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

Percentage Accurate: 86.0% → 93.8%

Time: 9.7s

Alternatives: 10

Speedup: 0.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{y}{\frac{t_1}{z}} - \frac{x}{t_1}\\ t_3 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t))
        (t_2 (- (/ y (/ t_1 z)) (/ x t_1)))
        (t_3 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_3 -5e-297)
     t_2
     (if (<= t_3 0.0)
       (- (/ y a) (/ (/ x a) z))
       (if (<= t_3 INFINITY) t_2 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = (y / (t_1 / z)) - (x / t_1);
	double t_3 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_3 <= -5e-297) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = (y / a) - ((x / a) / z);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} 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 = (y / (t_1 / z)) - (x / t_1);
	double t_3 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_3 <= -5e-297) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = (y / a) - ((x / a) / z);
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = (y / (t_1 / z)) - (x / t_1)
	t_3 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_3 <= -5e-297:
		tmp = t_2
	elif t_3 <= 0.0:
		tmp = (y / a) - ((x / a) / z)
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(Float64(y / Float64(t_1 / z)) - Float64(x / t_1))
	t_3 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_3 <= -5e-297)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	elseif (t_3 <= Inf)
		tmp = t_2;
	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 = (y / (t_1 / z)) - (x / t_1);
	t_3 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_3 <= -5e-297)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = (y / a) - ((x / a) / z);
	elseif (t_3 <= Inf)
		tmp = t_2;
	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[(y / N[(t$95$1 / z), $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, -5e-297], t$95$2, If[LessEqual[t$95$3, 0.0], N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -5e-297 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 89.8%

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

      1. sub-neg 89.8%

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

      2. +-commutative 89.8%

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

      3. neg-sub0 89.8%

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

      4. associate-+l- 89.8%

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

      5. sub0-neg 89.8%

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

      6. neg-mul-1 89.8%

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

      7. sub-neg 89.8%

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

      8. +-commutative 89.8%

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

      9. neg-sub0 89.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 89.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 89.8%

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

      12. neg-mul-1 89.8%

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

      13. times-frac 89.8%

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

      14. metadata-eval 89.8%

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

      15. *-lft-identity 89.8%

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

      16. *-commutative 89.8%

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

   3. Simplified 89.8%

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

      1. div-sub 89.4%

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

      2. associate-/l* 96.9%

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

   5. Applied egg-rr 96.9%

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

   if -5e-297 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 57.9%

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

      1. sub-neg 57.9%

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

      2. +-commutative 57.9%

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

      3. neg-sub0 57.9%

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

      4. associate-+l- 57.9%

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

      5. sub0-neg 57.9%

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

      6. neg-mul-1 57.9%

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

      7. sub-neg 57.9%

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

      8. +-commutative 57.9%

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

      9. neg-sub0 57.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 57.9%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 57.9%

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

      12. neg-mul-1 57.9%

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

      13. times-frac 57.9%

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

      14. metadata-eval 57.9%

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

      15. *-lft-identity 57.9%

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

      16. *-commutative 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in z around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. +-commutative 51.8%

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

      3. associate--l+ 51.8%

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

      4. associate-/r* 75.4%

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

      5. distribute-neg-frac 75.4%

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

      6. mul-1-neg 75.4%

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

      7. associate-/r* 75.4%

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

      8. associate-*r/ 75.4%

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

      9. div-sub 75.4%

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

      10. distribute-lft-out-- 75.4%

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

      11. associate-*r/ 75.4%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in x around inf 78.5%

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

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

   1. Initial program 0.0%

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

      1. sub-neg 0.0%

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

      2. +-commutative 0.0%

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

      3. neg-sub0 0.0%

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

      4. associate-+l- 0.0%

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

      5. sub0-neg 0.0%

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

      6. neg-mul-1 0.0%

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

      7. sub-neg 0.0%

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

      8. +-commutative 0.0%

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

      9. neg-sub0 0.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 0.0%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 0.0%

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

      12. neg-mul-1 0.0%

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

      13. times-frac 0.0%

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

      14. metadata-eval 0.0%

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

      15. *-lft-identity 0.0%

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

      16. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-297}:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}} - \frac{x}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}} - \frac{x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 2: 91.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 (- INFINITY))
     (/ y (/ (- (* z a) t) z))
     (if (<= t_1 -2e-298)
       t_1
       (if (<= t_1 0.0)
         (- (/ y a) (/ (/ x a) z))
         (if (<= t_1 5e+288) t_1 (/ (- y (/ x z)) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y / (((z * a) - t) / z);
	} else if (t_1 <= -2e-298) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (y / a) - ((x / a) / z);
	} else if (t_1 <= 5e+288) {
		tmp = t_1;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y / (((z * a) - t) / z);
	} else if (t_1 <= -2e-298) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (y / a) - ((x / a) / z);
	} else if (t_1 <= 5e+288) {
		tmp = t_1;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y / (((z * a) - t) / z)
	elif t_1 <= -2e-298:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (y / a) - ((x / a) / z)
	elif t_1 <= 5e+288:
		tmp = t_1
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y / Float64(Float64(Float64(z * a) - t) / z));
	elseif (t_1 <= -2e-298)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	elseif (t_1 <= 5e+288)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y / (((z * a) - t) / z);
	elseif (t_1 <= -2e-298)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (y / a) - ((x / a) / z);
	elseif (t_1 <= 5e+288)
		tmp = t_1;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y / N[(N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-298], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+288], t$95$1, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 40.4%

