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

Percentage Accurate: 85.5% → 94.5%

Time: 17.1s

Alternatives: 11

Speedup: 0.1×

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: 85.5% 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: 94.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, -a, t\right)\\ t_2 := \mathsf{fma}\left(-1, y \cdot \frac{z}{t\_1}, \frac{x}{t\_1}\right)\\ t_3 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{-32}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

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+29)
     t_2
     (if (<= t_3 4e-32) t_3 (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+29) {
		tmp = t_2;
	} else if (t_3 <= 4e-32) {
		tmp = t_3;
	} 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+29)
		tmp = t_2;
	elseif (t_3 <= 4e-32)
		tmp = t_3;
	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+29], t$95$2, If[LessEqual[t$95$3, 4e-32], t$95$3, 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))) < -1.99999999999999983e29 or 4.00000000000000022e-32 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 85.1%

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

      1. *-commutative 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in x around 0 84.3%

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

      1. fma-define 84.3%

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

      2. associate-/l* 99.0%

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

      3. cancel-sign-sub-inv 99.0%

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

      4. *-commutative 99.0%

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

      5. +-commutative 99.0%

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

      6. fma-define 99.0%

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

      7. cancel-sign-sub-inv 99.0%

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

      8. *-commutative 99.0%

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

      9. +-commutative 99.0%

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

      10. fma-define 99.0%

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

   7. Simplified 99.0%

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

   if -1.99999999999999983e29 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 4.00000000000000022e-32

   1. Initial program 91.4%

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

   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 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(-1, y \cdot \frac{z}{\mathsf{fma}\left(z, -a, t\right)}, \frac{x}{\mathsf{fma}\left(z, -a, t\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 4 \cdot 10^{-32}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-1, y \cdot \frac{z}{\mathsf{fma}\left(z, -a, t\right)}, \frac{x}{\mathsf{fma}\left(z, -a, t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := t - z \cdot a\\ t_3 := \frac{x - y \cdot z}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-313}:\\ \;\;\;\;\frac{y \cdot z}{t\_1} + \frac{x}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{y} - \frac{\frac{t}{y} - a \cdot \frac{x}{{y}^{2}}}{z}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (- t (* z a))) (t_3 (/ (- x (* y z)) t_2)))
   (if (<= t_3 (- INFINITY))
     (* y (/ z t_1))
     (if (<= t_3 -5e-313)
       (+ (/ (* y z) t_1) (/ x t_2))
       (if (<= t_3 0.0)
         (/ (- y (/ x z)) a)
         (if (<= t_3 5e+302)
           t_3
           (pow
            (- (/ a y) (/ (- (/ t y) (* a (/ x (pow y 2.0)))) z))
            -1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = t - (z * a);
	double t_3 = (x - (y * z)) / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = y * (z / t_1);
	} else if (t_3 <= -5e-313) {
		tmp = ((y * z) / t_1) + (x / t_2);
	} else if (t_3 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_3 <= 5e+302) {
		tmp = t_3;
	} else {
		tmp = pow(((a / y) - (((t / y) - (a * (x / pow(y, 2.0)))) / z)), -1.0);
	}
	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 = t - (z * a);
	double t_3 = (x - (y * z)) / t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z / t_1);
	} else if (t_3 <= -5e-313) {
		tmp = ((y * z) / t_1) + (x / t_2);
	} else if (t_3 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_3 <= 5e+302) {
		tmp = t_3;
	} else {
		tmp = Math.pow(((a / y) - (((t / y) - (a * (x / Math.pow(y, 2.0)))) / z)), -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = t - (z * a)
	t_3 = (x - (y * z)) / t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = y * (z / t_1)
	elif t_3 <= -5e-313:
		tmp = ((y * z) / t_1) + (x / t_2)
	elif t_3 <= 0.0:
		tmp = (y - (x / z)) / a
	elif t_3 <= 5e+302:
		tmp = t_3
	else:
		tmp = math.pow(((a / y) - (((t / y) - (a * (x / math.pow(y, 2.0)))) / z)), -1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(t - Float64(z * a))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(y * Float64(z / t_1));
	elseif (t_3 <= -5e-313)
		tmp = Float64(Float64(Float64(y * z) / t_1) + Float64(x / t_2));
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (t_3 <= 5e+302)
		tmp = t_3;
	else
		tmp = Float64(Float64(a / y) - Float64(Float64(Float64(t / y) - Float64(a * Float64(x / (y ^ 2.0)))) / z)) ^ -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = t - (z * a);
	t_3 = (x - (y * z)) / t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = y * (z / t_1);
	elseif (t_3 <= -5e-313)
		tmp = ((y * z) / t_1) + (x / t_2);
	elseif (t_3 <= 0.0)
		tmp = (y - (x / z)) / a;
	elseif (t_3 <= 5e+302)
		tmp = t_3;
	else
		tmp = ((a / y) - (((t / y) - (a * (x / (y ^ 2.0)))) / z)) ^ -1.0;
	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[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-313], N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$3, 5e+302], t$95$3, N[Power[N[(N[(a / y), $MachinePrecision] - N[(N[(N[(t / y), $MachinePrecision] - N[(a * N[(x / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 52.6%

