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

Percentage Accurate: 84.6% → 93.7%

Time: 15.3s

Alternatives: 10

Speedup: 0.2×

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: 84.6% 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: 93.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, -a, t\right)\\ t_2 := \mathsf{fma}\left(-1, y \cdot \frac{z}{t\_1}, \frac{x}{t\_1}\right)\\ t_3 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{-293}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma z (- a) t))
        (t_2 (fma -1.0 (* y (/ z t_1)) (/ x t_1)))
        (t_3 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_3 -2e-293)
     t_2
     (if (<= t_3 0.0)
       (/ (- y (/ x z)) a)
       (if (<= t_3 INFINITY) t_2 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(z, -a, t);
	double t_2 = fma(-1.0, (y * (z / t_1)), (x / t_1));
	double t_3 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_3 <= -2e-293) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(z, Float64(-a), t)
	t_2 = fma(-1.0, Float64(y * Float64(z / t_1)), Float64(x / t_1))
	t_3 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_3 <= -2e-293)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * (-a) + t), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 * N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-293], t$95$2, If[LessEqual[t$95$3, 0.0], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -2.0000000000000001e-293 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in x around 0 93.5%

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

      1. fma-define 93.5%

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

      2. associate-/l* 97.6%

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

      3. cancel-sign-sub-inv 97.6%

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

      4. *-commutative 97.6%

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

      5. +-commutative 97.6%

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

      6. fma-define 97.6%

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

      7. cancel-sign-sub-inv 97.6%

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

      8. *-commutative 97.6%

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

      9. +-commutative 97.6%

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

      10. fma-define 97.6%

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

   7. Simplified 97.6%

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

   if -2.0000000000000001e-293 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 52.2%

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

      1. *-commutative 52.2%

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

   3. Simplified 52.2%

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

   5. Taylor expanded in x around 0 52.2%

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

      1. fma-define 52.2%

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

      2. associate-/l* 52.2%

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

      3. cancel-sign-sub-inv 52.2%

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

      4. *-commutative 52.2%

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

      5. +-commutative 52.2%

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

      6. fma-define 52.2%

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

      7. cancel-sign-sub-inv 52.2%

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

      8. *-commutative 52.2%

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

      9. +-commutative 52.2%

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

      10. fma-define 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in a around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. unsub-neg 88.2%

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

   10. Simplified 88.2%

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

   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 3 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{-293}:\\ \;\;\;\;\mathsf{fma}\left(-1, y \cdot \frac{z}{\mathsf{fma}\left(z, -a, t\right)}, \frac{x}{\mathsf{fma}\left(z, -a, t\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-1, y \cdot \frac{z}{\mathsf{fma}\left(z, -a, t\right)}, \frac{x}{\mathsf{fma}\left(z, -a, t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 -2e-293)
     t_1
     (if (<= t_1 0.0)
       (/ (- y (/ x z)) a)
       (if (<= t_1 INFINITY) t_1 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -2e-293) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} 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)) / (t - (z * a));
	double tmp;
	if (t_1 <= -2e-293) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= -2e-293:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (y - (x / z)) / a
	elif t_1 <= math.inf:
		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)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_1 <= -2e-293)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (t_1 <= Inf)
		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 - (z * a));
	tmp = 0.0;
	if (t_1 <= -2e-293)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (y - (x / z)) / a;
	elseif (t_1 <= Inf)
		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] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-293], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -2.0000000000000001e-293 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 94.0%

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

   if -2.0000000000000001e-293 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 52.2%

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

      1. *-commutative 52.2%

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

   3. Simplified 52.2%

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

   5. Taylor expanded in x around 0 52.2%

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

      1. fma-define 52.2%

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

      2. associate-/l* 52.2%

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

      3. cancel-sign-sub-inv 52.2%

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

      4. *-commutative 52.2%

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

      5. +-commutative 52.2%

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

      6. fma-define 52.2%

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

      7. cancel-sign-sub-inv 52.2%

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

      8. *-commutative 52.2%

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

      9. +-commutative 52.2%

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

      10. fma-define 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in a around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. unsub-neg 88.2%

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

   10. Simplified 88.2%

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

   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 3 regimes into one program.