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

      1. sub-neg 40.4%

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

      2. +-commutative 40.4%

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

      3. neg-sub0 40.4%

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

      4. associate-+l- 40.4%

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

      5. sub0-neg 40.4%

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

      6. neg-mul-1 40.4%

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

      7. sub-neg 40.4%

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

      8. +-commutative 40.4%

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

      9. neg-sub0 40.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 40.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 40.4%

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

      12. neg-mul-1 40.4%

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

      13. times-frac 40.4%

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

      14. metadata-eval 40.4%

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

      15. *-lft-identity 40.4%

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

      16. *-commutative 40.4%

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

   3. Simplified 40.4%

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

   4. Taylor expanded in y around inf 19.7%

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

      1. associate-/l* 79.2%

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

   6. Simplified 79.2%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.99999999999999982e-298 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5.0000000000000003e288

   1. Initial program 99.7%

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

   if -1.99999999999999982e-298 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 56.7%

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

      1. sub-neg 56.7%

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

      2. +-commutative 56.7%

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

      3. neg-sub0 56.7%

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

      4. associate-+l- 56.7%

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

      5. sub0-neg 56.7%

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

      6. neg-mul-1 56.7%

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

      7. sub-neg 56.7%

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

      8. +-commutative 56.7%

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

      9. neg-sub0 56.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 56.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 56.7%

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

      12. neg-mul-1 56.7%

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

      13. times-frac 56.7%

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

      14. metadata-eval 56.7%

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

      15. *-lft-identity 56.7%

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

      16. *-commutative 56.7%

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

   3. Simplified 56.7%

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

   4. Taylor expanded in z around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. +-commutative 50.5%

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

      3. associate--l+ 50.5%

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

      4. associate-/r* 74.8%

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

      5. distribute-neg-frac 74.8%

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

      6. mul-1-neg 74.8%

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

      7. associate-/r* 74.8%

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

      8. associate-*r/ 74.8%

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

      9. div-sub 74.8%

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

      10. distribute-lft-out-- 74.8%

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

      11. associate-*r/ 74.8%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in x around inf 77.9%

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

   if 5.0000000000000003e288 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 34.1%

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

      1. sub-neg 34.1%

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

      2. +-commutative 34.1%

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

      3. neg-sub0 34.1%

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

      4. associate-+l- 34.1%

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

      5. sub0-neg 34.1%

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

      6. neg-mul-1 34.1%

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

      7. sub-neg 34.1%

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

      8. +-commutative 34.1%

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

      9. neg-sub0 34.1%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 34.1%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 34.1%