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

      1. *-commutative 52.6%

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

   3. Simplified 52.6%

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

   5. Taylor expanded in x around 0 36.4%

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

      1. associate-*r/ 36.4%

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

      2. sub-neg 36.4%

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

      3. mul-1-neg 36.4%

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

      4. +-commutative 36.4%

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

      5. mul-1-neg 36.4%

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

      6. distribute-rgt-neg-in 36.4%

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

      7. fma-undefine 36.4%

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

      8. associate-*r/ 36.4%

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

      9. neg-mul-1 36.4%

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

      10. distribute-neg-frac2 36.4%

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

      11. neg-sub0 36.4%

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

      12. fma-undefine 36.4%

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

      13. distribute-rgt-neg-in 36.4%

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

      14. distribute-lft-neg-in 36.4%

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

      15. *-commutative 36.4%

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

      16. associate--r+ 36.4%

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

      17. neg-sub0 36.4%

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

      18. distribute-rgt-neg-out 36.4%

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

      19. remove-double-neg 36.4%

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

   7. Simplified 36.4%

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

   8. Taylor expanded in y around 0 36.4%

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

      1. associate-/l* 83.6%

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

      2. *-commutative 83.6%

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

   10. Simplified 83.6%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -5.00000000002e-313

   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 -5.00000000002e-313 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 59.5%

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

      1. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   5. Taylor expanded in x around 0 59.5%

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

      1. fma-define 59.5%

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

      2. associate-/l* 59.5%

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

      3. cancel-sign-sub-inv 59.5%

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

      4. *-commutative 59.5%

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

      5. +-commutative 59.5%

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

      6. fma-define 59.5%

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

      7. cancel-sign-sub-inv 59.5%

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

      8. *-commutative 59.5%

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

      9. +-commutative 59.5%

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

      10. fma-define 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in a around inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. unsub-neg 78.7%

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

   10. Simplified 78.7%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5e302

   1. Initial program 99.7%

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

   if 5e302 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 29.3%

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

      1. *-commutative 29.3%

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

   3. Simplified 29.3%

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

      1. clear-num 29.3%

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

      2. inv-pow 29.3%

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

      3. sub-neg 29.3%

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

      4. +-commutative 29.3%

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

      5. *-commutative 29.3%

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

      6. distribute-rgt-neg-in 29.3%

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

      7. fma-define 29.3%

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

   6. Applied egg-rr 29.3%

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

   7. Taylor expanded in z around -inf 80.1%

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

      1. +-commutative 80.1%

         \[\leadsto {\color{blue}{\left(\frac{a}{y} + -1 \cdot \frac{\frac{t}{y} - \frac{a \cdot x}{{y}^{2}}}{z}\right)}}^{-1} \]

      2. mul-1-neg 80.1%

         \[\leadsto {\left(\frac{a}{y} + \color{blue}{\left(-\frac{\frac{t}{y} - \frac{a \cdot x}{{y}^{2}}}{z}\right)}\right)}^{-1} \]

      3. unsub-neg 80.1%

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

      4. associate-/l* 83.3%

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

   9. Simplified 83.3%

      \[\leadsto {\color{blue}{\left(\frac{a}{y} - \frac{\frac{t}{y} - a \cdot \frac{x}{{y}^{2}}}{z}\right)}}^{-1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-313}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} + \frac{x}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{y} - \frac{\frac{t}{y} - a \cdot \frac{x}{{y}^{2}}}{z}\right)}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-313}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;z \cdot \frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_2 (- INFINITY))
     (* y (/ z t_1))
     (if (<= t_2 -5e-313)
       t_2
       (if (<= t_2 0.0)
         (/ (- y (/ x z)) a)
         (if (<= t_2 5e+302)
           t_2
           (if (<= t_2 INFINITY) (* z (/ y t_1)) (/ 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)) / (t - (z * a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y * (z / t_1);
	} else if (t_2 <= -5e-313) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_2 <= 5e+302) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = z * (y / 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 = (z * a) - t;
	double t_2 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z / t_1);
	} else if (t_2 <= -5e-313) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_2 <= 5e+302) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = z * (y / t_1);
	} 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 - (z * a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y * (z / t_1)
	elif t_2 <= -5e-313:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (y - (x / z)) / a
	elif t_2 <= 5e+302:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = z * (y / t_1)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y * Float64(z / t_1));
	elseif (t_2 <= -5e-313)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (t_2 <= 5e+302)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(z * Float64(y / t_1));
	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 - (z * a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y * (z / t_1);
	elseif (t_2 <= -5e-313)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (y - (x / z)) / a;
	elseif (t_2 <= 5e+302)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = z * (y / t_1);
	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[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-313], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$2, 5e+302], t$95$2, If[LessEqual[t$95$2, Infinity], N[(z * N[(y / t$95$1), $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))) < -inf.0