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{-293}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+17}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+85)
   (/ y a)
   (if (<= z -1.3e+26)
     (* y (/ z (- t)))
     (if (<= z -8e+17)
       (/ y a)
       (if (<= z 6e-49)
         (/ x t)
         (if (<= z 1.32e+17)
           (/ (/ x z) (- a))
           (if (<= z 2.6e+39) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+85) {
		tmp = y / a;
	} else if (z <= -1.3e+26) {
		tmp = y * (z / -t);
	} else if (z <= -8e+17) {
		tmp = y / a;
	} else if (z <= 6e-49) {
		tmp = x / t;
	} else if (z <= 1.32e+17) {
		tmp = (x / z) / -a;
	} else if (z <= 2.6e+39) {
		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 <= (-2.7d+85)) then
        tmp = y / a
    else if (z <= (-1.3d+26)) then
        tmp = y * (z / -t)
    else if (z <= (-8d+17)) then
        tmp = y / a
    else if (z <= 6d-49) then
        tmp = x / t
    else if (z <= 1.32d+17) then
        tmp = (x / z) / -a
    else if (z <= 2.6d+39) 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 <= -2.7e+85) {
		tmp = y / a;
	} else if (z <= -1.3e+26) {
		tmp = y * (z / -t);
	} else if (z <= -8e+17) {
		tmp = y / a;
	} else if (z <= 6e-49) {
		tmp = x / t;
	} else if (z <= 1.32e+17) {
		tmp = (x / z) / -a;
	} else if (z <= 2.6e+39) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+85:
		tmp = y / a
	elif z <= -1.3e+26:
		tmp = y * (z / -t)
	elif z <= -8e+17:
		tmp = y / a
	elif z <= 6e-49:
		tmp = x / t
	elif z <= 1.32e+17:
		tmp = (x / z) / -a
	elif z <= 2.6e+39:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+85)
		tmp = Float64(y / a);
	elseif (z <= -1.3e+26)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= -8e+17)
		tmp = Float64(y / a);
	elseif (z <= 6e-49)
		tmp = Float64(x / t);
	elseif (z <= 1.32e+17)
		tmp = Float64(Float64(x / z) / Float64(-a));
	elseif (z <= 2.6e+39)
		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 <= -2.7e+85)
		tmp = y / a;
	elseif (z <= -1.3e+26)
		tmp = y * (z / -t);
	elseif (z <= -8e+17)
		tmp = y / a;
	elseif (z <= 6e-49)
		tmp = x / t;
	elseif (z <= 1.32e+17)
		tmp = (x / z) / -a;
	elseif (z <= 2.6e+39)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+85], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.3e+26], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e+17], N[(y / a), $MachinePrecision], If[LessEqual[z, 6e-49], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.32e+17], N[(N[(x / z), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[z, 2.6e+39], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.69999999999999983e85 or -1.30000000000000001e26 < z < -8e17 or 2.6e39 < z

   1. Initial program 61.8%

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

      1. *-commutative 61.8%

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

   3. Simplified 61.8%

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

   5. Taylor expanded in z around inf 57.7%

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

   if -2.69999999999999983e85 < z < -1.30000000000000001e26

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in x around 0 67.5%

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

      1. associate-*r/ 67.5%

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

      2. sub-neg 67.5%

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

      3. mul-1-neg 67.5%

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

      4. +-commutative 67.5%

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

      5. mul-1-neg 67.5%

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

      6. distribute-rgt-neg-in 67.5%

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

      7. fma-undefine 67.5%

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

      8. associate-*r/ 67.5%

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

      9. neg-mul-1 67.5%

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

      10. distribute-neg-frac2 67.5%

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

      11. neg-sub0 67.5%

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

      12. fma-undefine 67.5%

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

      13. distribute-rgt-neg-in 67.5%

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

      14. distribute-lft-neg-in 67.5%

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

      15. *-commutative 67.5%

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

      16. associate--r+ 67.5%

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

      17. neg-sub0 67.5%

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

      18. distribute-rgt-neg-out 67.5%

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

      19. remove-double-neg 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in z around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. associate-/l* 67.1%