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

      12. neg-mul-1 34.1%

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

      13. times-frac 34.1%

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

      14. metadata-eval 34.1%

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

      15. *-lft-identity 34.1%

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

      16. *-commutative 34.1%

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

   3. Simplified 34.1%

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

      1. div-sub 34.1%

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

      2. associate-/l* 65.4%

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

   5. Applied egg-rr 65.4%

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

   6. Taylor expanded in a around inf 74.9%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{-298}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 3: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{y}{\frac{t_1}{z}}\\ t_3 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+219}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{t_1}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-89}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 26500000000000 \lor \neg \left(z \leq 1.4 \cdot 10^{+123}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (/ y (/ t_1 z))) (t_3 (/ (- y (/ x z)) a)))
   (if (<= z -4.5e+219)
     t_3
     (if (<= z -7.5e+137)
       t_2
       (if (<= z -7000000000.0)
         t_3
         (if (<= z 1.55e-148)
           (/ (- x) t_1)
           (if (<= z 6.6e-89)
             (/ (- x (* y z)) t)
             (if (or (<= z 26500000000000.0) (not (<= z 1.4e+123)))
               t_3
               t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = y / (t_1 / z);
	double t_3 = (y - (x / z)) / a;
	double tmp;
	if (z <= -4.5e+219) {
		tmp = t_3;
	} else if (z <= -7.5e+137) {
		tmp = t_2;
	} else if (z <= -7000000000.0) {
		tmp = t_3;
	} else if (z <= 1.55e-148) {
		tmp = -x / t_1;
	} else if (z <= 6.6e-89) {
		tmp = (x - (y * z)) / t;
	} else if ((z <= 26500000000000.0) || !(z <= 1.4e+123)) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (z * a) - t
    t_2 = y / (t_1 / z)
    t_3 = (y - (x / z)) / a
    if (z <= (-4.5d+219)) then
        tmp = t_3
    else if (z <= (-7.5d+137)) then
        tmp = t_2
    else if (z <= (-7000000000.0d0)) then
        tmp = t_3
    else if (z <= 1.55d-148) then
        tmp = -x / t_1
    else if (z <= 6.6d-89) then
        tmp = (x - (y * z)) / t
    else if ((z <= 26500000000000.0d0) .or. (.not. (z <= 1.4d+123))) then
        tmp = t_3
    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 = (z * a) - t;
	double t_2 = y / (t_1 / z);
	double t_3 = (y - (x / z)) / a;
	double tmp;
	if (z <= -4.5e+219) {
		tmp = t_3;
	} else if (z <= -7.5e+137) {
		tmp = t_2;
	} else if (z <= -7000000000.0) {
		tmp = t_3;
	} else if (z <= 1.55e-148) {
		tmp = -x / t_1;
	} else if (z <= 6.6e-89) {
		tmp = (x - (y * z)) / t;
	} else if ((z <= 26500000000000.0) || !(z <= 1.4e+123)) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = y / (t_1 / z)
	t_3 = (y - (x / z)) / a
	tmp = 0
	if z <= -4.5e+219:
		tmp = t_3
	elif z <= -7.5e+137:
		tmp = t_2
	elif z <= -7000000000.0:
		tmp = t_3
	elif z <= 1.55e-148:
		tmp = -x / t_1
	elif z <= 6.6e-89:
		tmp = (x - (y * z)) / t
	elif (z <= 26500000000000.0) or not (z <= 1.4e+123):
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(y / Float64(t_1 / z))
	t_3 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -4.5e+219)
		tmp = t_3;
	elseif (z <= -7.5e+137)
		tmp = t_2;
	elseif (z <= -7000000000.0)
		tmp = t_3;
	elseif (z <= 1.55e-148)
		tmp = Float64(Float64(-x) / t_1);
	elseif (z <= 6.6e-89)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif ((z <= 26500000000000.0) || !(z <= 1.4e+123))
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = y / (t_1 / z);
	t_3 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -4.5e+219)
		tmp = t_3;
	elseif (z <= -7.5e+137)
		tmp = t_2;
	elseif (z <= -7000000000.0)
		tmp = t_3;
	elseif (z <= 1.55e-148)
		tmp = -x / t_1;
	elseif (z <= 6.6e-89)
		tmp = (x - (y * z)) / t;
	elseif ((z <= 26500000000000.0) || ~((z <= 1.4e+123)))
		tmp = t_3;
	else
		tmp = t_2;
	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[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -4.5e+219], t$95$3, If[LessEqual[z, -7.5e+137], t$95$2, If[LessEqual[z, -7000000000.0], t$95$3, If[LessEqual[z, 1.55e-148], N[((-x) / t$95$1), $MachinePrecision], If[LessEqual[z, 6.6e-89], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, 26500000000000.0], N[Not[LessEqual[z, 1.4e+123]], $MachinePrecision]], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.50000000000000023e219 or -7.50000000000000025e137 < z < -7e9 or 6.5999999999999993e-89 < z < 2.65e13 or 1.40000000000000006e123 < z

   1. Initial program 70.5%

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

      1. sub-neg 70.5%

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

      2. +-commutative 70.5%

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

      3. neg-sub0 70.5%

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

      4. associate-+l- 70.5%

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

      5. sub0-neg 70.5%

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

      6. neg-mul-1 70.5%

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

      7. sub-neg 70.5%

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

      8. +-commutative 70.5%

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

      9. neg-sub0 70.5%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 70.5%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 70.5%

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

      12. neg-mul-1 70.5%

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

      13. times-frac 70.5%

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

      14. metadata-eval 70.5%

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

      15. *-lft-identity 70.5%

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

      16. *-commutative 70.5%

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

   3. Simplified 70.5%

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

      1. div-sub 69.7%

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

      2. associate-/l* 77.3%

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

   5. Applied egg-rr 77.3%

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

   6. Taylor expanded in a around inf 76.3%

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

   if -4.50000000000000023e219 < z < -7.50000000000000025e137 or 2.65e13 < z < 1.40000000000000006e123

   1. Initial program 59.5%

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

      1. sub-neg 59.5%

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

      2. +-commutative 59.5%

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

      3. neg-sub0 59.5%

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

      4. associate-+l- 59.5%

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

      5. sub0-neg 59.5%

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

      6. neg-mul-1 59.5%

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

      7. sub-neg 59.5%

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

      8. +-commutative 59.5%

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

      9. neg-sub0 59.5%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 59.5%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 59.5%

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

      12. neg-mul-1 59.5%

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

      13. times-frac 59.5%

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

      14. metadata-eval 59.5%

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

      15. *-lft-identity 59.5%

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

      16. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   4. Taylor expanded in y around inf 51.0%