   1. Initial program 52.6%

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

      1. *-commutative 52.6%

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

   3. Simplified 52.6%

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

   5. Taylor expanded in x around 0 36.4%

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

      1. associate-*r/ 36.4%

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

      2. sub-neg 36.4%

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

      3. mul-1-neg 36.4%

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

      4. +-commutative 36.4%

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

      5. mul-1-neg 36.4%

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

      6. distribute-rgt-neg-in 36.4%

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

      7. fma-undefine 36.4%

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

      8. associate-*r/ 36.4%

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

      9. neg-mul-1 36.4%

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

      10. distribute-neg-frac2 36.4%

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

      11. neg-sub0 36.4%

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

      12. fma-undefine 36.4%

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

      13. distribute-rgt-neg-in 36.4%

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

      14. distribute-lft-neg-in 36.4%

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

      15. *-commutative 36.4%

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

      16. associate--r+ 36.4%

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

      17. neg-sub0 36.4%

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

      18. distribute-rgt-neg-out 36.4%

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

      19. remove-double-neg 36.4%

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

   7. Simplified 36.4%

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

   8. Taylor expanded in y around 0 36.4%

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

      1. associate-/l* 83.6%

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

      2. *-commutative 83.6%

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

   10. Simplified 83.6%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -5.00000000002e-313 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5e302

   1. Initial program 99.7%

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

   if -5.00000000002e-313 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 59.5%

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

      1. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   5. Taylor expanded in x around 0 59.5%

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

      1. fma-define 59.5%

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

      2. associate-/l* 59.5%

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

      3. cancel-sign-sub-inv 59.5%

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

      4. *-commutative 59.5%

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

      5. +-commutative 59.5%

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

      6. fma-define 59.5%

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

      7. cancel-sign-sub-inv 59.5%

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

      8. *-commutative 59.5%

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

      9. +-commutative 59.5%

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

      10. fma-define 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in a around inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. unsub-neg 78.7%