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

      3. distribute-lft-neg-in 67.1%

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

   10. Simplified 67.1%

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

   if -8e17 < z < 6e-49 or 1.32e17 < z < 2.6e39

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 63.5%

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

   if 6e-49 < z < 1.32e17

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf 31.1%

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

   6. Taylor expanded in t around 0 31.8%

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

      1. associate-*r/ 31.8%

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

      2. neg-mul-1 31.8%

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

      3. *-commutative 31.8%

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

   8. Simplified 31.8%

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

   9. Taylor expanded in x around 0 31.8%

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

       1. mul-1-neg 31.8%

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

       2. associate-/l/ 38.6%

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

   11. Simplified 38.6%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+17}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq 10^{+43}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+84)
   (/ y a)
   (if (<= z -5.2e+26)
     (* y (/ z (- t)))
     (if (<= z -6.8e+17)
       (/ y a)
       (if (<= z 4.9e-49)
         (/ x t)
         (if (<= z 1.16e+21)
           (/ (/ x a) (- z))
           (if (<= z 1e+43) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+84) {
		tmp = y / a;
	} else if (z <= -5.2e+26) {
		tmp = y * (z / -t);
	} else if (z <= -6.8e+17) {
		tmp = y / a;
	} else if (z <= 4.9e-49) {
		tmp = x / t;
	} else if (z <= 1.16e+21) {
		tmp = (x / a) / -z;
	} else if (z <= 1e+43) {
		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 <= (-3.2d+84)) then
        tmp = y / a
    else if (z <= (-5.2d+26)) then
        tmp = y * (z / -t)
    else if (z <= (-6.8d+17)) then
        tmp = y / a
    else if (z <= 4.9d-49) then
        tmp = x / t
    else if (z <= 1.16d+21) then
        tmp = (x / a) / -z
    else if (z <= 1d+43) 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 <= -3.2e+84) {
		tmp = y / a;
	} else if (z <= -5.2e+26) {
		tmp = y * (z / -t);
	} else if (z <= -6.8e+17) {
		tmp = y / a;
	} else if (z <= 4.9e-49) {
		tmp = x / t;
	} else if (z <= 1.16e+21) {
		tmp = (x / a) / -z;
	} else if (z <= 1e+43) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+84:
		tmp = y / a
	elif z <= -5.2e+26:
		tmp = y * (z / -t)
	elif z <= -6.8e+17:
		tmp = y / a
	elif z <= 4.9e-49:
		tmp = x / t
	elif z <= 1.16e+21:
		tmp = (x / a) / -z
	elif z <= 1e+43:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+84)
		tmp = Float64(y / a);
	elseif (z <= -5.2e+26)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= -6.8e+17)
		tmp = Float64(y / a);
	elseif (z <= 4.9e-49)
		tmp = Float64(x / t);
	elseif (z <= 1.16e+21)
		tmp = Float64(Float64(x / a) / Float64(-z));
	elseif (z <= 1e+43)
		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 <= -3.2e+84)
		tmp = y / a;
	elseif (z <= -5.2e+26)
		tmp = y * (z / -t);
	elseif (z <= -6.8e+17)
		tmp = y / a;
	elseif (z <= 4.9e-49)
		tmp = x / t;
	elseif (z <= 1.16e+21)
		tmp = (x / a) / -z;
	elseif (z <= 1e+43)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+84], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.2e+26], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e+17], N[(y / a), $MachinePrecision], If[LessEqual[z, 4.9e-49], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.16e+21], N[(N[(x / a), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 1e+43], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2000000000000001e84 or -5.20000000000000004e26 < z < -6.8e17 or 1.00000000000000001e43 < z