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

      1. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

   if -7e9 < z < 1.5500000000000001e-148

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 83.4%

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

      1. neg-mul-1 83.4%

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

   6. Simplified 83.4%

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

   if 1.5500000000000001e-148 < z < 6.5999999999999993e-89

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 80.9%

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

      1. associate-*r/ 80.9%

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

      2. neg-mul-1 80.9%

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

      3. neg-sub0 80.9%

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

      4. sub-neg 80.9%

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

      5. +-commutative 80.9%

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

      6. associate--r+ 80.9%

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

      7. neg-sub0 80.9%

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

      8. remove-double-neg 80.9%

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

      9. *-commutative 80.9%

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

   6. Simplified 80.9%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+219}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+137}:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}}\\ \mathbf{elif}\;z \leq -7000000000:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-148}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-89}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 26500000000000 \lor \neg \left(z \leq 1.4 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}}\\ \end{array} \]

Alternative 4: 63.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-89} \lor \neg \left(z \leq 1.05 \cdot 10^{-61}\right) \land z \leq 3.1 \cdot 10^{+123}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+71)
   (/ y a)
   (if (or (<= z 6.6e-89) (and (not (<= z 1.05e-61)) (<= z 3.1e+123)))
     (/ (- x (* y z)) t)
     (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+71) {
		tmp = y / a;
	} else if ((z <= 6.6e-89) || (!(z <= 1.05e-61) && (z <= 3.1e+123))) {
		tmp = (x - (y * z)) / 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 <= (-6.5d+71)) then
        tmp = y / a
    else if ((z <= 6.6d-89) .or. (.not. (z <= 1.05d-61)) .and. (z <= 3.1d+123)) then
        tmp = (x - (y * z)) / 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 <= -6.5e+71) {
		tmp = y / a;
	} else if ((z <= 6.6e-89) || (!(z <= 1.05e-61) && (z <= 3.1e+123))) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+71:
		tmp = y / a
	elif (z <= 6.6e-89) or (not (z <= 1.05e-61) and (z <= 3.1e+123)):
		tmp = (x - (y * z)) / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+71)
		tmp = Float64(y / a);
	elseif ((z <= 6.6e-89) || (!(z <= 1.05e-61) && (z <= 3.1e+123)))
		tmp = Float64(Float64(x - Float64(y * z)) / 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 <= -6.5e+71)
		tmp = y / a;
	elseif ((z <= 6.6e-89) || (~((z <= 1.05e-61)) && (z <= 3.1e+123)))
		tmp = (x - (y * z)) / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+71], N[(y / a), $MachinePrecision], If[Or[LessEqual[z, 6.6e-89], And[N[Not[LessEqual[z, 1.05e-61]], $MachinePrecision], LessEqual[z, 3.1e+123]]], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999954e71 or 6.5999999999999993e-89 < z < 1.05e-61 or 3.10000000000000006e123 < z

   1. Initial program 59.4%

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

      1. sub-neg 59.4%

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

      2. +-commutative 59.4%

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

      3. neg-sub0 59.4%

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

      4. associate-+l- 59.4%

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

      5. sub0-neg 59.4%

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

      6. neg-mul-1 59.4%

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

      7. sub-neg 59.4%

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

      8. +-commutative 59.4%

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

      9. neg-sub0 59.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 59.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 59.4%

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

      12. neg-mul-1 59.4%

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

      13. times-frac 59.4%

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

      14. metadata-eval 59.4%

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

      15. *-lft-identity 59.4%

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

      16. *-commutative 59.4%

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

   3. Simplified 59.4%

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

   4. Taylor expanded in z around inf 64.1%

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

   if -6.49999999999999954e71 < z < 6.5999999999999993e-89 or 1.05e-61 < z < 3.10000000000000006e123

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. +-commutative 95.0%

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

      3. neg-sub0 95.0%

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

      4. associate-+l- 95.0%

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

      5. sub0-neg 95.0%

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

      6. neg-mul-1 95.0%

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

      7. sub-neg 95.0%

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

      8. +-commutative 95.0%

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

      9. neg-sub0 95.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 95.0%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 95.0%

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

      12. neg-mul-1 95.0%

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

      13. times-frac 95.0%

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

      14. metadata-eval 95.0%

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

      15. *-lft-identity 95.0%

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

      16. *-commutative 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in a around 0 67.0%

