-73 < t < 4.49999999999999968e-21

   1. Initial program 99.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.0%

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

      1. *-commutative 86.0%

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

   7. Simplified 86.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-83}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-73}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;t \leq -4 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t)))
   (if (<= t -4e-83)
     t_1
     (if (<= t 3.3e-68)
       (- (/ y a) (/ x (* z a)))
       (if (<= t 4.5e-21) (/ x (- t (* z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double tmp;
	if (t <= -4e-83) {
		tmp = t_1;
	} else if (t <= 3.3e-68) {
		tmp = (y / a) - (x / (z * a));
	} else if (t <= 4.5e-21) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / t
    if (t <= (-4d-83)) then
        tmp = t_1
    else if (t <= 3.3d-68) then
        tmp = (y / a) - (x / (z * a))
    else if (t <= 4.5d-21) then
        tmp = x / (t - (z * a))
    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 t_1 = (x - (y * z)) / t;
	double tmp;
	if (t <= -4e-83) {
		tmp = t_1;
	} else if (t <= 3.3e-68) {
		tmp = (y / a) - (x / (z * a));
	} else if (t <= 4.5e-21) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	tmp = 0
	if t <= -4e-83:
		tmp = t_1
	elif t <= 3.3e-68:
		tmp = (y / a) - (x / (z * a))
	elif t <= 4.5e-21:
		tmp = x / (t - (z * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (t <= -4e-83)
		tmp = t_1;
	elseif (t <= 3.3e-68)
		tmp = Float64(Float64(y / a) - Float64(x / Float64(z * a)));
	elseif (t <= 4.5e-21)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / t;
	tmp = 0.0;
	if (t <= -4e-83)
		tmp = t_1;
	elseif (t <= 3.3e-68)
		tmp = (y / a) - (x / (z * a));
	elseif (t <= 4.5e-21)
		tmp = x / (t - (z * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -4e-83], t$95$1, If[LessEqual[t, 3.3e-68], N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-21], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.0000000000000001e-83 or 4.49999999999999968e-21 < t

   1. Initial program 88.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.8%

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

   if -4.0000000000000001e-83 < t < 3.2999999999999998e-68

   1. Initial program 86.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.0%

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

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 67.1%

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

      1. associate-*r/ 67.1%

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

      2. neg-mul-1 67.1%

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

      3. neg-sub0 67.1%

         \[\leadsto \frac{\color{blue}{0 - \left(x - y \cdot z\right)}}{a \cdot z} \]

      4. sub-neg 67.1%

         \[\leadsto \frac{0 - \color{blue}{\left(x + \left(-y \cdot z\right)\right)}}{a \cdot z} \]

      5. distribute-rgt-neg-out 67.1%

         \[\leadsto \frac{0 - \left(x + \color{blue}{y \cdot \left(-z\right)}\right)}{a \cdot z} \]

      6. +-commutative 67.1%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot \left(-z\right) + x\right)}}{a \cdot z} \]

      7. associate--r+ 67.1%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot \left(-z\right)\right) - x}}{a \cdot z} \]

      8. neg-sub0 67.1%

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

      9. distribute-rgt-neg-out 67.1%

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

      10. remove-double-neg 67.1%

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

      11. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in y around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. mul-1-neg 77.8%

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

      3. unsub-neg 77.8%

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

      4. *-commutative 77.8%

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

   10. Simplified 77.8%

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

   if 3.2999999999999998e-68 < t < 4.49999999999999968e-21

   1. Initial program 99.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.0%

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

      1. *-commutative 86.0%

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

   7. Simplified 86.0%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-83}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 90.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+216} \lor \neg \left(z \leq 5.2 \cdot 10^{+158}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e+216) (not (<= z 5.2e+158)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+216) || !(z <= 5.2e+158)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-8.5d+216)) .or. (.not. (z <= 5.2d+158))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+216) || !(z <= 5.2e+158)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.5e+216) or not (z <= 5.2e+158):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.5e+216) || !(z <= 5.2e+158))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.5e+216) || ~((z <= 5.2e+158)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.5e+216], N[Not[LessEqual[z, 5.2e+158]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999997e216 or 5.2e158 < z

   1. Initial program 62.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 62.3%

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

   3. Simplified 62.3%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.3%

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

   6. Taylor expanded in t around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. distribute-lft-out-- 83.7%

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

      3. sub-neg 83.7%

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

      4. neg-mul-1 83.7%

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

      5. remove-double-neg 83.7%

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

      6. +-commutative 83.7%

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

      7. mul-1-neg 83.7%

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

      8. unsub-neg 83.7%

         \[\leadsto \frac{\color{blue}{y - \frac{x}{z}}}{a} \]

   8. Simplified 83.7%

      \[\leadsto \color{blue}{\frac{y - \frac{x}{z}}{a}} \]

   if -8.4999999999999997e216 < z < 5.2e158

   1. Initial program 94.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+216} \lor \neg \left(z \leq 5.2 \cdot 10^{+158}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+37} \lor \neg \left(z \leq 3.5 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+37) (not (<= z 3.5e+46))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+37) || !(z <= 3.5e+46)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-2.8d+37)) .or. (.not. (z <= 3.5d+46))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+37) || !(z <= 3.5e+46)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+37) or not (z <= 3.5e+46):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+37) || !(z <= 3.5e+46))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.8e+37) || ~((z <= 3.5e+46)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+37], N[Not[LessEqual[z, 3.5e+46]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999998e37 or 3.49999999999999985e46 < z

   1. Initial program 71.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 71.7%

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

   3. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.2%

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

   if -2.7999999999999998e37 < z < 3.49999999999999985e46

   1. Initial program 99.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 63.7%

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

      1. *-commutative 63.7%

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

   7. Simplified 63.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+37} \lor \neg \left(z \leq 3.5 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+32} \lor \neg \left(z \leq 5 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.7e+32) (not (<= z 5e+46))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.7e+32) || !(z <= 5e+46)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-4.7d+32)) .or. (.not. (z <= 5d+46))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.7e+32) || !(z <= 5e+46)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.7e+32) or not (z <= 5e+46):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.7e+32) || !(z <= 5e+46))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.7e+32) || ~((z <= 5e+46)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.7e+32], N[Not[LessEqual[z, 5e+46]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.70000000000000023e32 or 5.0000000000000002e46 < z

   1. Initial program 72.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 72.2%

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

   3. Simplified 72.2%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 61.0%

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

   if -4.70000000000000023e32 < z < 5.0000000000000002e46

   1. Initial program 99.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 49.4%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+32} \lor \neg \left(z \leq 5 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.3% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = x / t
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return Float64(x / t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x / t), $MachinePrecision]

Derivation

1. Initial program 88.2%

   \[\frac{x - y \cdot z}{t - a \cdot z} \]
2. Step-by-step derivation

   1. *-commutative 88.2%

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

3. Simplified 88.2%

   \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 35.5%

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

6. Final simplification 35.5%

   \[\leadsto \frac{x}{t} \]
7. Add Preprocessing

Developer target: 97.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t\_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024130 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))