   1. Initial program 61.8%

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

      1. *-commutative 61.8%

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

   3. Simplified 61.8%

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

   5. Taylor expanded in z around inf 57.7%

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

   if -3.2000000000000001e84 < z < -5.20000000000000004e26

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in x around 0 67.5%

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

      1. associate-*r/ 67.5%

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

      2. sub-neg 67.5%

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

      3. mul-1-neg 67.5%

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

      4. +-commutative 67.5%

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

      5. mul-1-neg 67.5%

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

      6. distribute-rgt-neg-in 67.5%

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

      7. fma-undefine 67.5%

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

      8. associate-*r/ 67.5%

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

      9. neg-mul-1 67.5%

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

      10. distribute-neg-frac2 67.5%

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

      11. neg-sub0 67.5%

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

      12. fma-undefine 67.5%

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

      13. distribute-rgt-neg-in 67.5%

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

      14. distribute-lft-neg-in 67.5%

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

      15. *-commutative 67.5%

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

      16. associate--r+ 67.5%

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

      17. neg-sub0 67.5%

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

      18. distribute-rgt-neg-out 67.5%

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

      19. remove-double-neg 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in z around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. associate-/l* 67.1%

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

      3. distribute-lft-neg-in 67.1%

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

   10. Simplified 67.1%

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

   if -6.8e17 < z < 4.9000000000000002e-49 or 1.16e21 < z < 1.00000000000000001e43

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 63.5%

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

   if 4.9000000000000002e-49 < z < 1.16e21

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf 31.1%

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

   6. Taylor expanded in t around 0 31.8%

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

      1. mul-1-neg 31.8%

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

      2. associate-/r* 38.7%

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

      3. distribute-neg-frac2 38.7%

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

   8. Simplified 38.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq 10^{+43}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -2.8e+44)
     t_2
     (if (<= z 1.7e-76)
       t_1
       (if (<= z 7.5e+18)
         (/ (* y z) (- (* z a) t))
         (if (<= z 1.25e+43) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -2.8e+44) {
		tmp = t_2;
	} else if (z <= 1.7e-76) {
		tmp = t_1;
	} else if (z <= 7.5e+18) {
		tmp = (y * z) / ((z * a) - t);
	} else if (z <= 1.25e+43) {
		tmp = 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 = x / (t - (z * a))
    t_2 = (y - (x / z)) / a
    if (z <= (-2.8d+44)) then
        tmp = t_2
    else if (z <= 1.7d-76) then
        tmp = t_1
    else if (z <= 7.5d+18) then
        tmp = (y * z) / ((z * a) - t)
    else if (z <= 1.25d+43) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -2.8e+44) {
		tmp = t_2;
	} else if (z <= 1.7e-76) {
		tmp = t_1;
	} else if (z <= 7.5e+18) {
		tmp = (y * z) / ((z * a) - t);
	} else if (z <= 1.25e+43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -2.8e+44:
		tmp = t_2
	elif z <= 1.7e-76:
		tmp = t_1
	elif z <= 7.5e+18:
		tmp = (y * z) / ((z * a) - t)
	elif z <= 1.25e+43:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -2.8e+44)
		tmp = t_2;
	elseif (z <= 1.7e-76)
		tmp = t_1;
	elseif (z <= 7.5e+18)
		tmp = Float64(Float64(y * z) / Float64(Float64(z * a) - t));
	elseif (z <= 1.25e+43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -2.8e+44)
		tmp = t_2;
	elseif (z <= 1.7e-76)
		tmp = t_1;
	elseif (z <= 7.5e+18)
		tmp = (y * z) / ((z * a) - t);
	elseif (z <= 1.25e+43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -2.8e+44], t$95$2, If[LessEqual[z, 1.7e-76], t$95$1, If[LessEqual[z, 7.5e+18], N[(N[(y * z), $MachinePrecision] / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+43], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8000000000000001e44 or 1.2500000000000001e43 < z