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

      1. associate-*r/ 67.0%

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

      2. neg-mul-1 67.0%

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

      3. neg-sub0 67.0%

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

      4. sub-neg 67.0%

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

      5. +-commutative 67.0%

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

      6. associate--r+ 67.0%

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

      7. neg-sub0 67.0%

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

      8. remove-double-neg 67.0%

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

      9. *-commutative 67.0%

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

   6. Simplified 67.0%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-89} \lor \neg \left(z \leq 1.05 \cdot 10^{-61}\right) \land z \leq 3.1 \cdot 10^{+123}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.35 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t)) (t_2 (/ (- y (/ x z)) a)))
   (if (<= a -9.5e+18)
     t_2
     (if (<= a -4.35e-103)
       t_1
       (if (<= a -2.3e-145)
         (* y (/ z (- (* z a) t)))
         (if (<= a 4.6e+111) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (a <= -9.5e+18) {
		tmp = t_2;
	} else if (a <= -4.35e-103) {
		tmp = t_1;
	} else if (a <= -2.3e-145) {
		tmp = y * (z / ((z * a) - t));
	} else if (a <= 4.6e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (y * z)) / t
    t_2 = (y - (x / z)) / a
    if (a <= (-9.5d+18)) then
        tmp = t_2
    else if (a <= (-4.35d-103)) then
        tmp = t_1
    else if (a <= (-2.3d-145)) then
        tmp = y * (z / ((z * a) - t))
    else if (a <= 4.6d+111) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (a <= -9.5e+18) {
		tmp = t_2;
	} else if (a <= -4.35e-103) {
		tmp = t_1;
	} else if (a <= -2.3e-145) {
		tmp = y * (z / ((z * a) - t));
	} else if (a <= 4.6e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	t_2 = (y - (x / z)) / a
	tmp = 0
	if a <= -9.5e+18:
		tmp = t_2
	elif a <= -4.35e-103:
		tmp = t_1
	elif a <= -2.3e-145:
		tmp = y * (z / ((z * a) - t))
	elif a <= 4.6e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (a <= -9.5e+18)
		tmp = t_2;
	elseif (a <= -4.35e-103)
		tmp = t_1;
	elseif (a <= -2.3e-145)
		tmp = Float64(y * Float64(z / Float64(Float64(z * a) - t)));
	elseif (a <= 4.6e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / t;
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (a <= -9.5e+18)
		tmp = t_2;
	elseif (a <= -4.35e-103)
		tmp = t_1;
	elseif (a <= -2.3e-145)
		tmp = y * (z / ((z * a) - t));
	elseif (a <= 4.6e+111)
		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[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -9.5e+18], t$95$2, If[LessEqual[a, -4.35e-103], t$95$1, If[LessEqual[a, -2.3e-145], N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5e18 or 4.60000000000000004e111 < a

   1. Initial program 70.2%

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

      1. sub-neg 70.2%

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

      2. +-commutative 70.2%

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

      3. neg-sub0 70.2%

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

      4. associate-+l- 70.2%

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

      5. sub0-neg 70.2%

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

      6. neg-mul-1 70.2%

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

      7. sub-neg 70.2%

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

      8. +-commutative 70.2%

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

      9. neg-sub0 70.2%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 70.2%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 70.2%

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

      12. neg-mul-1 70.2%

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

      13. times-frac 70.2%

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

      14. metadata-eval 70.2%

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

      15. *-lft-identity 70.2%

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

      16. *-commutative 70.2%

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

   3. Simplified 70.2%

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

      1. div-sub 70.2%

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

      2. associate-/l* 73.9%

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

   5. Applied egg-rr 73.9%

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

   6. Taylor expanded in a around inf 77.1%

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

   if -9.5e18 < a < -4.3499999999999998e-103 or -2.30000000000000007e-145 < a < 4.60000000000000004e111

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. +-commutative 91.4%

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

      3. neg-sub0 91.4%

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

      4. associate-+l- 91.4%

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

      5. sub0-neg 91.4%

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

      6. neg-mul-1 91.4%

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

      7. sub-neg 91.4%

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

      8. +-commutative 91.4%

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

      9. neg-sub0 91.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 91.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 91.4%

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

      12. neg-mul-1 91.4%

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

      13. times-frac 91.4%

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

      14. metadata-eval 91.4%

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

      15. *-lft-identity 91.4%

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

      16. *-commutative 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in a around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. neg-mul-1 71.4%

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

      3. neg-sub0 71.4%

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

      4. sub-neg 71.4%

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

      5. +-commutative 71.4%

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

      6. associate--r+ 71.4%

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

      7. neg-sub0 71.4%

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

      8. remove-double-neg 71.4%

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

      9. *-commutative 71.4%

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

   6. Simplified 71.4%

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

   if -4.3499999999999998e-103 < a < -2.30000000000000007e-145

   1. Initial program 76.4%

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

      1. sub-neg 76.4%

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

      2. +-commutative 76.4%

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

      3. neg-sub0 76.4%

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

      4. associate-+l- 76.4%

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

      5. sub0-neg 76.4%

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

      6. neg-mul-1 76.4%

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

      7. sub-neg 76.4%

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

      8. +-commutative 76.4%

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

      9. neg-sub0 76.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 76.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 76.4%