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

   10. Simplified 78.7%

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

   if 5e302 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 43.9%

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

      1. *-commutative 43.9%

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

   3. Simplified 43.9%

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

   5. Taylor expanded in x around 0 19.6%

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

      1. associate-*r/ 19.6%

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

      2. sub-neg 19.6%

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

      3. mul-1-neg 19.6%

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

      4. +-commutative 19.6%

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

      5. mul-1-neg 19.6%

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

      6. distribute-rgt-neg-in 19.6%

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

      7. fma-undefine 19.6%

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

      8. associate-*r/ 19.6%

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

      9. neg-mul-1 19.6%

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

      10. distribute-neg-frac2 19.6%

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

      11. neg-sub0 19.6%

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

      12. fma-undefine 19.6%

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

      13. distribute-rgt-neg-in 19.6%

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

      14. distribute-lft-neg-in 19.6%

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

      15. *-commutative 19.6%

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

      16. associate--r+ 19.6%

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

      17. neg-sub0 19.6%

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

      18. distribute-rgt-neg-out 19.6%

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

      19. remove-double-neg 19.6%

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

   7. Simplified 19.6%

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

      1. *-commutative 19.6%

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

      2. associate-/l* 79.8%

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

      3. fma-neg 79.8%

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

   9. Applied egg-rr 79.8%

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

   10. Taylor expanded in y around 0 79.8%

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

       1. *-commutative 79.8%

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

   12. Simplified 79.8%

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

   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 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-313}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := t - z \cdot a\\ t_3 := \frac{x - y \cdot z}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-313}:\\ \;\;\;\;\frac{y \cdot z}{t\_1} + \frac{x}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;z \cdot \frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (- t (* z a))) (t_3 (/ (- x (* y z)) t_2)))
   (if (<= t_3 (- INFINITY))
     (* y (/ z t_1))
     (if (<= t_3 -5e-313)
       (+ (/ (* y z) t_1) (/ x t_2))
       (if (<= t_3 0.0)
         (/ (- y (/ x z)) a)
         (if (<= t_3 5e+302)
           t_3
           (if (<= t_3 INFINITY) (* z (/ y t_1)) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = t - (z * a);
	double t_3 = (x - (y * z)) / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = y * (z / t_1);
	} else if (t_3 <= -5e-313) {
		tmp = ((y * z) / t_1) + (x / t_2);
	} else if (t_3 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_3 <= 5e+302) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = z * (y / 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 = (z * a) - t;
	double t_2 = t - (z * a);
	double t_3 = (x - (y * z)) / t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z / t_1);
	} else if (t_3 <= -5e-313) {
		tmp = ((y * z) / t_1) + (x / t_2);
	} else if (t_3 <= 0.0) {
		tmp = (y - (x / z)) / a;
	} else if (t_3 <= 5e+302) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = z * (y / t_1);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = t - (z * a)
	t_3 = (x - (y * z)) / t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = y * (z / t_1)
	elif t_3 <= -5e-313:
		tmp = ((y * z) / t_1) + (x / t_2)
	elif t_3 <= 0.0:
		tmp = (y - (x / z)) / a
	elif t_3 <= 5e+302:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = z * (y / t_1)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(t - Float64(z * a))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(y * Float64(z / t_1));
	elseif (t_3 <= -5e-313)
		tmp = Float64(Float64(Float64(y * z) / t_1) + Float64(x / t_2));
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (t_3 <= 5e+302)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(z * Float64(y / t_1));
	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 = t - (z * a);
	t_3 = (x - (y * z)) / t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = y * (z / t_1);
	elseif (t_3 <= -5e-313)
		tmp = ((y * z) / t_1) + (x / t_2);
	elseif (t_3 <= 0.0)
		tmp = (y - (x / z)) / a;
	elseif (t_3 <= 5e+302)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = z * (y / t_1);
	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[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-313], N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$3, 5e+302], t$95$3, If[LessEqual[t$95$3, Infinity], N[(z * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

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

   1. Initial program 52.6%

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

      1. *-commutative 52.6%

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

   3. Simplified 52.6%

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

   5. Taylor expanded in x around 0 36.4%

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

      1. associate-*r/ 36.4%

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

      2. sub-neg 36.4%

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

      3. mul-1-neg 36.4%

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

      4. +-commutative 36.4%

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

      5. mul-1-neg 36.4%

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

      6. distribute-rgt-neg-in 36.4%

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

      7. fma-undefine 36.4%

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

      8. associate-*r/ 36.4%

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

      9. neg-mul-1 36.4%

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

      10. distribute-neg-frac2 36.4%

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

      11. neg-sub0 36.4%

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

      12. fma-undefine 36.4%

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

      13. distribute-rgt-neg-in 36.4%

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

      14. distribute-lft-neg-in 36.4%

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

      15. *-commutative 36.4%

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

      16. associate--r+ 36.4%

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

      17. neg-sub0 36.4%

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

      18. distribute-rgt-neg-out 36.4%

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

      19. remove-double-neg 36.4%

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

   7. Simplified 36.4%

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

   8. Taylor expanded in y around 0 36.4%

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

      1. associate-/l* 83.6%

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

      2. *-commutative 83.6%

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

   10. Simplified 83.6%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -5.00000000002e-313

   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 -5.00000000002e-313 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 59.5%

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

      1. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   5. Taylor expanded in x around 0 59.5%

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

      1. fma-define 59.5%

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

      2. associate-/l* 59.5%

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

      3. cancel-sign-sub-inv 59.5%

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

      4. *-commutative 59.5%

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

      5. +-commutative 59.5%

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

      6. fma-define 59.5%

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

      7. cancel-sign-sub-inv 59.5%

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

      8. *-commutative 59.5%

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

      9. +-commutative 59.5%

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

      10. fma-define 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in a around inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. unsub-neg 78.7%

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

   10. Simplified 78.7%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5e302

   1. Initial program 99.7%

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

   if 5e302 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 43.9%

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

      1. *-commutative 43.9%

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

   3. Simplified 43.9%

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

   5. Taylor expanded in x around 0 19.6%

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

      1. associate-*r/ 19.6%

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

      2. sub-neg 19.6%

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

      3. mul-1-neg 19.6%

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

      4. +-commutative 19.6%

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

      5. mul-1-neg 19.6%

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

      6. distribute-rgt-neg-in 19.6%

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

      7. fma-undefine 19.6%

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

      8. associate-*r/ 19.6%

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

      9. neg-mul-1 19.6%

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

      10. distribute-neg-frac2 19.6%

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

      11. neg-sub0 19.6%

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

      12. fma-undefine 19.6%

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

      13. distribute-rgt-neg-in 19.6%

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

      14. distribute-lft-neg-in 19.6%

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

      15. *-commutative 19.6%

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

      16. associate--r+ 19.6%

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

      17. neg-sub0 19.6%

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

      18. distribute-rgt-neg-out 19.6%

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

      19. remove-double-neg 19.6%

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

   7. Simplified 19.6%

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

      1. *-commutative 19.6%

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

      2. associate-/l* 79.8%

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

      3. fma-neg 79.8%

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

   9. Applied egg-rr 79.8%

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

   10. Taylor expanded in y around 0 79.8%

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

       1. *-commutative 79.8%

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

   12. Simplified 79.8%

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

   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 6 regimes into one program.