   1. Initial program 61.0%

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

      1. *-commutative 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in x around 0 61.0%

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

      1. fma-define 61.0%

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

      2. associate-/l* 73.7%

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

      3. cancel-sign-sub-inv 73.7%

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

      4. *-commutative 73.7%

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

      5. +-commutative 73.7%

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

      6. fma-define 73.7%

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

      7. cancel-sign-sub-inv 73.7%

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

      8. *-commutative 73.7%

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

      9. +-commutative 73.7%

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

      10. fma-define 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in a around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. unsub-neg 72.0%

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

   10. Simplified 72.0%

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

   if -2.8000000000000001e44 < z < 1.7e-76 or 7.5e18 < z < 1.2500000000000001e43

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 77.8%

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

   if 1.7e-76 < z < 7.5e18

   1. Initial program 94.6%

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

      1. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around 0 64.4%

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

      1. associate-*r/ 64.4%

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

      2. sub-neg 64.4%

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

      3. mul-1-neg 64.4%

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

      4. +-commutative 64.4%

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

      5. mul-1-neg 64.4%

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

      6. distribute-rgt-neg-in 64.4%

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

      7. fma-undefine 64.4%

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

      8. associate-*r/ 64.4%

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

      9. neg-mul-1 64.4%

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

      10. distribute-neg-frac2 64.4%

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

      11. neg-sub0 64.4%

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

      12. fma-undefine 64.4%

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

      13. distribute-rgt-neg-in 64.4%

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

      14. distribute-lft-neg-in 64.4%

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

      15. *-commutative 64.4%

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

      16. associate--r+ 64.4%

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

      17. neg-sub0 64.4%

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

      18. distribute-rgt-neg-out 64.4%

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

      19. remove-double-neg 64.4%

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

   7. Simplified 64.4%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+44}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+46)
   (/ y a)
   (if (<= z 2.2e-49)
     (/ x t)
     (if (<= z 1.52e+19)
       (/ (/ x z) (- a))
       (if (<= z 2.35e+39) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+46) {
		tmp = y / a;
	} else if (z <= 2.2e-49) {
		tmp = x / t;
	} else if (z <= 1.52e+19) {
		tmp = (x / z) / -a;
	} else if (z <= 2.35e+39) {
		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 <= (-3.5d+46)) then
        tmp = y / a
    else if (z <= 2.2d-49) then
        tmp = x / t
    else if (z <= 1.52d+19) then
        tmp = (x / z) / -a
    else if (z <= 2.35d+39) 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 <= -3.5e+46) {
		tmp = y / a;
	} else if (z <= 2.2e-49) {
		tmp = x / t;
	} else if (z <= 1.52e+19) {
		tmp = (x / z) / -a;
	} else if (z <= 2.35e+39) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+46:
		tmp = y / a
	elif z <= 2.2e-49:
		tmp = x / t
	elif z <= 1.52e+19:
		tmp = (x / z) / -a
	elif z <= 2.35e+39:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+46)
		tmp = Float64(y / a);
	elseif (z <= 2.2e-49)
		tmp = Float64(x / t);
	elseif (z <= 1.52e+19)
		tmp = Float64(Float64(x / z) / Float64(-a));
	elseif (z <= 2.35e+39)
		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 <= -3.5e+46)
		tmp = y / a;
	elseif (z <= 2.2e-49)
		tmp = x / t;
	elseif (z <= 1.52e+19)
		tmp = (x / z) / -a;
	elseif (z <= 2.35e+39)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+46], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.2e-49], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.52e+19], N[(N[(x / z), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[z, 2.35e+39], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999985e46 or 2.35e39 < z

   1. Initial program 61.0%

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

      1. *-commutative 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in z around inf 56.1%