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

      12. neg-mul-1 76.4%

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

      13. times-frac 76.4%

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

      14. metadata-eval 76.4%

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

      15. *-lft-identity 76.4%

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

      16. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in y around inf 52.7%

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

      1. *-commutative 52.7%

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

      2. associate-*r/ 75.9%

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

      3. *-commutative 75.9%

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

   6. Simplified 75.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;a \leq -4.35 \cdot 10^{-103}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+111}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 6: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t)))
   (if (<= a -2.9e+19)
     (- (/ y a) (/ (/ x a) z))
     (if (<= a -2.7e-103)
       t_1
       (if (<= a -2.35e-145)
         (* y (/ z (- (* z a) t)))
         (if (<= a 4.6e+111) t_1 (/ (- y (/ x z)) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double tmp;
	if (a <= -2.9e+19) {
		tmp = (y / a) - ((x / a) / z);
	} else if (a <= -2.7e-103) {
		tmp = t_1;
	} else if (a <= -2.35e-145) {
		tmp = y * (z / ((z * a) - t));
	} else if (a <= 4.6e+111) {
		tmp = t_1;
	} else {
		tmp = (y - (x / 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) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / t
    if (a <= (-2.9d+19)) then
        tmp = (y / a) - ((x / a) / z)
    else if (a <= (-2.7d-103)) then
        tmp = t_1
    else if (a <= (-2.35d-145)) then
        tmp = y * (z / ((z * a) - t))
    else if (a <= 4.6d+111) then
        tmp = t_1
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double tmp;
	if (a <= -2.9e+19) {
		tmp = (y / a) - ((x / a) / z);
	} else if (a <= -2.7e-103) {
		tmp = t_1;
	} else if (a <= -2.35e-145) {
		tmp = y * (z / ((z * a) - t));
	} else if (a <= 4.6e+111) {
		tmp = t_1;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	tmp = 0
	if a <= -2.9e+19:
		tmp = (y / a) - ((x / a) / z)
	elif a <= -2.7e-103:
		tmp = t_1
	elif a <= -2.35e-145:
		tmp = y * (z / ((z * a) - t))
	elif a <= 4.6e+111:
		tmp = t_1
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (a <= -2.9e+19)
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	elseif (a <= -2.7e-103)
		tmp = t_1;
	elseif (a <= -2.35e-145)
		tmp = Float64(y * Float64(z / Float64(Float64(z * a) - t)));
	elseif (a <= 4.6e+111)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / t;
	tmp = 0.0;
	if (a <= -2.9e+19)
		tmp = (y / a) - ((x / a) / z);
	elseif (a <= -2.7e-103)
		tmp = t_1;
	elseif (a <= -2.35e-145)
		tmp = y * (z / ((z * a) - t));
	elseif (a <= 4.6e+111)
		tmp = t_1;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[a, -2.9e+19], N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.7e-103], t$95$1, If[LessEqual[a, -2.35e-145], N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+111], t$95$1, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.9e19

   1. Initial program 71.7%

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

      1. sub-neg 71.7%

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

      2. +-commutative 71.7%

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

      3. neg-sub0 71.7%

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

      4. associate-+l- 71.7%

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

      5. sub0-neg 71.7%

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

      6. neg-mul-1 71.7%

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

      7. sub-neg 71.7%

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

      8. +-commutative 71.7%

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

      9. neg-sub0 71.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 71.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 71.7%

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

      12. neg-mul-1 71.7%

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

      13. times-frac 71.7%

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

      14. metadata-eval 71.7%

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

      15. *-lft-identity 71.7%

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

      16. *-commutative 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in z around inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. +-commutative 64.8%

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

      3. associate--l+ 64.8%

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

      4. associate-/r* 67.9%

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

      5. distribute-neg-frac 67.9%

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

      6. mul-1-neg 67.9%

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

      7. associate-/r* 68.2%

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

      8. associate-*r/ 68.2%

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

      9. div-sub 68.2%

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

      10. distribute-lft-out-- 68.2%

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

      11. associate-*r/ 68.2%

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

   6. Simplified 77.6%

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

   7. Taylor expanded in x around inf 78.7%

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

   if -2.9e19 < a < -2.7000000000000001e-103 or -2.3500000000000001e-145 < a < 4.60000000000000004e111

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. +-commutative 91.4%

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

      3. neg-sub0 91.4%

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

      4. associate-+l- 91.4%

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

      5. sub0-neg 91.4%

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

      6. neg-mul-1 91.4%

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

      7. sub-neg 91.4%

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

      8. +-commutative 91.4%

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

      9. neg-sub0 91.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 91.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 91.4%

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

      12. neg-mul-1 91.4%

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

      13. times-frac 91.4%

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

      14. metadata-eval 91.4%

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

      15. *-lft-identity 91.4%

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

      16. *-commutative 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in a around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. neg-mul-1 71.4%

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

      3. neg-sub0 71.4%

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

      4. sub-neg 71.4%

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

      5. +-commutative 71.4%

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

      6. associate--r+ 71.4%

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

      7. neg-sub0 71.4%

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

      8. remove-double-neg 71.4%

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

      9. *-commutative 71.4%

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

   6. Simplified 71.4%

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

   if -2.7000000000000001e-103 < a < -2.3500000000000001e-145

   1. Initial program 76.4%

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

      1. sub-neg 76.4%

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

      2. +-commutative 76.4%

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

      3. neg-sub0 76.4%

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

      4. associate-+l- 76.4%

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

      5. sub0-neg 76.4%

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

      6. neg-mul-1 76.4%

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

      7. sub-neg 76.4%

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

      8. +-commutative 76.4%

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

      9. neg-sub0 76.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 76.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 76.4%