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-313}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} + \frac{x}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-z}{t}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z) t))))
   (if (<= z -3.8e+117)
     (/ y a)
     (if (<= z -8.4e+15)
       t_1
       (if (<= z -6.6e-7)
         (/ y a)
         (if (<= z 4.6e-12) (/ x t) (if (<= z 5.5e+81) 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 <= -3.8e+117) {
		tmp = y / a;
	} else if (z <= -8.4e+15) {
		tmp = t_1;
	} else if (z <= -6.6e-7) {
		tmp = y / a;
	} else if (z <= 4.6e-12) {
		tmp = x / t;
	} else if (z <= 5.5e+81) {
		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 <= (-3.8d+117)) then
        tmp = y / a
    else if (z <= (-8.4d+15)) then
        tmp = t_1
    else if (z <= (-6.6d-7)) then
        tmp = y / a
    else if (z <= 4.6d-12) then
        tmp = x / t
    else if (z <= 5.5d+81) 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 <= -3.8e+117) {
		tmp = y / a;
	} else if (z <= -8.4e+15) {
		tmp = t_1;
	} else if (z <= -6.6e-7) {
		tmp = y / a;
	} else if (z <= 4.6e-12) {
		tmp = x / t;
	} else if (z <= 5.5e+81) {
		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 <= -3.8e+117:
		tmp = y / a
	elif z <= -8.4e+15:
		tmp = t_1
	elif z <= -6.6e-7:
		tmp = y / a
	elif z <= 4.6e-12:
		tmp = x / t
	elif z <= 5.5e+81:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-z) / t))
	tmp = 0.0
	if (z <= -3.8e+117)
		tmp = Float64(y / a);
	elseif (z <= -8.4e+15)
		tmp = t_1;
	elseif (z <= -6.6e-7)
		tmp = Float64(y / a);
	elseif (z <= 4.6e-12)
		tmp = Float64(x / t);
	elseif (z <= 5.5e+81)
		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 <= -3.8e+117)
		tmp = y / a;
	elseif (z <= -8.4e+15)
		tmp = t_1;
	elseif (z <= -6.6e-7)
		tmp = y / a;
	elseif (z <= 4.6e-12)
		tmp = x / t;
	elseif (z <= 5.5e+81)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+117], N[(y / a), $MachinePrecision], If[LessEqual[z, -8.4e+15], t$95$1, If[LessEqual[z, -6.6e-7], N[(y / a), $MachinePrecision], If[LessEqual[z, 4.6e-12], N[(x / t), $MachinePrecision], If[LessEqual[z, 5.5e+81], t$95$1, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e117 or -8.4e15 < z < -6.6000000000000003e-7 or 5.5000000000000003e81 < z

   1. Initial program 61.4%

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

      1. *-commutative 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in z around inf 61.5%

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

   if -3.8000000000000002e117 < z < -8.4e15 or 4.59999999999999979e-12 < z < 5.5000000000000003e81