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

   if -3.49999999999999985e46 < z < 2.1999999999999999e-49 or 1.52e19 < z < 2.35e39

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 61.9%

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

   if 2.1999999999999999e-49 < z < 1.52e19

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf 31.1%

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

   6. Taylor expanded in t around 0 31.8%

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

      1. associate-*r/ 31.8%

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

      2. neg-mul-1 31.8%

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

      3. *-commutative 31.8%

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

   8. Simplified 31.8%

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

   9. Taylor expanded in x around 0 31.8%

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

       1. mul-1-neg 31.8%

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

       2. associate-/l/ 38.6%

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

   11. Simplified 38.6%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+50} \lor \neg \left(z \leq 9.2 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.3e+50) (not (<= z 9.2e+55))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.3e+50) || !(z <= 9.2e+55)) {
		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 <= (-3.3d+50)) .or. (.not. (z <= 9.2d+55))) 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 <= -3.3e+50) || !(z <= 9.2e+55)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.3e+50) or not (z <= 9.2e+55):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.3e+50) || !(z <= 9.2e+55))
		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 <= -3.3e+50) || ~((z <= 9.2e+55)))
		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, -3.3e+50], N[Not[LessEqual[z, 9.2e+55]], $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 < -3.3e50 or 9.1999999999999995e55 < z

   1. Initial program 60.6%

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

      1. *-commutative 60.6%

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

   3. Simplified 60.6%

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

   5. Taylor expanded in z around inf 56.6%

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

   if -3.3e50 < z < 9.1999999999999995e55

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 72.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+50} \lor \neg \left(z \leq 9.2 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+52} \lor \neg \left(z \leq 7.2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e+52) (not (<= z 7.2e-10)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+52) || !(z <= 7.2e-10)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / 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 <= (-5.5d+52)) .or. (.not. (z <= 7.2d-10))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / 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 <= -5.5e+52) || !(z <= 7.2e-10)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e+52) or not (z <= 7.2e-10):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e+52) || !(z <= 7.2e-10))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.5e+52) || ~((z <= 7.2e-10)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e+52], N[Not[LessEqual[z, 7.2e-10]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999996e52 or 7.2e-10 < z

   1. Initial program 64.0%

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

      1. *-commutative 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in x around 0 64.0%

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

      1. fma-define 64.0%

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

      2. associate-/l* 75.5%

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

      3. cancel-sign-sub-inv 75.5%

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

      4. *-commutative 75.5%

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

      5. +-commutative 75.5%

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

      6. fma-define 75.5%

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

      7. cancel-sign-sub-inv 75.5%

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

      8. *-commutative 75.5%

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

      9. +-commutative 75.5%

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

      10. fma-define 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in a around inf 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

   10. Simplified 71.2%

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

   if -5.49999999999999996e52 < z < 7.2e-10

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 74.0%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+52} \lor \neg \left(z \leq 7.2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+44} \lor \neg \left(z \leq 1.7 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.1e+44) (not (<= z 1.7e-77))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.1e+44) || !(z <= 1.7e-77)) {
		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 <= (-3.1d+44)) .or. (.not. (z <= 1.7d-77))) 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 <= -3.1e+44) || !(z <= 1.7e-77)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.1e+44) or not (z <= 1.7e-77):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.1e+44) || !(z <= 1.7e-77))
		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 <= -3.1e+44) || ~((z <= 1.7e-77)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.1e+44], N[Not[LessEqual[z, 1.7e-77]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999996e44 or 1.69999999999999991e-77 < z

   1. Initial program 67.8%

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

      1. *-commutative 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in z around inf 50.5%

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

   if -3.09999999999999996e44 < z < 1.69999999999999991e-77

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 62.1%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+44} \lor \neg \left(z \leq 1.7 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.5% 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 84.6%

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

   1. *-commutative 84.6%

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

3. Simplified 84.6%

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

5. Taylor expanded in z around 0 38.1%

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

6. Final simplification 38.1%

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

Developer target: 97.2% 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 2024040 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (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))))