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

      12. neg-mul-1 76.4%

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

      13. times-frac 76.4%

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

      14. metadata-eval 76.4%

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

      15. *-lft-identity 76.4%

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

      16. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in y around inf 52.7%

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

      1. *-commutative 52.7%

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

      2. associate-*r/ 75.9%

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

      3. *-commutative 75.9%

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

   6. Simplified 75.9%

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

   if 4.60000000000000004e111 < a

   1. Initial program 65.8%

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

      1. sub-neg 65.8%

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

      2. +-commutative 65.8%

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

      3. neg-sub0 65.8%

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

      4. associate-+l- 65.8%

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

      5. sub0-neg 65.8%

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

      6. neg-mul-1 65.8%

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

      7. sub-neg 65.8%

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

      8. +-commutative 65.8%

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

      9. neg-sub0 65.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 65.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 65.8%

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

      12. neg-mul-1 65.8%

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

      13. times-frac 65.8%

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

      14. metadata-eval 65.8%

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

      15. *-lft-identity 65.8%

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

      16. *-commutative 65.8%

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

   3. Simplified 65.8%

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

      1. div-sub 65.9%

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

      2. associate-/l* 66.0%

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

   5. Applied egg-rr 66.0%

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

   6. Taylor expanded in a around inf 78.4%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-103}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+111}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 7: 54.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \left(-\frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e-12)
   (/ y a)
   (if (<= z 1.65e-112) (/ x t) (if (<= z 8e+106) (* y (- (/ z t))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e-12) {
		tmp = y / a;
	} else if (z <= 1.65e-112) {
		tmp = x / t;
	} else if (z <= 8e+106) {
		tmp = y * -(z / 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 <= (-6.2d-12)) then
        tmp = y / a
    else if (z <= 1.65d-112) then
        tmp = x / t
    else if (z <= 8d+106) then
        tmp = y * -(z / 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 <= -6.2e-12) {
		tmp = y / a;
	} else if (z <= 1.65e-112) {
		tmp = x / t;
	} else if (z <= 8e+106) {
		tmp = y * -(z / t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e-12:
		tmp = y / a
	elif z <= 1.65e-112:
		tmp = x / t
	elif z <= 8e+106:
		tmp = y * -(z / t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e-12)
		tmp = Float64(y / a);
	elseif (z <= 1.65e-112)
		tmp = Float64(x / t);
	elseif (z <= 8e+106)
		tmp = Float64(y * Float64(-Float64(z / 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 <= -6.2e-12)
		tmp = y / a;
	elseif (z <= 1.65e-112)
		tmp = x / t;
	elseif (z <= 8e+106)
		tmp = y * -(z / t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e-12], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.65e-112], N[(x / t), $MachinePrecision], If[LessEqual[z, 8e+106], N[(y * (-N[(z / t), $MachinePrecision])), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000002e-12 or 8.00000000000000073e106 < z

   1. Initial program 61.0%

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

      1. sub-neg 61.0%

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

      2. +-commutative 61.0%

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

      3. neg-sub0 61.0%

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

      4. associate-+l- 61.0%

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

      5. sub0-neg 61.0%

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

      6. neg-mul-1 61.0%

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

      7. sub-neg 61.0%

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

      8. +-commutative 61.0%

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

      9. neg-sub0 61.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 61.0%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 61.0%

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

      12. neg-mul-1 61.0%

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

      13. times-frac 61.0%

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

      14. metadata-eval 61.0%

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

      15. *-lft-identity 61.0%

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

      16. *-commutative 61.0%

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

   3. Simplified 61.0%

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

   4. Taylor expanded in z around inf 60.0%

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

   if -6.2000000000000002e-12 < z < 1.65e-112

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 62.2%

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

   if 1.65e-112 < z < 8.00000000000000073e106

   1. Initial program 88.3%

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

      1. sub-neg 88.3%

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

      2. +-commutative 88.3%

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

      3. neg-sub0 88.3%

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

      4. associate-+l- 88.3%

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

      5. sub0-neg 88.3%

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

      6. neg-mul-1 88.3%

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

      7. sub-neg 88.3%

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

      8. +-commutative 88.3%

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

      9. neg-sub0 88.3%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 88.3%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 88.3%