   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 x around 0 50.5%

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

      1. associate-*r/ 50.5%

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

      2. sub-neg 50.5%

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

      3. mul-1-neg 50.5%

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

      4. +-commutative 50.5%

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

      5. mul-1-neg 50.5%

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

      6. distribute-rgt-neg-in 50.5%

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

      7. fma-undefine 50.5%

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

      8. associate-*r/ 50.5%

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

      9. neg-mul-1 50.5%

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

      10. distribute-neg-frac2 50.5%

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

      11. neg-sub0 50.5%

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

      12. fma-undefine 50.5%

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

      13. distribute-rgt-neg-in 50.5%

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

      14. distribute-lft-neg-in 50.5%

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

      15. *-commutative 50.5%

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

      16. associate--r+ 50.5%

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

      17. neg-sub0 50.5%

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

      18. distribute-rgt-neg-out 50.5%

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

      19. remove-double-neg 50.5%

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

   7. Simplified 50.5%

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

   8. Taylor expanded in z around 0 37.2%

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

      1. mul-1-neg 37.2%

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

      2. associate-/l* 42.9%

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

      3. distribute-rgt-neg-in 42.9%

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

   10. Simplified 42.9%

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

   if -6.6000000000000003e-7 < z < 4.59999999999999979e-12

   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 58.4%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+81}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+117)
   (/ y a)
   (if (<= z -3.3e+16)
     (* y (/ (- z) t))
     (if (<= z -4.4e-8)
       (/ y a)
       (if (<= z 1.15e-10)
         (/ x t)
         (if (<= z 1.9e+91) (* z (/ (- y) t)) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+117) {
		tmp = y / a;
	} else if (z <= -3.3e+16) {
		tmp = y * (-z / t);
	} else if (z <= -4.4e-8) {
		tmp = y / a;
	} else if (z <= 1.15e-10) {
		tmp = x / t;
	} else if (z <= 1.9e+91) {
		tmp = z * (-y / 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 <= (-5.5d+117)) then
        tmp = y / a
    else if (z <= (-3.3d+16)) then
        tmp = y * (-z / t)
    else if (z <= (-4.4d-8)) then
        tmp = y / a
    else if (z <= 1.15d-10) then
        tmp = x / t
    else if (z <= 1.9d+91) then
        tmp = z * (-y / 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 <= -5.5e+117) {
		tmp = y / a;
	} else if (z <= -3.3e+16) {
		tmp = y * (-z / t);
	} else if (z <= -4.4e-8) {
		tmp = y / a;
	} else if (z <= 1.15e-10) {
		tmp = x / t;
	} else if (z <= 1.9e+91) {
		tmp = z * (-y / t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+117:
		tmp = y / a
	elif z <= -3.3e+16:
		tmp = y * (-z / t)
	elif z <= -4.4e-8:
		tmp = y / a
	elif z <= 1.15e-10:
		tmp = x / t
	elif z <= 1.9e+91:
		tmp = z * (-y / t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+117)
		tmp = Float64(y / a);
	elseif (z <= -3.3e+16)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= -4.4e-8)
		tmp = Float64(y / a);
	elseif (z <= 1.15e-10)
		tmp = Float64(x / t);
	elseif (z <= 1.9e+91)
		tmp = Float64(z * Float64(Float64(-y) / 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 <= -5.5e+117)
		tmp = y / a;
	elseif (z <= -3.3e+16)
		tmp = y * (-z / t);
	elseif (z <= -4.4e-8)
		tmp = y / a;
	elseif (z <= 1.15e-10)
		tmp = x / t;
	elseif (z <= 1.9e+91)
		tmp = z * (-y / t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+117], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.3e+16], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-8], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.15e-10], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.9e+91], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.49999999999999965e117 or -3.3e16 < z < -4.3999999999999997e-8 or 1.8999999999999999e91 < z

   1. Initial program 61.4%

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

      1. *-commutative 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in z around inf 61.5%

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

   if -5.49999999999999965e117 < z < -3.3e16

   1. Initial program 83.1%

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

      1. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in x around 0 55.3%

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

      1. associate-*r/ 55.3%

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

      2. sub-neg 55.3%

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

      3. mul-1-neg 55.3%

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

      4. +-commutative 55.3%

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

      5. mul-1-neg 55.3%

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

      6. distribute-rgt-neg-in 55.3%

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

      7. fma-undefine 55.3%

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

      8. associate-*r/ 55.3%

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

      9. neg-mul-1 55.3%

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

      10. distribute-neg-frac2 55.3%

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

      11. neg-sub0 55.3%

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

      12. fma-undefine 55.3%

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

      13. distribute-rgt-neg-in 55.3%

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

      14. distribute-lft-neg-in 55.3%

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

      15. *-commutative 55.3%

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

      16. associate--r+ 55.3%

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

      17. neg-sub0 55.3%

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

      18. distribute-rgt-neg-out 55.3%

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

      19. remove-double-neg 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in z around 0 42.3%

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

      1. mul-1-neg 42.3%

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

      2. associate-/l* 46.6%

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

      3. distribute-rgt-neg-in 46.6%

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

   10. Simplified 46.6%

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

   if -4.3999999999999997e-8 < z < 1.15000000000000004e-10

   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 58.4%

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

   if 1.15000000000000004e-10 < z < 1.8999999999999999e91

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in x around 0 46.4%

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

      1. associate-*r/ 46.4%

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

      2. sub-neg 46.4%

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

      3. mul-1-neg 46.4%

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

      4. +-commutative 46.4%

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

      5. mul-1-neg 46.4%

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

      6. distribute-rgt-neg-in 46.4%

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

      7. fma-undefine 46.4%

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

      8. associate-*r/ 46.4%

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

      9. neg-mul-1 46.4%

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

      10. distribute-neg-frac2 46.4%

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

      11. neg-sub0 46.4%

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

      12. fma-undefine 46.4%

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

      13. distribute-rgt-neg-in 46.4%

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

      14. distribute-lft-neg-in 46.4%

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

      15. *-commutative 46.4%

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

      16. associate--r+ 46.4%

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

      17. neg-sub0 46.4%

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

      18. distribute-rgt-neg-out 46.4%

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

      19. remove-double-neg 46.4%

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

   7. Simplified 46.4%

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

      1. *-commutative 46.4%

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

      2. associate-/l* 50.0%

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

      3. fma-neg 50.0%

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

   9. Applied egg-rr 50.0%

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

   10. Taylor expanded in z around 0 39.8%

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

       1. associate-*r/ 39.8%

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

       2. neg-mul-1 39.8%

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

   12. Simplified 39.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ t_2 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)) (t_2 (/ (- x (* y z)) t)))
   (if (<= t -1.25e-29)
     t_2
     (if (<= t 3.05e-93)
       t_1
       (if (<= t 1.42e+23) (/ x (- t (* z a))) (if (<= t 1.3e+78) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = (x - (y * z)) / t;
	double tmp;
	if (t <= -1.25e-29) {
		tmp = t_2;
	} else if (t <= 3.05e-93) {
		tmp = t_1;
	} else if (t <= 1.42e+23) {
		tmp = x / (t - (z * a));
	} else if (t <= 1.3e+78) {
		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 = (y - (x / z)) / a
    t_2 = (x - (y * z)) / t
    if (t <= (-1.25d-29)) then
        tmp = t_2
    else if (t <= 3.05d-93) then
        tmp = t_1
    else if (t <= 1.42d+23) then
        tmp = x / (t - (z * a))
    else if (t <= 1.3d+78) 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 = (y - (x / z)) / a;
	double t_2 = (x - (y * z)) / t;
	double tmp;
	if (t <= -1.25e-29) {
		tmp = t_2;
	} else if (t <= 3.05e-93) {
		tmp = t_1;
	} else if (t <= 1.42e+23) {
		tmp = x / (t - (z * a));
	} else if (t <= 1.3e+78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	t_2 = (x - (y * z)) / t
	tmp = 0
	if t <= -1.25e-29:
		tmp = t_2
	elif t <= 3.05e-93:
		tmp = t_1
	elif t <= 1.42e+23:
		tmp = x / (t - (z * a))
	elif t <= 1.3e+78:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	t_2 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (t <= -1.25e-29)
		tmp = t_2;
	elseif (t <= 3.05e-93)
		tmp = t_1;
	elseif (t <= 1.42e+23)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (t <= 1.3e+78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	t_2 = (x - (y * z)) / t;
	tmp = 0.0;
	if (t <= -1.25e-29)
		tmp = t_2;
	elseif (t <= 3.05e-93)
		tmp = t_1;
	elseif (t <= 1.42e+23)
		tmp = x / (t - (z * a));
	elseif (t <= 1.3e+78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -1.25e-29], t$95$2, If[LessEqual[t, 3.05e-93], t$95$1, If[LessEqual[t, 1.42e+23], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+78], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.24999999999999996e-29 or 1.3e78 < t

   1. Initial program 85.7%

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

      1. *-commutative 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around inf 72.4%

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

   if -1.24999999999999996e-29 < t < 3.04999999999999985e-93 or 1.42000000000000004e23 < t < 1.3e78

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in x around 0 81.5%

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

      1. fma-define 81.5%

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

      2. associate-/l* 89.3%

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

      3. cancel-sign-sub-inv 89.3%

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

      4. *-commutative 89.3%

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

      5. +-commutative 89.3%

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

      6. fma-define 89.3%

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

      7. cancel-sign-sub-inv 89.3%

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

      8. *-commutative 89.3%

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

      9. +-commutative 89.3%

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

      10. fma-define 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in a around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. unsub-neg 74.8%

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

   10. Simplified 74.8%

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

   if 3.04999999999999985e-93 < t < 1.42000000000000004e23

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around inf 72.6%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-29}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-93}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+78}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{t} - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= t -2.6e-29)
     (- (/ x t) (* y (/ z t)))
     (if (<= t 2.9e-82)
       t_1
       (if (<= t 8.4e+24)
         (/ x (- t (* z a)))
         (if (<= t 9e+79) t_1 (/ (- x (* y z)) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (t <= -2.6e-29) {
		tmp = (x / t) - (y * (z / t));
	} else if (t <= 2.9e-82) {
		tmp = t_1;
	} else if (t <= 8.4e+24) {
		tmp = x / (t - (z * a));
	} else if (t <= 9e+79) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (t <= (-2.6d-29)) then
        tmp = (x / t) - (y * (z / t))
    else if (t <= 2.9d-82) then
        tmp = t_1
    else if (t <= 8.4d+24) then
        tmp = x / (t - (z * a))
    else if (t <= 9d+79) then
        tmp = t_1
    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 t_1 = (y - (x / z)) / a;
	double tmp;
	if (t <= -2.6e-29) {
		tmp = (x / t) - (y * (z / t));
	} else if (t <= 2.9e-82) {
		tmp = t_1;
	} else if (t <= 8.4e+24) {
		tmp = x / (t - (z * a));
	} else if (t <= 9e+79) {
		tmp = t_1;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if t <= -2.6e-29:
		tmp = (x / t) - (y * (z / t))
	elif t <= 2.9e-82:
		tmp = t_1
	elif t <= 8.4e+24:
		tmp = x / (t - (z * a))
	elif t <= 9e+79:
		tmp = t_1
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (t <= -2.6e-29)
		tmp = Float64(Float64(x / t) - Float64(y * Float64(z / t)));
	elseif (t <= 2.9e-82)
		tmp = t_1;
	elseif (t <= 8.4e+24)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (t <= 9e+79)
		tmp = t_1;
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (t <= -2.6e-29)
		tmp = (x / t) - (y * (z / t));
	elseif (t <= 2.9e-82)
		tmp = t_1;
	elseif (t <= 8.4e+24)
		tmp = x / (t - (z * a));
	elseif (t <= 9e+79)
		tmp = t_1;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t, -2.6e-29], N[(N[(x / t), $MachinePrecision] - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-82], t$95$1, If[LessEqual[t, 8.4e+24], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+79], t$95$1, N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6000000000000002e-29