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

      12. neg-mul-1 88.3%

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

      13. times-frac 88.3%

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

      14. metadata-eval 88.3%

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

      15. *-lft-identity 88.3%

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

      16. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. associate-*r/ 59.6%

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

      3. *-commutative 59.6%

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

   6. Simplified 59.6%

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

   7. Taylor expanded in z around 0 40.2%

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

      1. associate-*r/ 40.2%

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

      2. neg-mul-1 40.2%

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

   9. Simplified 40.2%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \left(-\frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+21} \lor \neg \left(a \leq 4.2 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6e+21) (not (<= a 4.2e+111)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e+21) || !(a <= 4.2e+111)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6d+21)) .or. (.not. (a <= 4.2d+111))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e+21) || !(a <= 4.2e+111)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6e+21) or not (a <= 4.2e+111):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6e+21) || !(a <= 4.2e+111))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6e+21) || ~((a <= 4.2e+111)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6e+21], N[Not[LessEqual[a, 4.2e+111]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6e21 or 4.1999999999999999e111 < a

   1. Initial program 70.2%

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

      1. sub-neg 70.2%

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

      2. +-commutative 70.2%

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

      3. neg-sub0 70.2%

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

      4. associate-+l- 70.2%

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

      5. sub0-neg 70.2%

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

      6. neg-mul-1 70.2%

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

      7. sub-neg 70.2%

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

      8. +-commutative 70.2%

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

      9. neg-sub0 70.2%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 70.2%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 70.2%

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

      12. neg-mul-1 70.2%

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

      13. times-frac 70.2%

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

      14. metadata-eval 70.2%

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

      15. *-lft-identity 70.2%

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

      16. *-commutative 70.2%

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

   3. Simplified 70.2%

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

      1. div-sub 70.2%

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

      2. associate-/l* 73.9%

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

   5. Applied egg-rr 73.9%

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

   6. Taylor expanded in a around inf 77.1%

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

   if -6e21 < a < 4.1999999999999999e111

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. +-commutative 90.1%

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

      3. neg-sub0 90.1%

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

      4. associate-+l- 90.1%

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

      5. sub0-neg 90.1%

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

      6. neg-mul-1 90.1%

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

      7. sub-neg 90.1%

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

      8. +-commutative 90.1%

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

      9. neg-sub0 90.1%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 90.1%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 90.1%

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

      12. neg-mul-1 90.1%

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

      13. times-frac 90.1%

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

      14. metadata-eval 90.1%

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

      15. *-lft-identity 90.1%

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

      16. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in a around 0 67.8%

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

      1. associate-*r/ 67.8%

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

      2. neg-mul-1 67.8%

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

      3. neg-sub0 67.8%

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

      4. sub-neg 67.8%

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

      5. +-commutative 67.8%

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

      6. associate--r+ 67.8%

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

      7. neg-sub0 67.8%

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

      8. remove-double-neg 67.8%

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

      9. *-commutative 67.8%

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

   6. Simplified 67.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+21} \lor \neg \left(a \leq 4.2 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]

Alternative 9: 54.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e-12) (/ y a) (if (<= z 2.6e-110) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-12) {
		tmp = y / a;
	} else if (z <= 2.6e-110) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.2d-12)) then
        tmp = y / a
    else if (z <= 2.6d-110) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-12) {
		tmp = y / a;
	} else if (z <= 2.6e-110) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e-12:
		tmp = y / a
	elif z <= 2.6e-110:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e-12)
		tmp = Float64(y / a);
	elseif (z <= 2.6e-110)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e-12)
		tmp = y / a;
	elseif (z <= 2.6e-110)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e-12], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.6e-110], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.19999999999999992e-12 or 2.5999999999999999e-110 < z

   1. Initial program 69.3%

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

      1. sub-neg 69.3%

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

      2. +-commutative 69.3%

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

      3. neg-sub0 69.3%

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

      4. associate-+l- 69.3%

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

      5. sub0-neg 69.3%

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

      6. neg-mul-1 69.3%

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

      7. sub-neg 69.3%

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

      8. +-commutative 69.3%

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

      9. neg-sub0 69.3%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 69.3%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 69.3%

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

      12. neg-mul-1 69.3%

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

      13. times-frac 69.3%

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

      14. metadata-eval 69.3%

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

      15. *-lft-identity 69.3%

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

      16. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in z around inf 50.6%

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

   if -2.19999999999999992e-12 < z < 2.5999999999999999e-110

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 61.9%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 10: 36.2% 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 81.5%

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

   1. sub-neg 81.5%

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

   2. +-commutative 81.5%

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

   3. neg-sub0 81.5%

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

   4. associate-+l- 81.5%

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

   5. sub0-neg 81.5%

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

   6. neg-mul-1 81.5%

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

   7. sub-neg 81.5%

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

   8. +-commutative 81.5%

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

   9. neg-sub0 81.5%

      \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

   10. associate-+l- 81.5%

       \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

   11. sub0-neg 81.5%

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

   12. neg-mul-1 81.5%

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

   13. times-frac 81.5%

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

   14. metadata-eval 81.5%

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

   15. *-lft-identity 81.5%

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

   16. *-commutative 81.5%

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

3. Simplified 81.5%

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

4. Taylor expanded in z around 0 31.5%

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

5. Final simplification 31.5%

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

Developer target: 97.2% accurate, 0.6× 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 2023199 
(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))))