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around 0 84.8%

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

      1. fma-define 84.8%

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

      2. associate-/l* 95.2%

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

      3. cancel-sign-sub-inv 95.2%

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

      4. *-commutative 95.2%

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

      5. +-commutative 95.2%

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

      6. fma-define 95.2%

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

      7. cancel-sign-sub-inv 95.2%

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

      8. *-commutative 95.2%

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

      9. +-commutative 95.2%

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

      10. fma-define 95.3%

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

   7. Simplified 95.3%

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

   8. Taylor expanded in a around 0 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. sub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. div-sub 61.2%

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

   10. Simplified 61.2%

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

       1. div-sub 61.2%

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

       2. *-commutative 61.2%

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

       3. associate-/l* 67.3%

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

   12. Applied egg-rr 67.3%

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

   if -2.6000000000000002e-29 < t < 2.89999999999999977e-82 or 8.4000000000000005e24 < t < 8.99999999999999987e79

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in x around 0 81.5%

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

      1. fma-define 81.5%

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

      2. associate-/l* 89.3%

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

      3. cancel-sign-sub-inv 89.3%

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

      4. *-commutative 89.3%

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

      5. +-commutative 89.3%

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

      6. fma-define 89.3%

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

      7. cancel-sign-sub-inv 89.3%

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

      8. *-commutative 89.3%

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

      9. +-commutative 89.3%

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

      10. fma-define 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in a around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. unsub-neg 74.8%

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

   10. Simplified 74.8%

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

   if 2.89999999999999977e-82 < t < 8.4000000000000005e24

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around inf 72.6%

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

   if 8.99999999999999987e79 < t

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in t around inf 84.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{t} - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-82}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+79}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+142} \lor \neg \left(z \leq 4.8 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e+142) (not (<= z 4.8e+79))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e+142) || !(z <= 4.8e+79)) {
		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 <= (-4.4d+142)) .or. (.not. (z <= 4.8d+79))) 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 <= -4.4e+142) || !(z <= 4.8e+79)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e+142) or not (z <= 4.8e+79):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e+142) || !(z <= 4.8e+79))
		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 <= -4.4e+142) || ~((z <= 4.8e+79)))
		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, -4.4e+142], N[Not[LessEqual[z, 4.8e+79]], $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 < -4.39999999999999974e142 or 4.79999999999999971e79 < z

   1. Initial program 56.4%

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

      1. *-commutative 56.4%

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

   3. Simplified 56.4%

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

   5. Taylor expanded in z around inf 62.7%

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

   if -4.39999999999999974e142 < z < 4.79999999999999971e79

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf 67.6%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+142} \lor \neg \left(z \leq 4.8 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-9} \lor \neg \left(z \leq 1.4 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e-9) (not (<= z 1.4e+80))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e-9) || !(z <= 1.4e+80)) {
		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 <= (-8d-9)) .or. (.not. (z <= 1.4d+80))) 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 <= -8e-9) || !(z <= 1.4e+80)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e-9) or not (z <= 1.4e+80):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e-9) || !(z <= 1.4e+80))
		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 <= -8e-9) || ~((z <= 1.4e+80)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e-9], N[Not[LessEqual[z, 1.4e+80]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000005e-9 or 1.39999999999999992e80 < z

   1. Initial program 65.3%

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

      1. *-commutative 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in z around inf 52.6%

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

   if -8.0000000000000005e-9 < z < 1.39999999999999992e80

   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 z around 0 52.2%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-9} \lor \neg \left(z \leq 1.4 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.7% 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 84.5%

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

   1. *-commutative 84.5%

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

3. Simplified 84.5%

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

5. Taylor expanded in z around 0 36.0%

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

6. Final simplification 36.0%

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

Developer target: 97.4% 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 2024041 
(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))))